adding finite difference check test harness; adding FD checks for hyp…

…erelastic objectives; adding FD check for J2 objective (is failing)

optimism/inverse/test/FiniteDifferenceFixture.py

@@ -0,0 +1,50 @@
+from optimism.test.MeshFixture import *
+from collections import namedtuple
+import numpy
+
+class FiniteDifferenceFixture(MeshFixture):
+    def assertFiniteDifferenceCheckHasVShape(self, errors, tolerance=1e-6):
+        minError = min(errors)
+        self.assertLess(minError, tolerance, "Smallest finite difference error not less than tolerance.")
+        self.assertLess(minError, errors[0], "Finite difference error does not decrease from initial step size.")
+        self.assertLess(minError, errors[-1], "Finite difference error does not increase after reaching minimum. Try more finite difference steps.")
+
+    def build_direction_vector(self, numDesignVars, seed=123):
+
+        numpy.random.seed(seed)
+        directionVector = numpy.random.uniform(-1.0, 1.0, numDesignVars)
+        normVector = directionVector / numpy.linalg.norm(directionVector)
+
+        return np.array(normVector)
+
+    def compute_finite_difference_errors(self, stepSize, steps, initialParameters, printOutput=True):
+        storedState = self.forward_solve(initialParameters)
+        originalObjective = self.compute_objective_function(storedState, initialParameters) 
+        gradient = self.compute_gradient(storedState, initialParameters) 
+
+        directionVector = self.build_direction_vector(initialParameters.shape[0])
+        directionalDerivative = np.tensordot(directionVector, gradient, axes=1)
+
+        fd_values = []
+        errors = []
+        for i in range(0, steps):
+            perturbedParameters = initialParameters + stepSize * directionVector
+            storedState = self.forward_solve(perturbedParameters)
+            perturbedObjective = self.compute_objective_function(storedState, perturbedParameters) 
+
+            fd_value = (perturbedObjective - originalObjective) / stepSize
+            fd_values.append(fd_value)
+
+            error = abs(directionalDerivative - fd_value)
+            errors.append(error)
+
+            stepSize *= 1e-1
+
+        if printOutput:
+            print("\n       grad'*dir          |         FD approx        |         abs error")
+            print("--------------------------------------------------------------------------------")
+            for i in range(0, steps):
+                print(f" {directionalDerivative}   |   {fd_values[i]}   |   {errors[i]}")
+
+        return errors
+

