diff --git a/examples/channel_inversion/inverse_problem.py b/examples/channel_inversion/inverse_problem.py index 45ce5f61f..4b42d05e9 100644 --- a/examples/channel_inversion/inverse_problem.py +++ b/examples/channel_inversion/inverse_problem.py @@ -90,7 +90,7 @@ ] sta_manager = inversion_tools.StationObservationManager( mesh2d, output_directory=options.output_directory) -sta_manager.load_observation_data(observation_data_dir, station_names, variable) +sta_manager.load_elev_observation_data(observation_data_dir, station_names, variable) sta_manager.set_model_field(solver_obj.fields.elev_2d) # Define the scaling for the cost function so that J ~ O(1) @@ -111,9 +111,11 @@ # Extract the regularized cost function cost_function = inv_manager.get_cost_function(solver_obj) +cost_function_callback = inversion_tools.CostFunctionCallback(solver_obj, cost_function) +solver_obj.add_callback(cost_function_callback, 'timestep') # Solve and setup reduced functional -solver_obj.iterate(export_func=cost_function) # note that export time should equal dt if not using a custom callback +solver_obj.iterate() inv_manager.stop_annotating() # Run inversion diff --git a/examples/headland_inversion/Makefile b/examples/headland_inversion/Makefile new file mode 100644 index 000000000..6f8961c7d --- /dev/null +++ b/examples/headland_inversion/Makefile @@ -0,0 +1,21 @@ +all: invert plot + +CASE ?= Constant # Regions IndependentPointsScheme NodalFreedom +STATIONS = stationA stationB stationC stationD stationE +PARALLEL ?= 0 # Default to serial execution + +invert: +ifeq ($(PARALLEL), 0) + python3 inverse_problem.py --case $(CASE) --no-consistency-test --no-taylor-test +else + mpiexec -np $(PARALLEL) python inverse_problem.py --case $(CASE) --no-consistency-test --no-taylor-test; +endif + +plot: + for station in $(STATIONS); do \ + python3 plot_velocity_progress.py -s $$station --case $(CASE); \ + done; \ + +clean: + rm -rf __pycache__ + rm -rf *.png diff --git a/examples/headland_inversion/README.md b/examples/headland_inversion/README.md new file mode 100644 index 000000000..e1609922a --- /dev/null +++ b/examples/headland_inversion/README.md @@ -0,0 +1,237 @@ +# Headland Channel - Friction Field Calibration + +This example shows how adjoint methods can be used in gradient-based optimisation of a control parameter/field to +minimise the difference between measured and modelled data at gauging stations. Here, synthetic measured velocity data +is generated using a forward run with known input parameters. The calibration/optimisation problem is then performed +using the adjoint technique, keeping all the parameters the same except for our `Control`. 5 stations are used, as shown +in the forward run section. + +The control field used here is the Manning parameter, which controls the bottom drag i.e. the friction. This field can +take various 'mappings', which are covered case-by-case in the Inversion run sections: + +- Full nodal flexibility: the `Control` is the entire friction field, which is allowed to change at every single node on +the mesh, within the prescribed lower and upper limits. Hessian regularisation can be used to ensure node-to-node +changes are not too severe. See [Kärnä et al., 2023](https://doi.org/10.1029/2022MS003169) for detailed explanations. +- Uniform bed friction: the `Control` is one `Constant` value, which keeps the bed friction uniform across the domain. +- Region-based friction: the `Control` is a set of values, corresponding to certain regions of the model. These regions +may be a simple split between areas of the domain or may be based on seabed particle data - see +[Warder et al., 2022](http://dx.doi.org/https://doi.org/10.1007/s10236-022-01507-x), for example. +- Independent point scheme: as for the region-based approach, the `Control` is a set of values, but this time it is +associated with a set of points. Between points, the value of the friction parameter is interpolated - see +[Lu and Zhang, 2006](https://doi.org/10.1016/j.csr.2006.06.007), for example. + +## Forward run + +The synthetic data is stored in the time series `.hdf5` files for each station. The forward run is provided so that the +input parameters can be changed by the user for further experimentation. + +The forward run used to generate this uses the same model configuration as provided by `model_config.py` which +configures the `solver object`, but with a friction field based on a sea bed particle sizes as shown below: + +![Sea Bed Particle Sizes](images/seabed_classification.png) + +The idealised headland is 20km long and 6km wide, with a coastline depth of 3m and a main channel depth of 40m. The left +and right boundaries are forced by a sinusoidal elevation function, emulating a single tidal signal. A viscosity sponge +is used at the left hand boundary to provide some model stability. + +## Inversion run + +The inversion problem is currently run from a `Makefile`. User arguments are specified here i.e. mapping to use, serial +or parallel execution, and then the Makefile runs the scripts with the inputs provided. + +The solver object is set up using `construct_solver` and then initial values for each field (in this case we only +optimise for bed friction) are specified. The station manager, `StationObservationManager` , is then defined, which is +from the modified version of the inversion tools provided by Thetis. In this case, as the calibration points have been +defined by a forward run, we can use `load_observation_data` to interpolate the observation time series to the model +time and also stores the time series data to disk. The station manager will also include the variable that is being +optimised for, in this case, the velocity components. + +We can then set up the inversion manager, `InversionManager`, again from the modified version of the inversion tools of +Thetis. The station manager is the first argument and the two key other arguments are the penalty parameters and cost +scaling. We will use the penalty parameters only for the full nodal flexibility case, as the others are effectively +spatially regularised by their mappings. The cost function, J(u), is defined using the inversion manager as the L2 norm, +except in the full nodal flexibility case, where it has additional regularisation. + +The forward model is run using `solver_obj.iterate`, with the cost function embedded via a callback, which is an +important step for the adjoint method. Passing the cost function callback effectively embeds the dependency of the model +state on the control variables into the cost function, forming the **reduced functional**. The **reduced functional**, +J_hat(c), is not just the original cost function, J(u), plus a regularization term — it **includes the entire forward +model**. This means that to evaluate the reduced functional, all computations required to solve the model equations and +obtain the model state u(c) corresponding to a given control, c, are taken into account. Running the forward model not +only gives the baseline cost, but also calculates the gradients of the reduced functional with respect to the control +variables (e.g., friction), which are then passed to the adjoint method. Finally, the annotation process (which has been +recording all computations related to the cost function, its derivatives, and the forward model) is stopped. This +process allows us to efficiently compute the gradients needed for calibration. + +Optimisation parameters are then defined, which are the maximum number of iterations and the tolerance for the +optimisation convergence criterion (threshold for the relative change in the cost function, below which the optimisation +process will terminate). The optimisation is run by calling `inv_manager.minimize`. The L-BFGS-B algorithm is used as it +is suitable for bound-constrained problems, which are specified earlier alongside the penalty parameters for the cost +functional. These are the minimum and maximum values of bed friction allowed. + +The remainder of the script performs file saving and preparation for visualisation in ParaView. + +### Full Nodal Flexibility + +```sh +source ~/firedrake/bin/activate +make invert CASE=NodalFreedom +``` + +In the full nodal flexibility case, the friction values can vary freely within the lower and upper limits defined by the +control bounds. However, the cost function is regularised by an additional term, in this case, the Hessian (second +derivative) of the elevation field. This prevents overfitting of the Manning field i.e. having a highly variable field. +The penalty parameters are the regularisation parameters that control the strength of the regularisation. Higher values +increase the weight of the penalty term, leading to a smoother friction field, while lower values allow more +variability. The cost scaling normalises the