Clean the Trapping variable names,

examples/8_trapping_sindy_examples/example.py

@@ -43,7 +43,7 @@
     sindy_library_no_bias,
     make_fits,
     make_lissajou,
-    check_stability,
+    check_local_stability,
     trapping_region,
     make_progress_plots,
     galerkin_model,
@@ -133,7 +133,7 @@
 print("Frobenius Error = ", E_pred)
 mean_val = np.mean(x_test_pred, axis=0)
 mean_val = np.sqrt(np.sum(mean_val**2))
-check_stability(r, Xi, sindy_opt, mean_val)
+check_local_stability(Xi, sindy_opt, mean_val)
 
 # compute relative Frobenius error in the model coefficients
 terms = sindy_library.get_feature_names()
@@ -154,15 +154,6 @@
     ) / np.dot(xdot_test[i, :], xdot_test[i, :])
 print("Time-averaged derivative error = ", np.nanmean(deriv_error))
 
-# %% [markdown]
-# Awesome! The trapping algorithm gets exactly the right model and produces a negative definite matrix,
-# $$\mathbf{A}^S = \begin{bmatrix}
-#     -1.32 & 0 & 0 \\
-#     0 & -1.31 & 0 \\
-#     0 & 0 & -1
-#     \end{bmatrix},$$
-# i.e. it identifies $\epsilon \approx 1.3$ from above. Note that with different algorithm hyperparameters it will produce different $\epsilon$, since the algorithm only cares that the matrix is negative definite (i.e. only cares about the largest eigenvalue), not the precise value of $\epsilon$. Moreover, these eigenvalues can change as the algorithm converges further.
-
 # %% [markdown]
 #
 #
@@ -235,13 +226,14 @@
 # define hyperparameters
 eta = 1.0e8
 
-# run trapping SINDy, reusing previous threshold, max_iter and constraints
+# run trapping SINDy, reusing previous reg_weight_lam, max_iter and constraints
 sindy_opt = ps.TrappingSR3(
     _n_tgts=3,
     _include_bias=True,
     reg_weight_lam=reg_weight_lam,
     eta=eta,
     max_iter=max_iter,
+    verbose=True,
 )
 model = ps.SINDy(
     optimizer=sindy_opt,
@@ -270,7 +262,7 @@
 print("Frobenius error = ", E_pred)
 mean_val = np.mean(x_test_pred, axis=0)
 mean_val = np.sqrt(np.sum(mean_val**2))
-check_stability(r, Xi, sindy_opt, mean_val)
+check_local_stability(Xi, sindy_opt, mean_val)
 
 # compute relative Frobenius error in the model coefficients
 terms = sindy_library.get_feature_names()
@@ -416,7 +408,7 @@
 
 mean_val = np.mean(x_test_pred, axis=0)
 mean_val = np.sqrt(np.sum(mean_val**2))
-check_stability(r, Xi, sindy_opt, mean_val)
+check_local_stability(Xi, sindy_opt, mean_val)
 E_pred = np.linalg.norm(x_test - x_test_pred) / np.linalg.norm(x_test)
 print("Frobenius error = ", E_pred)
 
@@ -501,9 +493,9 @@
 nu = 0.0  # viscosity
 mu = 0.0  # resistivity
 
-# define training and testing data
+# define training and testing data (low resolution)
 dt = 0.02
-T = 50
+T = 40
 t = np.arange(0, T + dt, dt)
 t_span = (t[0], t[-1])
 x0 = rng.random((6,)) - 0.5
@@ -515,7 +507,7 @@
 reg_weight_lam = 0.0
 max_iter = 1000
 eta = 1.0e10
-alpha_m = 5.0e-1 * eta
+alpha_m = 9.0e-1 * eta
 
 
 sindy_opt = ps.TrappingSR3(
@@ -551,7 +543,7 @@
 make_lissajou(r, x_train, x_test, x_train_pred, x_test_pred, "mhd")
 mean_val = np.mean(x_test_pred, axis=0)
 mean_val = np.sqrt(np.sum(mean_val**2))
-check_stability(r, Xi, sindy_opt, mean_val)
+check_local_stability(Xi, sindy_opt, mean_val)
 E_pred = np.linalg.norm(x_test - x_test_pred) / np.linalg.norm(x_test)
 print(E_pred)
 
@@ -639,7 +631,6 @@
 L, Q = burgers_galerkin(sigma, nu, U)
 rhs = lambda t, a: galerkin_model(a, L, Q)  # noqa: E731
 
-
 # Generate initial condition from unstable eigenvectors
 lamb, Phi = np.linalg.eig(L)
 idx = np.argsort(-np.real(lamb))
@@ -742,7 +733,6 @@
 galerkin5["Q"] = galerkin9["Q"][inds5]
 model5 = lambda t, a: galerkin_model(a, galerkin5["L"], galerkin5["Q"])  # noqa: E731
 
-
 # make the 3D, 5D, and 9D POD-Galerkin trajectories
 t_span = (t[0], t[-1])
 a_galerkin5 = solve_ivp(model5, t_span, a0[:5], t_eval=t, **integrator_keywords).y.T
@@ -790,14 +780,13 @@
 x_test = a
 
 # define hyperparameters
-max_iter = 5000
-eta = 1.0e2
+max_iter = 10000
+eta = 1.0
 
-# don't need a threshold if eta is sufficiently small
+# don't need a reg_weight_lam if eta is sufficiently small
 # which is good news because CVXPY is much slower
 reg_weight_lam = 0
-alpha_m = 9e-1 * eta
-
+alpha_m = 1e-1 * eta
 
 # run trapping SINDy
 sindy_opt = ps.TrappingSR3(
@@ -824,7 +813,7 @@
 Q = np.tensordot(PQ_tensor, Xi, axes=([4, 3], [0, 1]))
 Q_sum = np.max(np.abs((Q + np.transpose(Q, [1, 2, 0]) + np.transpose(Q, [2, 0, 1]))))
 print("Max deviation from the constraints = ", Q_sum)
-if check_stability(r, Xi, sindy_opt, 1):
+if check_local_stability(Xi, sindy_opt, 1):
     x_train_pred = model.simulate(x_train[0, :], t, integrator_kws=integrator_keywords)
     x_test_pred = model.simulate(a0, t, integrator_kws=integrator_keywords)
     make_progress_plots(r, sindy_opt)
@@ -834,7 +823,7 @@
     make_lissajou(r, x_train, x_test, x_train_pred, x_test_pred, "VonKarman")
     mean_val = np.mean(x_test_pred, axis=0)
     mean_val = np.sqrt(np.sum(mean_val**2))
-    check_stability(r, Xi, sindy_opt, mean_val)
+    check_local_stability(Xi, sindy_opt, mean_val)
     A_guess = sindy_opt.A_history_[-1]
     m_guess = sindy_opt.m_history_[-1]
     E_pred = np.linalg.norm(x_test - x_test_pred) / np.linalg.norm(x_test)