optimism/inverse/test/test_Hyperelastic_inverse.py

@@ -0,0 +1,213 @@
+import unittest
+
+import jax
+import jax.numpy as np
+from matplotlib import pyplot as plt
+
+from optimism import EquationSolver as EqSolver
+from optimism import QuadratureRule
+from optimism import FunctionSpace
+from optimism import Mechanics
+from optimism import Objective
+from optimism import Mesh
+from optimism.material import Neohookean
+
+from optimism.inverse.test.FiniteDifferenceFixture import FiniteDifferenceFixture
+
+# for adjoint
+import numpy as onp
+from scipy.sparse import linalg
+
+# misc. modules in test directory for now while I test
+import adjoint_problem_function_space as AdjointFunctionSpace
+
+class NeoHookeanGlobalMeshAdjointSolveFixture(FiniteDifferenceFixture):
+    def setUp(self):
+        dispGrad0 =  np.array([[0.4, -0.2],
+                               [-0.04, 0.68]])
+        self.initialMesh, self.U = self.create_mesh_and_disp(4,4,[0.,1.],[0.,1.],
+                                            lambda x: dispGrad0@x)
+
+        shearModulus = 0.855 # MPa
+        bulkModulus = 100*shearModulus # MPa
+        youngModulus = 9.0*bulkModulus*shearModulus / (3.0*bulkModulus + shearModulus)
+        poissonRatio = (3.0*bulkModulus - 2.0*shearModulus) / 2.0 / (3.0*bulkModulus + shearModulus)
+        props = {
+            'elastic modulus': youngModulus,
+            'poisson ratio': poissonRatio,
+            'version': 'coupled'
+        }
+        self.materialModel = Neohookean.create_material_model_functions(props)
+
+        self.quadRule = QuadratureRule.create_quadrature_rule_on_triangle(degree=1)
+
+        self.EBCs = [FunctionSpace.EssentialBC(nodeSet='all_boundary', component=0),
+                FunctionSpace.EssentialBC(nodeSet='all_boundary', component=1)]
+
+        self.steps = 2
+
+    def forward_solve(self, parameters):
+
+        self.mesh = Mesh.construct_mesh_from_basic_data(parameters.reshape(self.initialMesh.coords.shape),\
+                                                        self.initialMesh.conns, self.initialMesh.blocks,\
+                                                        self.initialMesh.nodeSets, self.initialMesh.sideSets)
+
+        functionSpace = FunctionSpace.construct_function_space(self.mesh, self.quadRule)
+        mechFuncs = Mechanics.create_mechanics_functions(functionSpace,
+                                                         "plane strain",
+                                                         self.materialModel)
+        self.dofManager = FunctionSpace.DofManager(functionSpace, 2, self.EBCs)
+        Ubc = self.dofManager.get_bc_values(self.U)
+
+        Ubc_inc = Ubc / self.steps
+        ivs = mechFuncs.compute_initial_state()
+        p = Objective.Params(bc_data=np.zeros(Ubc.shape), state_data=ivs)
+
+        def compute_energy(Uu, p):
+            U = self.dofManager.create_field(Uu, p.bc_data)
+            internalVariables = p.state_data
+            return mechFuncs.compute_strain_energy(U, internalVariables)
+
+        Uu = 0.0*self.dofManager.get_unknown_values(self.U) 
+        self.objective = Objective.Objective(compute_energy, Uu, p)
+
+        storedState = []
+        storedState.append((Uu, p))
+
+        for step in range(1, self.steps+1):
+            p = Objective.param_index_update(p, 0, step*Ubc_inc)
+            Uu = EqSolver.nonlinear_equation_solve(self.objective, Uu, p, EqSolver.get_settings(), useWarmStart=False)
+            storedState.append((Uu, p))
+
+        return storedState
+
+    def strain_energy_objective(self, storedState, parameters):
+        coords = parameters.reshape(self.mesh.coords.shape)
+        adjoint_func_space = AdjointFunctionSpace.construct_function_space_for_adjoint(coords, self.mesh, self.quadRule)
+        mech_funcs = Mechanics.create_mechanics_functions(adjoint_func_space, mode2D='plane strain', materialModel=self.materialModel)
+
+        def energy_function_coords(Uu, p, coords):
+            U = self.dofManager.create_field(Uu, p.bc_data)
+            internal_vars = p[1]
+            return mech_funcs.compute_strain_energy(U, internal_vars)
+
+        return energy_function_coords(storedState[-1][0], storedState[-1][1], parameters) 
+
+    def strain_energy_gradient(self, storedState, parameters):
+        return jax.grad(self.strain_energy_objective, argnums=1)(storedState, parameters)
+
+    def total_work_increment(self, Uu, Uu_prev, p, p_prev, coordinates):
+        coords = coordinates.reshape(self.mesh.coords.shape)
+        adjoint_func_space = AdjointFunctionSpace.construct_function_space_for_adjoint(coords, self.mesh, self.quadRule)
+        mech_funcs = Mechanics.create_mechanics_functions(adjoint_func_space, mode2D='plane strain', materialModel=self.materialModel)
+
+        def energy_function_all_dofs(U, p):
+            internal_variables = p[1]