regularisation term by the local mesh element size, so that the degree of +penalization adapts to the local mesh resolution. In regions with finer mesh resolution, the scaling ensures that higher +variability in friction is allowed, whilst in regions of lower resolution less variability is allowed to prevent +overfitting to sparse data points. The cost function that is defined using the inversion manager here, is the Hessian +regularised L2 norm. The actual class, `HessianRecoverer2D`, for calculating this loss can be found in +`thetis.diagnostics.py`. + +### Uniform Bed Friction + +```sh +source ~/firedrake/bin/activate +make invert CASE=Constant +``` + +For a uniform bed friction, there are some differences which are enforced by changing the case entry, as explained +below. + +Firstly, we do not need penalty parameters in the inversion problem as we will not have any variation across the field +and thus there is no smoothing required. Now, instead of adding the Manning field as a `Control`, we will define the +friction through a `Constant`, and then project this `Constant` onto the Manning field. This `Constant` then becomes our +`Control`, and as it is a `Constant`, it cannot vary. This is inherently dealt with by `Firedrake` and `pyadjoint`. + +The standard implementation of `InversionManager` in Thetis is not flexible in dealing with the `Control` not being +a `Function` i.e. the Manning, bathymetry etc., so we this is where modifications start to come in. +We need to export the Manning at each iteration, so we need to extract the mesh from the `StationObservationManager`, +extract the function space and create a `Function` to assign the `Control` value to. This can then be exported to `.vtu` +at each iteration. + +### Region Based Bed Friction + +```sh +source ~/firedrake/bin/activate +make invert CASE=Regions +``` + +For region-based bed friction, the `InversionManager` has again been modified so that we can export things +correctly. Here, we need to create a mapping that relates the Manning values to the regions of the mesh. Again, there is +no need for penalising the Hessian. We also need to use a `Constant` for each area, and each `Constant` is one +`Control`. The adjoint works on graphical connections, so we need to ensure that the adjoint process can back-propagate +through the various layers to our `Controls`. This is why we need to store our values as `Functions` on our `mesh` +`FunctionSpace`. + +We can define four regions, for example, in the following manner: + +``` +mask_values = [np.logical_and(x < 50e3, y < 6e3).astype(float), + np.logical_and(x < 50e3, y >= 6e3).astype(float), + np.logical_and(x >= 50e3, y < 6e3).astype(float), + np.logical_and(x >= 50e3, y >= 6e3).astype(float)] + +# Create Function objects to store the coefficients +m_true = [Constant(i+1., domain=mesh2d) for i in range(len(mask_values))] +masks = [Function(V) for _ in range(len(m_true))] + +# Assign the mask values to the Functions +for i, mask_ in enumerate(masks): + mask_.dat.data[:] = mask_values[i] +``` + +Importantly, the masks i.e. our regions, will remain consistent. The only thing that will change will be the values +associated with each mask. This means we can define each mask by assigning its values from `NumPy` operators using +`mask.dat.data[:] = mask_values[i]`. In the case of bed particle size mapping, this is important, because it would be +challenging to have to define a series of `conditional` or other operators to define each area. Note that if we +included this assignment of the masks at each iteration of the adjoint, it would not work as there is no graphical +connection when we do assignments with `function.dat.data[:] = values`. We can then map our values as follows: + +``` +manning_2d.assign(0) +# Add the weighted masks to n +for m_, mask_ in zip(m_true, masks): + manning_2d += m_ * mask_ +``` + +We then iterate through each mask (region) and then add the corresponding value of Manning (n) friction. We now have a +mapping that `PyAdjoint` can understand. + +As for the `InversionManager`, we can then provide this mapping through an `update_n` function which allows us to export +the `Control` and `Gradient` fields correctly, rather than having `m` outputs for `m` controls. We can then run the +forward, inverse and plotting scripts in order. + +### Independent Point Scheme + +```sh +source ~/firedrake/bin/activate +make invert CASE=IndependentPointsScheme +``` + +The independent point scheme approach works in the same way as the region-based approach, where we have a mapping +function which tells us how the Manning field changes with respect to our input independent point values. We can use the +same `InversionManager` updates, and the only thing we need to do is change the masks we generate. For a linear +interpolation of the points, this mapping is generated as follows: + +``` +# Get domain limits, define independent points and specify their values +lx, ly = np.max(x), np.max(y) # done differently in parallel +points = [(lx/4, ly/4), (lx/4, 3*ly/4), (lx/2, ly/4), (lx/2, 3*ly/4), + (3*lx/4, ly/4), (3*lx/4, 3*ly/4)] +m_true = [Constant(0.01*(i+1), domain=mesh2d) for i in range(len(points))] +M = len(m_true) + +# Use Python's numpy to create arrays for the interpolation points +interp_x = np.array([p[0] for p in points]) +interp_y = np.array([p[1] for p in points]) +points = np.column_stack((interp_x, interp_y)) + +# Create the interpolators, use nearest neighbour interpolation outside the convex +# hull of the linear interpolator +linear_interpolator = LinearNDInterpolator(points, np.eye(len(points))) +nearest_interpolator = NearestNDInterpolator(points, np.eye(len(points))) + +# Apply the interpolators to the mesh coordinates to get linear coefficients +# (these do not depend on the magnitude of the points) +linear_coefficients = linear_interpolator(coordinates) +nan_mask = np.isnan(linear_coefficients).any(axis=1) +linear_coefficients[nan_mask] = nearest_interpolator(coordinates[nan_mask]) + +# Create Function objects to store the coefficients +masks = [Function(V) for _ in range(len(points))] + +# Assign the linear coefficients to the masks +for i, mask in enumerate(masks): + mask.dat.data[:] = linear_coefficients[:, i] +``` + +Now, instead of masks with 0/1 values, we have masks which describe the contribution of each point to the rest of the +domain. Note that this will only work for linear interpolation, as we cannot generate static coefficients for non-linear +mappings (RBF, quadratic, cubic etc.). In those cases, we would need to 'annotate' the interpolation functions for +`PyAdjoint` to track the gradient through. + +## Post-processing + +```sh +source ~/firedrake/bin/activate +make plot CASE=NodalFreedom +make plot CASE=Constant +make plot CASE=Regions +make plot CASE=IndependentPointsScheme +``` + +To plot the progress, we can use the Makefile to run `plot_velocity_progress.py`. This plots the velocity over time at +each of the station locations for each iteration of the optimisation, relative to the ground truth from the forward run. + +## Running in parallel + +The default settings run these scripts in parallel, however we can leverage parallel processing to accelerate the +simulations by partioning the mesh. To do so, simply provide the number of processors you would like to use after the +PARALLEL option, e.g.: + +```sh +source ~/firedrake/bin/activate +make invert CASE=IndependentPointsScheme PARALLEL=4 +``` diff --git a/examples/headland_inversion/forward_run.py b/examples/headland_inversion/forward_run.py new file mode 100644 index 000000000..abd517400 --- /dev/null +++ b/examples/headland_inversion/forward_run.py @@ -0,0 +1,108 @@ +from thetis import * +from firedrake import * +from firedrake import VTKFile +import geopandas as gpd +from model_config import construct_solver +from shapely.geometry import Point +from mpi4py import MPI + +# Initialize MPI +comm = MPI.COMM_WORLD +rank = comm.Get_rank() +size = comm.Get_size() + + +# ---------------------------------------- Step 1: set up mesh and ground truth ---------------------------------------- + +pwd = os.path.abspath(os.path.dirname(__file__)) +output_dir_forward = f'{pwd}/outputs/outputs_forward' + +solver_obj, update_forcings = construct_solver( + output_directory=output_dir_forward, + store_station_time_series=True, + no_exports=False, +) + +mesh2d = solver_obj.mesh2d +options = solver_obj.options +manning_2d = solver_obj.fields.manning_2d +elev_init_2d = solver_obj.fields.elev_2d + +coordinates = mesh2d.coordinates.dat.data[:] +x, y = coordinates[:, 0], coordinates[:, 1] +local_lx = np.max(x) # for parallel runs, the mesh is partioned so we need to get the maximum from each processor! +local_ly = np.max(y) + +all_lx = comm.gather(local_lx, root=0) +all_ly = comm.gather(local_ly, root=0) +if