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remove clipping function
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change to rank adaptation problem for sw-edmd
modify weighted cost func for new rank values
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@EthanJamesLew
EthanJamesLew committed Apr 22, 2024
1 parent 96a40cf commit 6a4b37b
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Showing 2 changed files with 53 additions and 14 deletions.
19 changes: 13 additions & 6 deletions autokoopman/estimator/koopman.py
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Original file line number Diff line number Diff line change
Expand Up @@ -81,14 +81,21 @@ def swdmdc(X, Xp, U, r, Js, W):
# so the objective isn't numerically unstable
sf = (1.0 / n_snap)

# check that rank is less than the number of observations
if r > n_obs:
warnings.warn("Rank must be less than the number of observations. Reducing rank to n_obs.")
r = n_obs

# koopman operator
K = cp.Variable((n_obs, n_obs + n_inps))
# Variables for the low-rank approximation
K_U = cp.Variable((n_obs, r))
K_V = cp.Variable((r, n_obs + n_inps))

# SW-eDMD objective
weights_obj = np.vstack([(np.clip(np.abs(J), 0.0, 1.0) @ w) for J, w in zip(Js, W)]).T
P = sf * cp.multiply(weights_obj, Yp.T - K @ Y.T)
weights_obj = np.vstack([(np.abs(J) @ w) for J, w in zip(Js, W)]).T
P = sf * cp.multiply(weights_obj, Yp.T - (K_U @ K_V) @ Y.T)
# add regularization
objective = cp.Minimize(cp.sum_squares(P) + 1E-4 * 1.0 / (n_obs**2) * cp.norm(K, "fro"))
objective = cp.Minimize(cp.sum_squares(P) + 1E-4 * 1.0 / (n_obs**2) * cp.norm(K_U @ K_V, "fro"))

# unconstrained problem
constraints = None
Expand All @@ -100,14 +107,14 @@ def swdmdc(X, Xp, U, r, Js, W):
try:
_ = prob.solve(solver=cp.CLARABEL)
#_ = prob.solve(solver=cp.ECOS)
if K.value is None:
if K_U.value is None or K_V.value is None:
raise Exception("SW-eDMD (cvxpy) Optimization failed to converge.")
except:
warnings.warn("SW-eDMD (cvxpy) Optimization failed to converge. Switching to unweighted DMDc.")
return dmdc(X, Xp, U, r)

# get the transformation
Atilde = K.value
Atilde = K_U.value @ K_V.value
return Atilde[:, :state_size], Atilde[:, state_size:]


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48 changes: 40 additions & 8 deletions notebooks/weighted-cost-func.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -16,7 +16,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"id": "dfdb47e2-0ea0-4bf8-8279-8500ff3cf21f",
"metadata": {},
"outputs": [],
Expand All @@ -36,7 +36,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 2,
"id": "291d3409-1c8c-44cb-8380-44f08019b57d",
"metadata": {},
"outputs": [],
Expand All @@ -45,7 +45,7 @@
"import autokoopman.benchmark.fhn as fhn\n",
"fhn = fhn.FitzHughNagumo()\n",
"training_data = fhn.solve_ivps(\n",
" initial_states=np.random.uniform(low=-2.0, high=2.0, size=(1, 2)),\n",
" initial_states=np.random.uniform(low=-2.0, high=2.0, size=(10, 2)),\n",
" tspan=[0.0, 6.0],\n",
" sampling_period=0.1\n",
")\n",
Expand All @@ -68,7 +68,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 3,
"id": "e2d42e41-46c2-467c-9ce7-9bd6a7c509a1",
"metadata": {},
"outputs": [],
Expand All @@ -92,6 +92,7 @@
" w = np.ones(traj.states.shape)\n",
" w[:, -3:] = 0.0\n",
" w[:, :2] = 1.0\n",
" w[:, 0] = 1.0\n",
" weights.append(w)\n",
"\n",
" # weight garbage trajectory to zero\n",
Expand All @@ -103,6 +104,25 @@
"#weights = {idx: w for idx, w in enumerate(weights)}"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "ddd76415-6d19-4a38-a2b0-84eb48d0fdfc",
"metadata": {},
"outputs": [],
"source": [
"from autokoopman.observable import ReweightedRFFObservable\n",
"import autokoopman.observable as akobs\n",
"\n",
"X, WX = list(zip(*list((trajectories[i], w) for i, w in enumerate(weights))))\n",
"X, WX = np.vstack(X), np.vstack(WX)\n",
"X, WX = np.tile(X, (3, 1)), np.tile(WX, (3, 1))\n",
"idxs = np.random.permutation(np.arange(len(X)))\n",
"Y, WY = X[idxs], WX[idxs]\n",
"\n",
"reweight_obs = akobs.IdentityObservable() | akobs.ReweightedRFFObservable(5, 40, 1.0, X, Y, WX, WY, 'rff')"
]
},
{
"cell_type": "markdown",
"id": "a706f212-36cd-4203-b209-cb7c5ce4ad94",
Expand All @@ -122,7 +142,19 @@
"execution_count": null,
"id": "98510aa7-3416-4181-a493-00500be53f61",
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Tuning GridSearchTuner: 0%| | 0/40 [00:00<?, ?it/s]/home/elew/AutoKoopman/notebooks/../autokoopman/estimator/koopman.py:113: UserWarning: SW-eDMD (cvxpy) Optimization failed to converge. Switching to unweighted DMDc.\n",
" warnings.warn(\"SW-eDMD (cvxpy) Optimization failed to converge. Switching to unweighted DMDc.\")\n",
"Tuning GridSearchTuner: 12%|▊ | 5/40 [00:23<03:07, 5.37s/it]/home/elew/anaconda3/envs/autokoopman/lib/python3.12/site-packages/numpy/linalg/linalg.py:2582: RuntimeWarning: overflow encountered in multiply\n",
" s = (x.conj() * x).real\n",
"Tuning GridSearchTuner: 30%|█▌ | 12/40 [00:52<02:04, 4.44s/it]"
]
}
],
"source": [
"# learn model from weighted data\n",
"experiment_results = auto_koopman(\n",
Expand All @@ -136,8 +168,8 @@
" n_obs=40, # maximum number of observables to try\n",
" max_opt_iter=200, # maximum number of optimization iterations\n",
" grid_param_slices=5, # for grid search, number of slices for each parameter\n",
" n_splits=None, # k-folds validation for tuning, helps stabilize the scoring\n",
" rank=(40, 41, 1) # NOTE: don't rank tune (for now)--SW-eDMD already optimizes for this\n",
" n_splits=5, # k-folds validation for tuning, helps stabilize the scoring\n",
" rank=(1, 41, 5) # rank (SW-eDMD now uses rank adaptation)\n",
")"
]
},
Expand Down Expand Up @@ -290,7 +322,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.0"
"version": "3.12.3"
}
},
"nbformat": 4,
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