+            return mech_funcs.compute_strain_energy(U, internal_variables)
+
+        nodal_forces = jax.grad(energy_function_all_dofs, argnums=0)
+
+        index = (self.mesh.nodeSets['left'], 1) # arbitrarily choosing left side nodeset for reaction force
+
+        U = self.dofManager.create_field(Uu, p.bc_data)
+        force = np.array(nodal_forces(U, p).at[index].get())
+        disp = U.at[index].get()
+
+        U_prev = self.dofManager.create_field(Uu_prev, p_prev.bc_data)
+        force_prev = np.array(nodal_forces(U_prev, p_prev).at[index].get())
+        disp_prev = U_prev.at[index].get()
+
+        return 0.5*np.tensordot((force + force_prev),(disp - disp_prev), axes=1)
+
+    def total_work_objective(self, storedState, parameters):
+        val = 0.0
+        for step in range(1, self.steps+1):
+            val += self.total_work_increment(storedState[step][0], storedState[step-1][0], storedState[step][1], storedState[step-1][1], parameters)
+
+        return val
+
+    def total_work_gradient_just_jax(self, storedState, parameters):
+        return jax.grad(self.total_work_objective, argnums=1)(storedState, parameters)
+
+    def total_work_gradient_with_adjoint(self, storedState, parameters):
+        compute_df = jax.grad(self.total_work_increment, (0, 1, 4))
+
+        def energy_function_coords(Uu, Uu_prev, p, coordinates):
+            coords = coordinates.reshape(self.mesh.coords.shape)
+            adjoint_func_space = AdjointFunctionSpace.construct_function_space_for_adjoint(coords, self.mesh, self.quadRule)
+            mech_funcs = Mechanics.create_mechanics_functions(adjoint_func_space, mode2D='plane strain', materialModel=self.materialModel)
+            U = self.dofManager.create_field(Uu, p.bc_data)
+            internal_vars = p[1]
+            return mech_funcs.compute_strain_energy(U, internal_vars)
+
+        gradient = np.zeros(parameters.shape)
+        adjointLoad = np.zeros(storedState[0][0].shape)
+
+        for step in reversed(range(1, self.steps+1)):
+            Uu = storedState[step][0]
+            p = storedState[step][1]
+
+            Uu_prev = storedState[step-1][0]
+            p_prev = storedState[step-1][1]
+
+            df_du, df_dun, df_dx = compute_df(Uu, Uu_prev, p, p_prev, parameters)
+
+            adjointLoad -= df_du
+
+            n = self.dofManager.get_unknown_size()
+            self.objective.p = p # have to update parameters to get precond to work
+            self.objective.update_precond(Uu) # update preconditioner for use in cg (will converge in 1 iteration as long as the preconditioner is not approximate)
+            dRdu = linalg.LinearOperator((n, n), lambda V: onp.asarray(self.objective.hessian_vec(Uu, V)))
+            dRdu_decomp = linalg.LinearOperator((n, n), lambda V: onp.asarray(self.objective.apply_precond(V)))
+            adjointVector = linalg.cg(dRdu, onp.array(adjointLoad, copy=False), tol=1e-10, atol=0.0, M=dRdu_decomp)[0]
+
+            gradient += df_dx
+            # The action dRdX * lambda (the same as lambda^T * dRdX)
+            gradient += jax.vjp(lambda z: jax.grad(energy_function_coords, 0)(Uu, Uu_prev, p, z), parameters)[1](adjointVector)[0]
+
+            adjointLoad = -df_dun
+            # The action dRdU * lambda (the same as lambda^T * dRdU) - For Hyperelastic the residual is not dependent on Uu_prev, so don't actually need this term
+            # adjointLoad -= jax.vjp(lambda z: jax.grad(energy_function_coords, 0)(Uu, z, p, parameters), Uu_prev)[1](adjointVector)[0]
+
+        return gradient
+
+
+
+    def test_self_adjoint_gradient(self):
+        self.compute_objective_function = self.strain_energy_objective
+        self.compute_gradient = self.strain_energy_gradient
+
+        initialStepSize = 1e-5
+        numSteps = 4
+
+        errors = self.compute_finite_difference_errors(initialStepSize, numSteps, self.initialMesh.coords.ravel())
+
+        self.assertFiniteDifferenceCheckHasVShape(errors)
+
+    @unittest.expectedFailure
+    def test_non_self_adjoint_gradient_without_adjoint_solve(self):
+        self.compute_objective_function = self.total_work_objective
+        self.compute_gradient = self.total_work_gradient_just_jax
+
+        initialStepSize = 1e-5
+        numSteps = 4
+
+        errors = self.compute_finite_difference_errors(initialStepSize, numSteps, self.initialMesh.coords.ravel())
+
+        self.assertFiniteDifferenceCheckHasVShape(errors)
+
+    def test_non_self_adjoint_gradient_with_adjoint_solve(self):
+        self.compute_objective_function = self.total_work_objective
+        self.compute_gradient = self.total_work_gradient_with_adjoint
+
+        initialStepSize = 1e-5
+        numSteps = 4
+
+        errors = self.compute_finite_difference_errors(initialStepSize, numSteps, self.initialMesh.coords.ravel())
+
+        self.assertFiniteDifferenceCheckHasVShape(errors)
+
+
+
+if __name__ == '__main__':
+    unittest.main()