rank == 0: + lx_ = np.max(all_lx) + ly_ = np.max(all_ly) +else: + lx_ = None + ly_ = None +lx = comm.bcast(lx_, root=0) +ly = comm.bcast(ly_, root=0) + +# Create a FunctionSpace on the mesh (corresponds to Manning) +V = get_functionspace(mesh2d, 'CG', 1) + +# Load the shapefile +shapefile_path = 'inputs/bed_classes.shp' +gdf = gpd.read_file(shapefile_path) +polygons_by_id = gdf.groupby('id') + +sediment_to_manning = { + 'ROCK': 0.0420, + 'SAND': 0.0171, + 'SANDY CLAY': 0.0132, + 'MUDDY SAND': 0.0163, + 'CLAY': 0.0100 +} + +mask_values = [] +masks = [Function(V) for _ in range(len(polygons_by_id))] +m_true = [] + +for i, (region_id, group) in enumerate(polygons_by_id): + multi_polygon = group.unary_union + + # Get the sediment type for this region (assuming one sediment type per ID) + sediment_type = group['Sediment'].iloc[0] + manning_value = sediment_to_manning.get(sediment_type, None) + values = [] + + for (x_, y_) in zip(x, y): + # Check if the point is inside the multi-polygon + point = Point(x_, y_) + if multi_polygon.buffer(1).contains(point): + values.append(1) + else: + values.append(0) + + mask_values.append(values) + m_true.append(Constant(manning_value, domain=mesh2d)) + +overlap_counts = np.zeros(len(x)) + +for values in mask_values: + overlap_counts += np.array(values) + +for values in mask_values: + for i in range(len(values)): + if overlap_counts[i] > 1: + values[i] /= overlap_counts[i] + +for mask, values in zip(masks, mask_values): + mask.dat.data[:] = values + +manning_2d.assign(0) +for m_, mask_ in zip(m_true, masks): + manning_2d += m_ * mask_ + +VTKFile(output_dir_forward + '/manning_init.pvd').write(manning_2d) + +print_output('Exporting to ' + solver_obj.options.output_directory) + +print_output('Solving the forward problem...') +solver_obj.iterate(update_forcings=update_forcings) diff --git a/examples/headland_inversion/headland.geo b/examples/headland_inversion/headland.geo new file mode 100644 index 000000000..68d2c3e4f --- /dev/null +++ b/examples/headland_inversion/headland.geo @@ -0,0 +1,51 @@ +basin_x = 20000; +basin_y = 6000; + +headland_x_scale = 0.2; +headland_y = 2000; + +site_x = 1600; +site_y = 1000; +site_x_start = basin_x/2-site_x/2; +site_x_end = basin_x/2+site_x/2; + +site_y_start = basin_y/2 - 500; +site_y_end = site_y_start+site_y; + +element_size = 150; +element_size_coarse = 400; + +Point(1) = {0, 0, 0, element_size_coarse}; +Point(2) = {basin_x, 0, 0, element_size_coarse}; + + +// Generate nodes for the headland +res = 100; +For k In {0:res:1} + x = basin_x/res*k; + b = 100; + y = basin_y - headland_y*Exp(-0.5*((headland_x_scale*(x-basin_x/2))/b)^2); + Point(10+k) = {x, y, 0, element_size_coarse}; +EndFor + +// Generate lines for the headland + +BSpline(100) = { 10 : res+10 }; + +Line(101) = {10, 1}; +Line(102) = {1, 2}; +Line(103) = {2, res+10}; +Line Loop(104) = {100, -103, -102, -101}; + +// Generate site nodes +Point(1000) = {site_x_start, site_y_start, 0, element_size}; +Extrude{site_x, 0, 0} { Point{1000}; Layers{site_x/element_size}; } +Extrude{0, site_y, 0} { Line{105}; Layers{site_y/element_size}; } +Line Loop(110) = {106, -108, -105, 107}; +Plane Surface(111) = {104, 110}; +Plane Surface(112) = {110}; +Physical Line(1) = {101}; +Physical Line(2) = {103}; +Physical Line(3) = {100, 102}; +Physical Surface(1) = {111}; +Physical Surface(2) = {112}; diff --git a/examples/headland_inversion/headland.msh 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1337 1327 +$EndElements diff --git a/examples/headland_inversion/images/seabed_classification.png b/examples/headland_inversion/images/seabed_classification.png new file mode 100644 index 000000000..7abf92410 Binary files /dev/null and b/examples/headland_inversion/images/seabed_classification.png differ diff --git a/examples/headland_inversion/inputs/bed_classes.cpg b/examples/headland_inversion/inputs/bed_classes.cpg new file mode 100644 index 000000000..3ad133c04 --- /dev/null +++ b/examples/headland_inversion/inputs/bed_classes.cpg @@ -0,0 +1 @@ +UTF-8 \ No newline at end of file diff --git a/examples/headland_inversion/inputs/bed_classes.dbf b/examples/headland_inversion/inputs/bed_classes.dbf new file mode 100644 index 000000000..f80e9ff80 Binary files /dev/null and b/examples/headland_inversion/inputs/bed_classes.dbf differ diff --git a/examples/headland_inversion/inputs/bed_classes.prj b/examples/headland_inversion/inputs/bed_classes.prj new file mode 100644 index 000000000..9855fcc1f --- /dev/null +++ b/examples/headland_inversion/inputs/bed_classes.prj @@ -0,0 +1 @@ +PROJCS["WGS_1984_UTM_Zone_30N",GEOGCS["GCS_WGS_1984",DATUM["D_WGS_1984",SPHEROID["WGS_1984",6378137.0,298.257223563]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Transverse_Mercator"],PARAMETER["False_Easting",500000.0],PARAMETER["False_Northing",0.0],PARAMETER["Central_Meridian",-3.0],PARAMETER["Scale_Factor",0.9996],PARAMETER["Latitude_Of_Origin",0.0],UNIT["Meter",1.0]] \ No newline at end of file diff --git a/examples/headland_inversion/inputs/bed_classes.shp b/examples/headland_inversion/inputs/bed_classes.shp new file mode 100644 index 000000000..f055cc0f0 Binary files /dev/null and b/examples/headland_inversion/inputs/bed_classes.shp differ diff --git a/examples/headland_inversion/inputs/bed_classes.shx b/examples/headland_inversion/inputs/bed_classes.shx new file mode 100644 index 000000000..aa68f3636 Binary files /dev/null and b/examples/headland_inversion/inputs/bed_classes.shx differ diff --git a/examples/headland_inversion/inverse_problem.py b/examples/headland_inversion/inverse_problem.py new file mode 100644 index 000000000..4d1222ba9 --- /dev/null +++ b/examples/headland_inversion/inverse_problem.py @@ -0,0 +1,279 @@ +from thetis import * +import thetis.inversion_tools as inversion_tools +from firedrake import * +from firedrake.adjoint import * +from model_config import construct_solver +from scipy.interpolate import LinearNDInterpolator, NearestNDInterpolator +import h5py +import argparse +from mpi4py import MPI + +# Initialize MPI +comm = MPI.COMM_WORLD +rank = comm.Get_rank() +size = comm.Get_size() + +# ---------------------------------------- Step 1: set up mesh and ground truth ---------------------------------------- + +# parse user input +parser = argparse.ArgumentParser( + description='Channel inversion problem', + # includes default values in help entries + formatter_class=argparse.ArgumentDefaultsHelpFormatter, +) +parser.add_argument('--case', nargs='+', + help='Method of Manning field representation', + choices=['Constant', 'Regions', 'IndependentPointsScheme', 'NodalFreedom'], + default=['IndependentPointsScheme'], + ) +parser.add_argument('--no-consistency-test', action='store_true', + help='Skip consistency test') +parser.add_argument('--no-taylor-test', action='store_true', + help='Skip Taylor test') +args = parser.parse_args() +do_consistency_test = not args.no_consistency_test +do_taylor_test = not args.no_taylor_test +no_exports = os.getenv('THETIS_REGRESSION_TEST') is not None + +case_to_output_dir = { + 'Constant': 'constant_friction', + 'Regions': 'region_based', + 'IndependentPointsScheme': 'independent_points_scheme', + 'NodalFreedom': 'full_nodal_flexibility' +} + +selected_case = args.case[0] +pwd = os.path.abspath(os.path.dirname(__file__)) +output_dir_forward = f'{pwd}/outputs/outputs_forward' +output_dir_invert = f'{pwd}/outputs/outputs_inverse/' + case_to_output_dir[selected_case] + +continue_annotation() + +solver_obj, update_forcings = construct_solver( + output_directory=output_dir_invert, + store_station_time_series=False, + no_exports=True, +) +options = solver_obj.options +mesh2d = solver_obj.mesh2d +bathymetry_2d = solver_obj.fields.bathymetry_2d +manning_2d = solver_obj.fields.manning_2d + +coordinates = mesh2d.coordinates.dat.data[:] +x, y = coordinates[:, 0], coordinates[:, 1] +local_lx = np.max(x) # for parallel runs, the mesh is partioned so we need to get the maximum from each processor! +local_ly = np.max(y) + +all_lx = comm.gather(local_lx, root=0) +all_ly = comm.gather(local_ly, root=0) +if rank == 0: + lx_ = np.max(all_lx) + ly_ = np.max(all_ly) +else: + lx_ = None + ly_ = None +lx = comm.bcast(lx_, root=0) +ly = comm.bcast(ly_, root=0) + +local_N = coordinates.shape[0] +N = comm.allreduce(local_N, op=MPI.SUM) # allreduce sums the local numbers to get the total number of coordinates +masks, M, m_true = None, 0, [] + +# Create a FunctionSpace on the mesh (corresponds to Manning) +V = get_functionspace(mesh2d, 'CG', 1) + +if selected_case == 'Constant': + manning_const = Constant(0.02, name='Manning') # TODO - do we need to set up like this? + manning_2d.assign(domain_constant(manning_const, mesh2d)) +elif selected_case == 'Regions': + # Define our values for n + mask_values = np.array([ + ((x < lx / 2) & (y < ly / 6)), + ((x >= lx / 2) & (y < ly / 6)), + ((x < lx / 2) & (y >= ly / 6) & (y < 8 * ly / 15)), + ((x >= lx / 2) & (y >= ly / 6) & (y < 8 * ly / 15)), + ((x < 3 * lx / 8) & (y >= 8 * ly / 15) & (y < 5 * ly / 6)), + ((x >= 3 * lx / 8) & (x < 0.5 * lx) & (y >= 8 * ly / 15)), + ((x >= 0.5 * lx) & (x < 5 * lx / 8) & (y >= 8 * ly / 15)), + ((x >= 5 * lx / 8) & (y >= 8 * ly / 15) & (y < 5 * ly / 6)), + ((x < 3 * lx / 8) & (y >= 5 * ly / 6)), + ((x >= 5 * lx / 8) & (y >= 5 * ly / 6)) + ], dtype=float) + + m_true = [Constant(0.03 - 0.0005 * i, domain=mesh2d) for i in range(len(mask_values))] + masks = [Function(V) for _ in range(len(mask_values))] + for mask, values in zip(masks, mask_values): + mask.dat.data[:] = values + + M = len(m_true) + + manning_2d.assign(0) + for m_, mask_ in zip(m_true, masks): + manning_2d += m_ * mask_ +elif selected_case == 'IndependentPointsScheme': + # Define our values for n + points = np.array([ + [0, 0], [0, 0.5], [0, 1], [0.5, 0], [1, 0], [1, 0.5], [1, 1], [0.5, 0.5], + [0.1, 0.9], [0.3, 0.9], [0.7, 0.9], [0.9, 0.9], + [0.1, 0.7], [0.3, 0.7], [0.7, 0.7], [0.9, 0.7], + [0.3, 0.75], [0.7, 0.75], [0.5, 0.4], [0.5, 0.1], + [0.1, 0.25], [0.3, 0.25], [0.7, 0.25], [0.9, 0.25], + [0.1, 0.05], [0.3, 0.05], [0.7, 0.05], [0.9, 0.05] + ]) * np.array([lx, ly]) + m_true = [Constant(0.03 - 0.0005 * i, domain=mesh2d) for i in range(len(points))] + M = len(m_true) + + # Use Python's numpy to create arrays for the interpolation points + interp_x = np.array([p[0] for p in points]) + interp_y = np.array([p[1] for p in points]) + points = np.column_stack((interp_x, interp_y)) + + linear_interpolator = LinearNDInterpolator(points, np.eye(len(points))) + nearest_interpolator = NearestNDInterpolator(points, np.eye(len(points))) + + # Apply the interpolators to the mesh coordinates + linear_coefficients = linear_interpolator(coordinates) + nan_mask = np.isnan(linear_coefficients).any(axis=1) + linear_coefficients[nan_mask] = nearest_interpolator(coordinates[nan_mask]) + + # Create Function objects to store the coefficients + masks = [Function(V) for _ in range(len(points))] + + # Assign the linear coefficients to the masks + for i, mask in enumerate(masks): + mask.dat.data[:] = linear_coefficients[:, i] + + manning_2d.assign(0) + for m_, mask_ in zip(m_true, masks): + manning_2d += m_ * mask_ +else: + pass + +# Setup controls and regularization parameters (regularisation only needed where lots of values are being changed) +gamma_hessian_list = [] +control_bounds_list = [] +gamma_hessian = None +bounds = [0.01, 0.06] +if selected_case == 'NodalFreedom': + gamma_hessian = Constant(1.0) +if gamma_hessian is not None: + print_output(f'Manning regularization params: hess={float(gamma_hessian):.3g}') + gamma_hessian_list.append(gamma_hessian) +control_bounds_list.append(bounds) +# reshape to [[lo1, lo2, ...], [hi1, hi2, ...]] +control_bounds = numpy.array(control_bounds_list).T + +# Assign initial conditions +print_output('Exporting to ' + options.output_directory) + +# Create station manager +observation_data_dir = output_dir_forward +variable = 'uv' +stations = [ + ('stationA', (lx/10, ly/2)), + ('stationB', (lx/2, ly/2)), + ('stationC', (3*lx/4, ly/4)), + ('stationD', (3*lx/4, 3*ly/4)), + ('stationE', (9*lx/10, ly/2)), +] +sta_manager = inversion_tools.StationObservationManager(mesh2d, output_directory=options.output_directory, + observation_param='uv') +print_output('Station Manager instantiated.') +station_names, observation_coords, observation_time, observation_u, observation_v = [], [], [], [], [] +for name, (sta_x, sta_y) in stations: + file = f'{output_dir_forward}/'f'diagnostic_timeseries_{name}_{variable}.hdf5' + with h5py.File(file) as h5file: + t = h5file['time'][:].flatten() + var = h5file[name][:] + station_names.append(name) + observation_coords.append((sta_x, sta_y)) + observation_time.append(t) + observation_u.append(var[:, 0]) + observation_v.append(var[:, 1]) +observation_x, observation_y = numpy.array(observation_coords).T +sta_manager.register_observation_data(station_names, variable, observation_time, observation_x, observation_y, + u=observation_u, v=observation_v, start_times=None, end_times=None) +print_output('Data registered.') +sta_manager.construct_evaluator() +sta_manager.set_model_field(solver_obj.fields.uv_2d) +print_output('Station Manager set-up complete.') + +# -------------------------------------- Step 3: define the optimisation problem --------------------------------------- + +# Define the scaling for the cost function so that J ~ O(1) +J_scalar = Constant(solver_obj.dt / options.simulation_end_time, domain=mesh2d) + +# Create inversion manager and add controls +inv_manager = inversion_tools.InversionManager( + sta_manager, output_dir=options.output_directory, no_exports=False, penalty_parameters=gamma_hessian_list, + cost_function_scaling=J_scalar, test_consistency=False, test_gradient=False) + +print_output('Inversion Manager instantiated.') + +if selected_case == 'Constant': + manning_const = Constant(0.03, name='Manning', domain=mesh2d) + manning_2d.project(manning_const) + inv_manager.add_control(manning_const) +elif selected_case == 'Regions' or selected_case == 'IndependentPointsScheme': + m_values = [Constant(0.03 - 0.0005 * i, domain=mesh2d) for i in range(M)] + manning_2d.assign(0) + for m_, mask_ in zip(m_values, masks): + manning_2d += m_ * mask_ + for i, control in enumerate(m_values): + if i == 0: + inv_manager.add_control(control, masks[0], new_map=True) + else: + inv_manager.add_control(control, masks[i]) +else: + manning_2d.assign(0.04) + inv_manager.add_control(manning_2d) +if not no_exports: + VTKFile(output_dir_invert + '/manning_init.pvd').write(manning_2d) + +# Extract the regularized cost function +cost_function = inv_manager.get_cost_function(solver_obj, weight_by_variance=True) +cost_function_callback = inversion_tools.CostFunctionCallback(solver_obj, cost_function) +solver_obj.add_callback(cost_function_callback, 'timestep') + +# Solve and setup reduced functional +solver_obj.iterate(update_forcings=update_forcings) +inv_manager.stop_annotating() + +# Run inversion +opt_verbose = -1 # scipy diagnostics -1, 0, 1, 99, 100, 101 +opt_options = { + 'maxiter': 20, # NOTE increase to run iteration longer + 'ftol': 1e-5, + 'disp': opt_verbose if mesh2d.comm.rank == 0 else -1, +} +if os.getenv('THETIS_REGRESSION_TEST') is not None: + opt_options['maxiter'] = 1 +control_opt_list = inv_manager.minimize( + opt_method='L-BFGS-B', bounds=control_bounds, **opt_options) +if isinstance(control_opt_list, Function): + control_opt_list = [control_opt_list] +for oc, cc in zip(control_opt_list, inv_manager.control_coeff_list): + print_function_value_range(oc, prefix='Optimal') + # NOTE: This would need to be updated to match the controls if bathymetry was also added! + if selected_case == 'Constant': + P1_2d = get_functionspace(mesh2d, 'CG', 1) + manning_2d = Function(P1_2d, name='Manning coefficient') + manning_2d.assign(domain_constant(inv_manager.m_list[-1], mesh2d)) + if not no_exports: + VTKFile(f'{options.output_directory}/manning_optimised.pvd').write(manning_2d) + elif selected_case == 'Regions' or selected_case == 'IndependentPointsScheme': + P1_2d = get_functionspace(mesh2d, 'CG', 1) + manning_2d = Function(P1_2d, name='manning2d') + manning_2d.assign(0) + for m_, mask_ in zip(inv_manager.m_list, masks): + manning_2d += m_ * mask_ + VTKFile(f'{options.output_directory}/manning_optimised.pvd').write(manning_2d) + else: + name = cc.name() + oc.rename(name) + print_function_value_range(oc, prefix='Optimal') + if not no_exports: + VTKFile(f'{options.output_directory}/{name}_optimised.pvd').write(oc) + +if selected_case == 'Regions' or selected_case == 'IndependentPointsScheme': + print_output("Optimised vector m:\n" + str([np.round(control_opt_list[i].dat.data[0], 4) for i in range(len(control_opt_list))])) diff --git a/examples/headland_inversion/model_config.py b/examples/headland_inversion/model_config.py new file mode 100644 index 000000000..c0ed393d9 --- /dev/null +++ b/examples/headland_inversion/model_config.py @@ -0,0 +1,205 @@ +from thetis import * +from firedrake import VTKFile +from mpi4py import MPI + +# Initialize MPI +comm = MPI.COMM_WORLD +rank = comm.Get_rank() +size = comm.Get_size() + + +def generate_bathymetry(mesh, H, output_directory, exporting=True): + """ + Generates a bathymetry function for a given mesh file by solving the Eikonal + equation and projects the result onto a bathymetry function. + + Parameters: + ----------- + mesh_file : str + Path to the mesh file used to create the computational mesh. + H : float + The depth value used for the bathymetry, reduces to 5 at the shoreline (ID = 3). + output_directory : str + Directory where the output files (distance and bathymetry) will be saved. + + Returns: + -------- + bathymetry : firedrake.Function + The computed bathymetry function. + """ + + # create function space + V = FunctionSpace(mesh, 'CG', 1) + + print_output("Calculating distance for bathymetry gradient") + + # Boundary + bcs = [DirichletBC(V, 0.0, 3)] # 3 = coasts PhysID + + L = 500 # distance to shore + v = TestFunction(V) + u = Function(V) + + solver_parameters = { + 'snes_type': 'ksponly', + 'ksp_rtol': 1e-4, + 'ksp_type': 'preonly', + 'pc_type': 'lu', + 'pc_factor_mat_solver_packages': 'mumps' + } + + # Before we solve the Eikonal equation, let's solve a Laplace equation to + # generate an initial guess + F = L ** 2 * (inner(grad(u), grad(v))) * dx - v * dx + solve(F == 0, u, bcs, solver_parameters=solver_parameters) + # Relax the solver parameters for the Eikonal equation + solver_parameters.update({ + 'snes_type': 'newtonls', + 'ksp_rtol': 1e-4, + 'ksp_type': 'preonly', + 'pc_type': 'lu', + 'pc_factor_mat_solver_packages': 'mumps' + }) + + epss = [500., 200., 100., 50., 20.] + + for i, eps in enumerate(epss): + print_output("Solving Eikonal with eps == " + str(float(eps))) + F = inner(sqrt(inner(grad(u), grad(u))), v) * dx - v * dx + eps * inner(grad(u), grad(v)) * dx + solve(F == 0, u, bcs, solver_parameters=solver_parameters) + + if exporting: + VTKFile(output_directory + "/dist.pvd").write(u) + + """ + Adding viscocity sponge + """ + + bathymetry = Function(V, name="bathymetry") + bathymetry.project(conditional(ge(u, L), H, (H - 5) * (u / L) + 5.)) + if exporting: + VTKFile(output_directory + '/bathymetry.pvd').write(bathymetry) + + return bathymetry + + +def construct_solver(store_station_time_series=True, **model_options): + mesh2d = Mesh('headland.msh') + pwd = os.path.abspath(os.path.dirname(__file__)) + output_directory = model_options.get('output_directory', f'{pwd}/outputs_forward') + exporting = not model_options.get('no_exports', False) + + tidal_amplitude = 1. + tidal_period = 12.42 * 60 * 60 + t_end = tidal_period + H = 40 + dt = 800. + t_export = dt + + if os.getenv('THETIS_REGRESSION_TEST') is not None: + t_end = 5*dt + + # bathymetry + P1_2d = get_functionspace(mesh2d, 'CG', 1) + bathymetry_2d = Function(P1_2d, name="bathymetry") + bathy = generate_bathymetry(mesh2d, H, output_directory, exporting) + bathymetry_2d.project(bathy) + + x, y = SpatialCoordinate(mesh2d) + local_lx = np.max(mesh2d.coordinates.dat.data[:, + 0]) # for parallel runs, the mesh is partioned so we need to get the maximum from each processor! + local_ly = np.max(mesh2d.coordinates.dat.data[:, 1]) + + all_lx = comm.gather(local_lx, root=0) + all_ly = comm.gather(local_ly, root=0) + if rank == 0: + lx_ = np.max(all_lx) + ly_ = np.max(all_ly) + else: + lx_ = None + ly_ = None + lx = comm.bcast(lx_, root=0) + ly = comm.bcast(ly_, root=0) + + # friction Manning coefficient + manning_2d = Function(P1_2d, name='Manning coefficient') + manning_low = 0.02 + manning_high = 0.05 + manning_2d.interpolate( + conditional(x < 11e3, manning_high, manning_low)) + if exporting: + VTKFile(output_directory + '/manning_init.pvd').write(manning_2d) + + # viscosity + h_viscosity = Function(P1_2d).interpolate(conditional(le(x, 1e3), 0.1*(1e3 - x), 1.0)) + if exporting: + VTKFile(output_directory + '/h_viscosity.pvd').write(h_viscosity) + + # create solver + solver_obj = solver2d.FlowSolver2d(mesh2d, bathymetry_2d) + options = solver_obj.options + + options.simulation_export_time = t_export + options.simulation_end_time = t_end + options.output_directory = output_directory + options.check_volume_conservation_2d = True + options.fields_to_export = ['uv_2d', 'elev_2d'] + options.element_family = 'dg-cg' + options.swe_timestepper_type = 'CrankNicolson' + options.swe_timestepper_options.implicitness_theta = 0.6 + options.swe_timestepper_options.solver_parameters = {'snes_rtol': 1e-9, + 'ksp_type': 'preonly', + 'pc_type': 'lu', + 'pc_factor_mat_solver_type': 'mumps', + 'mat_type': 'aij' + } + options.horizontal_viscosity = h_viscosity + options.timestep = dt + options.update(model_options) + + options.manning_drag_coefficient = manning_2d + solver_obj.add_new_field(manning_2d, 'manning_2d', + manning_2d.name(), + 'Manning2d', unit='s m-1/3') + + solver_obj.create_equations() + + if store_station_time_series: + # store elevation time series at stations + stations = [ + ('stationA', (lx/10, ly/2)), + ('stationB', (lx/2, ly/2)), + ('stationC', (3*lx/4, ly/4)), + ('stationD', (3*lx/4, 3*ly/4)), + ('stationE', (9*lx/10, ly/2)), + ] + for name, (sta_x, sta_y) in stations: + cb = DetectorsCallback(solver_obj, [(sta_x, sta_y)], ['uv_2d'], name='timeseries_'+name+'_uv', + detector_names=[name], append_to_log=False) + solver_obj.add_callback(cb) + + left_tag = 1 + right_tag = 2 + coasts_tag = 3 + tidal_elev = Function(get_functionspace(mesh2d, "CG", 1), name='tidal_elev') + tidal_elev_bc = {'elev': tidal_elev} + # noslip currently doesn't work (vector Constants are broken in firedrake adjoint) + freeslip_bc = {'un': Constant(0.0)} + solver_obj.bnd_functions['shallow_water'] = { + left_tag: tidal_elev_bc, + right_tag: tidal_elev_bc, + coasts_tag: freeslip_bc + } + + # a function to update the tidal_elev bc value every timestep + g = 9.81 + omega = 2 * pi / tidal_period + + def update_forcings(t): + print_output("Updating tidal elevation at t = {}".format(t)) + tidal_elev.project(tidal_amplitude * sin(omega * t + omega / pow(g * H, 0.5) * x)) + + # set initial condition for elevation, piecewise linear function + solver_obj.assign_initial_conditions(uv=as_vector((1e-7, 0.0)), elev=tidal_elev) + + return solver_obj, update_forcings diff --git a/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationA_uv.hdf5 b/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationA_uv.hdf5 new file mode 100644 index 000000000..c1f184483 Binary files /dev/null and b/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationA_uv.hdf5 differ diff --git a/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationB_uv.hdf5 b/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationB_uv.hdf5 new file mode 100644 index 000000000..8f3b34c55 Binary files /dev/null and b/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationB_uv.hdf5 differ diff --git a/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationC_uv.hdf5 b/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationC_uv.hdf5 new file mode 100644 index 000000000..48f43a218 Binary files /dev/null and b/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationC_uv.hdf5 differ diff --git a/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationD_uv.hdf5 b/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationD_uv.hdf5 new file mode 100644 index 000000000..522ab143e Binary files /dev/null and b/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationD_uv.hdf5 differ diff --git a/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationE_uv.hdf5 b/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationE_uv.hdf5 new file mode 100644 index 000000000..3d9d2331a Binary files /dev/null and b/examples/headland_inversion/outputs/outputs_forward/diagnostic_timeseries_stationE_uv.hdf5 differ diff --git a/examples/headland_inversion/plot_velocity_progress.py b/examples/headland_inversion/plot_velocity_progress.py new file mode 100644 index 000000000..2415b780c --- /dev/null +++ b/examples/headland_inversion/plot_velocity_progress.py @@ -0,0 +1,77 @@ +import h5py +import matplotlib +import matplotlib.pyplot as plt +import argparse + +matplotlib.rc('font', size=18) + +# parse user input +parser = argparse.ArgumentParser( + description='Plot velocity time series progress.', +) +parser.add_argument('-s', '--station', nargs='+', + help='Station(s) to plot. Multiple can be defined.', + required=True, + choices=['stationA', 'stationB', 'stationC', 'stationD', 'stationE'] + ) +parser.add_argument('--case', nargs='+', + help='Method of Manning field representation', + choices=['Constant', 'Regions', 'IndependentPointsScheme', 'NodalFreedom'], + default=['IndependentPointsScheme'], + ) +args = parser.parse_args() +station_names = sorted(args.station) + +station_str = '-'.join(station_names) + +case_to_output_dir = { + 'Constant': 'constant_friction', + 'Regions': 'region_based', + 'IndependentPointsScheme': 'independent_points_scheme', + 'NodalFreedom': 'full_nodal_flexibility' +} + +selected_case = args.case[0] +output_dir_forward = 'outputs//outputs_forward' +output_dir_invert = 'outputs/outputs_inverse/' + case_to_output_dir[selected_case] + +niter = 0 +nplots = len(station_names) + +for i, sta in enumerate(station_names): + fig, ax = plt.subplots(2, 1, figsize=(12, 10)) + + f = output_dir_forward + f'/diagnostic_timeseries_{sta}_uv.hdf5' + with h5py.File(f, 'r') as h5file: + time = h5file['time'][:].flatten() + var = h5file[sta][:] + u_vals = var[:, 0] + v_vals = var[:, 1] + + g = output_dir_invert + f'/diagnostic_timeseries_progress_{sta}_uv.hdf5' + with h5py.File(g, 'r') as h5file: + iter_times = h5file['time'][:].flatten() + u_iter_vals = h5file['u'][:] + v_iter_vals = h5file['v'][:] + + niter = u_iter_vals.shape[0] - 1 + + ax[0].plot(time, u_vals, 'k:', zorder=3, label='observation', lw=1.3) + ax[1].plot(time, v_vals, 'k:', zorder=3, label='observation', lw=1.3) + for j, u in enumerate(u_iter_vals): + ax[0].plot(iter_times, u, label=f'iteration {j}', lw=0.5) + for j, v in enumerate(v_iter_vals): + ax[1].plot(iter_times, v, lw=0.5) + ax[0].set_title(f'{sta}', size='small') + ax[0].set_ylabel('u component of velocity (m/s)') + ax[1].set_ylabel('v component of velocity (m/s)') + ax[0].grid(True), ax[1].grid(True) + ax[0].legend(ncol=1, prop={'size': 10}) + ax[1].set_xlabel('Time (s)') + + ax[0].text(0.5, 1.1, f'Optimizing Manning, {niter} iterations', ha='center', transform=ax[0].transAxes) + + # plt.show() + imgfile = f'{output_dir_invert}/optimization_progress_{selected_case}_{station_str}_ts.png' + print(f'Saving to {imgfile}') + plt.savefig(imgfile, dpi=200, bbox_inches='tight') diff --git a/examples/tohoku_inversion/inverse_problem.py b/examples/tohoku_inversion/inverse_problem.py index c72858e8c..f623dada8 100644 --- a/examples/tohoku_inversion/inverse_problem.py +++ b/examples/tohoku_inversion/inverse_problem.py @@ -73,7 +73,7 @@ sta_manager = inversion_tools.StationObservationManager( mesh2d, output_directory=options.output_directory ) -sta_manager.load_observation_data( +sta_manager.load_elev_observation_data( observation_data_dir, station_names, variable, @@ -99,9 +99,11 @@ # Extract the regularized cost function cost_function = inv_manager.get_cost_function(solver_obj, weight_by_variance=True) +cost_function_callback = inversion_tools.CostFunctionCallback(solver_obj, cost_function) +solver_obj.add_callback(cost_function_callback, 'timestep') # Solve and setup the reduced functional -solver_obj.iterate(export_func=cost_function) +solver_obj.iterate() inv_manager.stop_annotating() # Run inversion diff --git a/test/examples/test_examples.py b/test/examples/test_examples.py index 1a53238e0..894581541 100644 --- a/test/examples/test_examples.py +++ b/test/examples/test_examples.py @@ -39,6 +39,11 @@ 'tidalfarm/tidalfarm.py', 'tidal_barrage/plotting.py', 'channel_inversion/plot_elevation_progress.py', + 'channel_inversion/inverse_problem.py', + 'headland_inversion/forward_run.py', + 'headland_inversion/inverse_problem.py', + 'headland_inversion/inversion_tools_vel.py', + 'headland_inversion/plot_velocity_progress.py', 'tohoku_inversion/okada.py', 'tohoku_inversion/plot_convergence.py', 'tohoku_inversion/plot_elevation_initial_guess.py', diff --git a/test_adjoint/examples/test_examples.py b/test_adjoint/examples/test_examples.py index 84658fbf6..5c830e705 100644 --- a/test_adjoint/examples/test_examples.py +++ b/test_adjoint/examples/test_examples.py @@ -15,7 +15,8 @@ # list of all adjoint examples to run adjoint_files = [ 'tidalfarm/tidalfarm.py', - # 'channel_inversion/inverse_problem.py', # FIXME requires obs time series + 'channel_inversion/inverse_problem.py', + 'headland_inversion/inverse_problem.py', ] cwd = os.path.abspath(os.path.dirname(__file__)) diff --git a/thetis/callback.py b/thetis/callback.py index 52195e926..1efa51e76 100644 --- a/thetis/callback.py +++ b/thetis/callback.py @@ -209,6 +209,7 @@ def __init__(self, solver_obj, array_dim=1, attrs=None, if init_date is not None and include_time: time_units = 'seconds since ' + init_date.isoformat() self.var_attrs['time'] = {'units': time_units} + self.attrs['simulation_initial_date'] = init_date.isoformat() def set_write_mode(self, mode): """ diff --git a/thetis/inversion_tools.py b/thetis/inversion_tools.py index a46706929..20678bc00 100644 --- a/thetis/inversion_tools.py +++ b/thetis/inversion_tools.py @@ -7,6 +7,7 @@ from .log import print_output from .diagnostics import HessianRecoverer2D from .exporter import HDF5Exporter +from .callback import DiagnosticCallback import abc import numpy import h5py @@ -15,6 +16,50 @@ import os +def group_consecutive_elements(indices): + grouped_list = [] + current_group = [] + + for index in indices: + if not current_group or index == current_group[-1]: + current_group.append(index) + else: + grouped_list.append(current_group) + current_group = [index] + + # Append the last group + if current_group: + grouped_list.append(current_group) + + return grouped_list + + +class CostFunctionCallback(DiagnosticCallback): + def __init__(self, solver_obj, cost_function, **kwargs): + # Disable logging and HDF5 export + kwargs.setdefault('append_to_log', False) + kwargs.setdefault('export_to_hdf5', False) + super().__init__(solver_obj, **kwargs) + self.cost_function = cost_function + + @property + def name(self): + return 'cost_function_callback' + + @property + def variable_names(self): + return ['cost_function'] + + def __call__(self): + # Evaluate the cost function + cost_value = self.cost_function() + return [cost_value] + + def message_str(self, cost_value): + # Return a string representation of the cost function value + return f"Cost function value: {cost_value}" + + class InversionManager(FrozenHasTraits): """ Class for handling inversion problems and stashing @@ -45,6 +90,7 @@ def __init__(self, sta_manager, output_dir='outputs', no_exports=False, real=Fal self.output_dir = output_dir self.no_exports = no_exports or real self.real = real + self.maps = [] self.penalty_parameters = penalty_parameters self.cost_function_scaling = cost_function_scaling or fd.Constant(1.0) self.sta_manager.cost_function_scaling = self.cost_function_scaling @@ -52,6 +98,7 @@ def __init__(self, sta_manager, output_dir='outputs', no_exports=False, real=Fal self.test_gradient = test_gradient self.outfiles_m = [] self.outfiles_dJdm = [] + self.outfile_index = [] self.control_exporters = [] self.initialized = False @@ -71,6 +118,7 @@ def __init__(self, sta_manager, output_dir='outputs', no_exports=False, real=Fal self.nb_grad_evals = 0 self.control_coeff_list = [] self.control_list = [] + self.control_family = [] def initialize(self): if not self.no_exports: @@ -78,29 +126,58 @@ def initialize(self): raise ValueError("Exports are not supported in Real mode.") create_directory(self.output_dir) create_directory(self.output_dir + '/hdf5') - for i in range(len(self.control_coeff_list)): + for i in range(max(self.outfile_index)+1): self.outfiles_m.append( fd.VTKFile(f'{self.output_dir}/control_progress_{i:02d}.pvd')) self.outfiles_dJdm.append( fd.VTKFile(f'{self.output_dir}/gradient_progress_{i:02d}.pvd')) self.initialized = True - def add_control(self, f): + def add_control(self, f, mapping=None, new_map=False): """ Add a control field. Can be called multiple times in case of multiparameter optimization. :arg f: Function or Constant to be used as a control variable. + :kwarg mapping: map that dictates how each Control relates to the function being altered + :kwarg new_map: if True, create a new exporter """ + if len(self.control_coeff_list) == 0: + new_map = True + if mapping: + self.maps.append(mapping) + else: + self.maps.append(None) self.control_coeff_list.append(f) self.control_list.append(Control(f)) + function_space = f.function_space() + element = function_space.ufl_element() + family = element.family() + self.control_family.append(family) if isinstance(f, fd.Function) and not self.no_exports: j = len(self.control_coeff_list) - 1 prefix = f'control_{j:02d}' - self.control_exporters.append( - HDF5Exporter(f.function_space(), self.output_dir + '/hdf5', prefix) - ) + if family == 'Real': # i.e. Control is a Constant (assigned to a mesh, so won't register as one) + if new_map: + self.control_exporters.append( + HDF5Exporter(get_functionspace(self.sta_manager.mesh, 'CG', 1), self.output_dir + '/hdf5', + prefix) + ) + if len(self.control_coeff_list) == 1: + self.outfile_index.append(0) + else: + self.outfile_index.append(self.outfile_index[-1] + 1) + else: + self.outfile_index.append(self.outfile_index[-1]) + else: # i.e. Control is a Function + self.control_exporters.append( + HDF5Exporter(function_space, self.output_dir + '/hdf5', prefix) + ) + if len(self.control_coeff_list) == 1: + self.outfile_index.append(0) + else: + self.outfile_index.append(self.outfile_index[-1] + 1) def reset_counters(self): self.nb_grad_evals = 0 @@ -145,7 +222,7 @@ def update_progress(self): toc = self.stop_clock() if self.i == 0: for f in self.control_coeff_list: - print_function_value_range(f, prefix='Initial') + print_function_value_range(f, name=f.name, prefix='Initial') elapsed = '-' if self.tic is None else f'{toc - self.tic:.1f} s' self.tic = toc @@ -179,21 +256,54 @@ def update_progress(self): f'grad_ev={self.nb_grad_evals}, duration {elapsed}') if not self.no_exports: - # control output - for j in range(len(self.control_coeff_list)): - m = self.m_list[j] - # vtk format - o = self.outfiles_m[j] - m.rename(self.control_coeff_list[j].name()) - o.write(m) - # hdf5 format + grouped_indices = group_consecutive_elements(self.outfile_index) + ref_index = 0 + for j in range(len(self.outfiles_m)): + m = self.m_list[ref_index] + o_m = self.outfiles_m[j] + o_jm = self.outfiles_dJdm[j] + self.dJdm_list[ref_index].rename('Gradient') e = self.control_exporters[j] - e.export(m) - # gradient output - for f, o in zip(self.dJdm_list, self.outfiles_dJdm): - # store gradient in vtk format - f.rename('Gradient') - o.write(f) + if len(grouped_indices[j]) > 1: + # can only be Constants + mesh2d = self.sta_manager.mesh + P1_2d = get_functionspace(mesh2d, 'CG', 1) + # vtk format + field = fd.Function(P1_2d, name='control') + self.update_n(field, self.m_list[ref_index:ref_index + len(grouped_indices[j])], + ref_index, ref_index + len(grouped_indices[j])) + o_m.write(field) + # hdf5 format + e.export(field) + # gradient output + gradient = fd.Function(P1_2d, name='Gradient') + self.update_n(gradient, self.dJdm_list[ref_index:ref_index + len(grouped_indices[j])], + ref_index, ref_index + len(grouped_indices[j])) + o_jm.write(gradient) + else: + if self.control_family[ref_index] == 'Real': + mesh2d = self.sta_manager.mesh + P1_2d = get_functionspace(mesh2d, 'CG', 1) + # vtk format + field = fd.Function(P1_2d, name='control') + field.assign(domain_constant(m, mesh2d)) + o_m.write(field) + # hdf5 format + e.export(field) + # gradient output + gradient = fd.Function(P1_2d, name='Gradient') + gradient.assign(domain_constant(self.dJdm_list[ref_index], mesh2d)) + o_jm.write(gradient) + else: + # control output + # vtk format + m.rename(self.control_coeff_list[j].name()) + o_m.write(m) + # hdf5 format + e.export(m) + # gradient output + o_jm.write(self.dJdm_list[ref_index]) + ref_index += len(grouped_indices[j]) self.i += 1 self.reset_counters() @@ -248,9 +358,17 @@ def get_cost_function(self, solver_obj, weight_by_variance=False): if weight_by_variance: var = fd.Function(self.sta_manager.fs_points_0d) - for i, j in enumerate(self.sta_manager.local_station_index): - var.dat.data[i] = numpy.var(self.sta_manager.observation_values[j]) - self.sta_manager.station_weight_0d.interpolate(1/var) + # in parallel access to .dat.data should be collective + if len(var.dat.data[:]) > 0: + for i, j in enumerate(self.sta_manager.local_station_index): + if self.sta_manager.obs_param == 'elev': + var.dat.data[i] = numpy.var(self.sta_manager.observation_elev[j]) + else: + obs_speed = numpy.sqrt( + numpy.array(self.sta_manager.observation_u[j]) ** 2 + + numpy.array(self.sta_manager.observation_v[j]) ** 2) + var.dat.data[i] = numpy.var(obs_speed) + self.sta_manager.station_weight_0d.interpolate(1 / var) def cost_fn(): t = solver_obj.simulation_time @@ -296,6 +414,25 @@ def optimization_callback(m): return optimization_callback + def update_n(self, n, m, start_index, end_index): + """ + Update the function `n` by adding weighted masks from `m`. + + This method resets `n` to zero and then adds the weighted masks defined in + `self.maps` to `n`. Each element in `m` is multiplied by the corresponding + mask before being added to `n`. + + :param n: Function or Field to be updated. + :param m: List of Constants/Functions to be combined with the masks. + :param start_index: Starting map. + :param end_index: Final map. + :raises ValueError: If the lengths of `m` and `self.maps` do not match. + """ + n.assign(0) + # Add the weighted masks to n + for m_, mask_ in zip(m, self.maps[start_index:end_index]): + n += m_ * mask_ + def minimize(self, opt_method="BFGS", bounds=None, **opt_options): """ Minimize the reduced functional using a given optimization routine. @@ -354,8 +491,14 @@ class StationObservationManager: This object evaluates the model fields at the station locations, interpolates the observations time series to the model time, computes the error functional, and also stores the model's time series data to disk. + + :param observation_param: The type of observation being compared. It can be either + 'elev' for elevation data or 'uv' for velocity data. + Elevation data refers to the surface elevation time series, + while velocity data ('uv') refers to the horizontal velocity + components (u, v) at each station location. """ - def __init__(self, mesh, output_directory='outputs'): + def __init__(self, mesh, output_directory='outputs', observation_param='elev'): """ :arg mesh: the 2D mesh object. :kwarg output_directory: directory where model time series are stored. @@ -367,35 +510,47 @@ def __init__(self, mesh, output_directory='outputs'): self.cost_function_scaling = fd.Constant(1.0) self.output_directory = output_directory # keep observation time series in memory - self.obs_func_list = [] + self.obs_func_elev_list = [] + self.obs_func_u_list = [] + self.obs_func_v_list = [] # keep model time series in memory during optimization progress - self.station_value_progress = [] + self.station_value_elev_progress = [] + self.station_value_u_progress = [] + self.station_value_v_progress = [] # model time when cost function was evaluated self.simulation_time = [] + self.obs_param = observation_param self.model_observation_field = None self.initialized = False def register_observation_data(self, station_names, variable, time, - values, x, y, start_times=None, end_times=None): + x, y, u=None, v=None, elev=None, start_times=None, end_times=None): """ Add station time series data to the object. The `x`, and `y` coordinates must be such that they allow extraction of model data at the same coordinates. + Observation data is either elevation or velocity u, v components. + :arg list station_names: list of station names :arg str variable: canonical variable name, e.g. 'elev' :arg list time: array of time stamps, one for each station - :arg list values: array of observations, one for each station + :arg list elev: array of elevation observations, one for each station :arg list x: list of station x coordinates :arg list y: list of station y coordinates :kwarg list start_times: optional start times for the observation periods :kwarg list end_times: optional end times for the observation periods """ + if elev is None and (u is None or v is None): + raise ValueError("Either 'elev' must be provided, or both 'u' and 'v' must be provided.") + self.station_names = station_names self.variable = variable self.observation_time = time - self.observation_values = values + self.observation_elev = elev + self.observation_u = u + self.observation_v = v self.observation_x = x self.observation_y = y num_stations = len(station_names) @@ -408,12 +563,12 @@ def set_model_field(self, function): """ self.model_observation_field = function - def load_observation_data(self, observation_data_dir, station_names, variable, - start_times=None, end_times=None): + def load_elev_observation_data(self, observation_data_dir, station_names, variable, + start_times=None, end_times=None): """ - Load observation data from disk. + Load elevation observation data from disk. - Assumes that observation data were stored with + Assumes that elevation observation data were stored with `TimeSeriesCallback2D` during the forward run. For generic case, use `register_observation_data` instead. @@ -445,7 +600,7 @@ def load_observation_data(self, observation_data_dir, station_names, variable, observation_x, observation_y = numpy.array(observation_coords).T self.register_observation_data( station_names, variable, observation_time, - observation_values, observation_x, observation_y, + observation_x, observation_y, elev=observation_values, start_times=start_times, end_times=end_times, ) self.construct_evaluator() @@ -473,11 +628,17 @@ def construct_evaluator(self): xy = numpy.array((self.observation_x, self.observation_y)).T mesh0d = fd.VertexOnlyMesh(self.mesh, xy) self.fs_points_0d = fd.FunctionSpace(mesh0d, 'DG', 0) - self.obs_values_0d = fd.Function(self.fs_points_0d, name='observations') - self.mod_values_0d = fd.Function(self.fs_points_0d, name='model values') + if self.obs_param == 'elev': + self.obs_values_0d_elev = fd.Function(self.fs_points_0d, name='elev observations') + self.mod_values_0d_elev = fd.Function(self.fs_points_0d, name='elev model values') + else: + self.obs_values_0d_u = fd.Function(self.fs_points_0d, name='u observations') + self.obs_values_0d_v = fd.Function(self.fs_points_0d, name='v observations') + self.mod_values_0d_u = fd.Function(self.fs_points_0d, name='u model values') + self.mod_values_0d_v = fd.Function(self.fs_points_0d, name='v model values') self.indicator_0d = fd.Function(self.fs_points_0d, name='station use indicator') self.indicator_0d.assign(1.0) - self.cost_function_scaling_0d = domain_constant(0.0, mesh0d) + self.cost_function_scaling_0d = fd.Constant(0.0, domain=mesh0d) self.cost_function_scaling_0d.assign(self.cost_function_scaling) self.station_weight_0d = fd.Function(self.fs_points_0d, name='station-wise weighting') self.station_weight_0d.assign(1.0) @@ -486,8 +647,11 @@ def construct_evaluator(self): interp_kw.update({'bounds_error': False, 'fill_value': 0.0}) # Construct timeseries interpolator - self.station_interpolators = [] + self.station_interpolators_elev = [] + self.station_interpolators_u = [] + self.station_interpolators_v = [] self.local_station_index = [] + if len(mesh0d.coordinates.dat.data[:]) > 0: for i in range(self.fs_points_0d.dof_dset.size): # loop over local DOFs and match coordinates to observations @@ -500,15 +664,23 @@ def construct_evaluator(self): x, y = xy[j, :] t = self.observation_time[j] - v = self.observation_values[j] x_mesh, y_mesh = mesh0d.coordinates.dat.data[i, :] msg = 'bad station location ' \ - f'{j} {i} {x} {x_mesh} {y} {y_mesh} {x-x_mesh} {y-y_mesh}' + f'{j} {i} {x} {x_mesh} {y} {y_mesh} {x - x_mesh} {y - y_mesh}' assert numpy.allclose([x, y], [x_mesh, y_mesh]), msg - # create temporal interpolator - ip = interp1d(t, v, **interp_kw) - self.station_interpolators.append(ip) + if self.obs_param == 'elev': + elev = self.observation_elev[j] + # create temporal interpolator + ip_elev = interp1d(t, elev, **interp_kw) + self.station_interpolators_elev.append(ip_elev) + else: + u = self.observation_u[j] + v = self.observation_v[j] + ip_u = interp1d(t, u, **interp_kw) + ip_v = interp1d(t, v, **interp_kw) + self.station_interpolators_u.append(ip_u) + self.station_interpolators_v.append(ip_v) # Process start and end times for observations self.obs_start_times = numpy.array([ @@ -519,7 +691,13 @@ def construct_evaluator(self): ]) # expressions for cost function - self.misfit_expr = self.obs_values_0d - self.mod_values_0d + if self.obs_param == 'elev': + self.misfit_expr_elev = self.obs_values_0d_elev - self.mod_values_0d_elev + self.misfit_expr = self.misfit_expr_elev + else: + self.misfit_expr_u = self.obs_values_0d_u - self.mod_values_0d_u + self.misfit_expr_v = self.obs_values_0d_v - self.mod_values_0d_v + self.misfit_expr = (self.misfit_expr_u ** 2 + self.misfit_expr_v ** 2) ** (1/2) self.initialized = True def eval_observation_at_time(self, t): @@ -530,7 +708,13 @@ def eval_observation_at_time(self, t): :returns: list of observation time series values at time `t` """ self.update_stations_in_use(t) - return [float(ip(t)) for ip in self.station_interpolators] + if self.obs_param == 'elev': + ip = [float(ip(t)) for ip in self.station_interpolators_elev] + return ip + else: + ip1 = [float(ip(t)) for ip in self.station_interpolators_u] + ip2 = [float(ip(t)) for ip in self.station_interpolators_v] + return ip1, ip2 def eval_cost_function(self, t): """ @@ -542,16 +726,39 @@ def eval_cost_function(self, t): assert self.model_observation_field is not None, 'Model field not set.' self.simulation_time.append(t) # evaluate observations at simulation time and stash the result - obs_func = fd.Function(self.fs_points_0d) - obs_func.dat.data[:] = self.eval_observation_at_time(t) - self.obs_func_list.append(obs_func) - - # compute square error - self.obs_values_0d.assign(obs_func) - self.mod_values_0d.interpolate(self.model_observation_field, ad_block_tag='observation') - s = self.cost_function_scaling_0d * self.indicator_0d * self.station_weight_0d - self.J_misfit = fd.assemble(s * self.misfit_expr ** 2 * fd.dx, ad_block_tag='misfit_eval') - return self.J_misfit + if self.obs_param == 'elev': + obs_func_elev = fd.Function(self.fs_points_0d) + obs_func_elev.dat.data[:] = self.eval_observation_at_time(t) + self.obs_func_elev_list.append(obs_func_elev) + + # compute square error + self.obs_values_0d_elev.assign(obs_func_elev) + P1_2d = get_functionspace(self.mesh, 'CG', 1) + elev_mod = fd.Function(P1_2d, name='elev') + elev_mod.project(self.model_observation_field) + self.mod_values_0d_elev.interpolate(elev_mod, ad_block_tag='elev observation') + s = self.cost_function_scaling_0d * self.indicator_0d * self.station_weight_0d + self.J_misfit = fd.assemble(s * self.misfit_expr ** 2 * fd.dx, ad_block_tag='misfit_eval') + return self.J_misfit + else: + obs_func_u, obs_func_v = fd.Function(self.fs_points_0d), fd.Function(self.fs_points_0d) + obs_func_u.dat.data[:], obs_func_v.dat.data[:] = self.eval_observation_at_time(t) + self.obs_func_u_list.append(obs_func_u) + self.obs_func_v_list.append(obs_func_v) + + # compute square error + self.obs_values_0d_u.assign(obs_func_u) + self.obs_values_0d_v.assign(obs_func_v) + P1_2d = get_functionspace(self.mesh, 'CG', 1) + u_mod = fd.Function(P1_2d, name='u velocity') + v_mod = fd.Function(P1_2d, name='v velocity') + u_mod.project(self.model_observation_field[0]) + v_mod.project(self.model_observation_field[1]) + self.mod_values_0d_u.interpolate(u_mod, ad_block_tag='u observation') + self.mod_values_0d_v.interpolate(v_mod, ad_block_tag='v observation') + s = self.cost_function_scaling_0d * self.indicator_0d * self.station_weight_0d + self.J_misfit = fd.assemble(s * self.misfit_expr ** 2 * fd.dx, ad_block_tag='misfit_eval') + return self.J_misfit def dump_time_series(self): """ @@ -571,28 +778,58 @@ def dump_time_series(self): create_directory(self.output_directory) tape = get_working_tape() - blocks = tape.get_blocks(tag='observation') - ts_data = [b.get_outputs()[0].saved_output.dat.data for b in blocks] - # shape (ntimesteps, nstations) - ts_data = numpy.array(ts_data) - # append - self.station_value_progress.append(ts_data) - var = self.variable - for ilocal, iglobal in enumerate(self.local_station_index): - name = self.station_names[iglobal] - # collect time series data, shape (niters, ntimesteps) - ts = numpy.array([s[:, ilocal] for s in self.station_value_progress]) - fn = f'diagnostic_timeseries_progress_{name}_{var}.hdf5' - fn = os.path.join(self.output_directory, fn) - with h5py.File(fn, 'w') as hdf5file: - hdf5file.create_dataset(var, data=ts) - hdf5file.create_dataset('time', data=numpy.array(self.simulation_time)) - attrs = { - 'x': self.observation_x[iglobal], - 'y': self.observation_y[iglobal], - 'location_name': name, - } - hdf5file.attrs.update(attrs) + if self.obs_param == 'elev': + blocks_elev = tape.get_blocks(tag='elev observation') + ts_data_elev = [b.get_outputs()[0].saved_output.dat.data for b in blocks_elev] + # shape (ntimesteps, nstations) + ts_data_elev = numpy.array(ts_data_elev) + # append + self.station_value_elev_progress.append(ts_data_elev) + var = self.variable + for ilocal, iglobal in enumerate(self.local_station_index): + name = self.station_names[iglobal] + # collect time series data, shape (niters, ntimesteps) + ts_elev = numpy.array([s[:, ilocal] for s in self.station_value_elev_progress]) + fn = f'diagnostic_timeseries_progress_{name}_{var}.hdf5' + fn = os.path.join(self.output_directory, fn) + with h5py.File(fn, 'w') as hdf5file: + hdf5file.create_dataset('elev', data=ts_elev) + hdf5file.create_dataset('time', data=numpy.array(self.simulation_time)) + attrs = { + 'x': self.observation_x[iglobal], + 'y': self.observation_y[iglobal], + 'location_name': name, + } + hdf5file.attrs.update(attrs) + else: + blocks_u = tape.get_blocks(tag='u observation') + blocks_v = tape.get_blocks(tag='v observation') + ts_data_u = [b.get_outputs()[0].saved_output.dat.data for b in blocks_u] + ts_data_v = [b.get_outputs()[0].saved_output.dat.data for b in blocks_v] + # shape (ntimesteps, nstations) + ts_data_u = numpy.array(ts_data_u) + ts_data_v = numpy.array(ts_data_v) + # append + self.station_value_u_progress.append(ts_data_u) + self.station_value_v_progress.append(ts_data_v) + var = self.variable + for ilocal, iglobal in enumerate(self.local_station_index): + name = self.station_names[iglobal] + # collect time series data, shape (niters, ntimesteps) + ts_u = numpy.array([s[:, ilocal] for s in self.station_value_u_progress]) + ts_v = numpy.array([s[:, ilocal] for s in self.station_value_v_progress]) + fn = f'diagnostic_timeseries_progress_{name}_{var}.hdf5' + fn = os.path.join(self.output_directory, fn) + with h5py.File(fn, 'w') as hdf5file: + hdf5file.create_dataset('u', data=ts_u) + hdf5file.create_dataset('v', data=ts_v) + hdf5file.create_dataset('time', data=numpy.array(self.simulation_time)) + attrs = { + 'x': self.observation_x[iglobal], + 'y': self.observation_y[iglobal], + 'location_name': name, + } + hdf5file.attrs.update(attrs) class RegularizationCalculator(abc.ABC): @@ -613,7 +850,7 @@ def __init__(self, function, scaling=1.0): self.regularization_expr = 0 self.mesh = function.function_space().mesh() # calculate mesh area (to scale the cost function) - self.mesh_area = fd.assemble(fd.Constant(1.0) * fd.dx(domain=self.mesh)) + self.mesh_area = fd.assemble(fd.Constant(1.0, domain=self.mesh) * fd.dx) self.name = function.name() def eval_cost_function(self):