modify weighting example for the state weighted formulation

notebooks/weighted-cost-func.ipynb

@@ -39,7 +39,7 @@
     "fhn = fhn.FitzHughNagumo()\n",
     "training_data = fhn.solve_ivps(\n",
     "    initial_states=np.random.uniform(low=-2.0, high=2.0, size=(10, 2)),\n",
-    "    tspan=[0.0, 10.0],\n",
+    "    tspan=[0.0, 6.0],\n",
     "    sampling_period=0.1\n",
     ")"
    ]
@@ -66,15 +66,27 @@
     "    \n",
     "\n",
     "    # weight good trajectory by its 1 norm\n",
-    "    w = np.sum(traj.abs().states, axis=1)\n",
+    "    #w = np.sum(traj.abs().states, axis=1)\n",
+    "    w = np.ones(traj.states.shape)\n",
     "    weights.append(w)\n",
     "\n",
     "    # weight garbage trajectory to zero\n",
-    "    w = np.zeros(len(traj.states))\n",
+    "    #w = np.zeros(len(traj.states))\n",
+    "    w = np.zeros(traj.states.shape)\n",
     "    weights.append(w)\n",
     "\n",
     "# you can also use a dict to name the trajectories if using TrajectoriesData (numpy arrays are named by their index number)\n",
-    "weights = {idx: w for idx, w in enumerate(weights)}"
+    "#weights = {idx: w for idx, w in enumerate(weights)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "280b4bb3-4f7d-4a94-a983-663c6255bc83",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "weights[1].shape"
    ]
   },
   {
@@ -93,7 +105,7 @@
     "    learning_weights=weights, # weight the eDMD algorithm objectives\n",
     "    scoring_weights=weights, # pass weights as required for cost_func=\"weighted\"\n",
     "    opt=\"grid\",             # grid search to find best hyperparameters\n",
-    "    n_obs=200,              # maximum number of observables to try\n",
+    "    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=5,             # k-folds validation for tuning, helps stabilize the scoring\n",
@@ -117,7 +129,7 @@
     "    learning_weights=None,  # don't use eDMD weighting\n",
     "    scoring_weights=weights, # pass weights as required for cost_func=\"weighted\"\n",
     "    opt=\"grid\",             # grid search to find best hyperparameters\n",
-    "    n_obs=200,              # maximum number of observables to try\n",
+    "    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=5,             # k-folds validation for tuning, helps stabilize the scoring\n",
@@ -178,9 +190,10 @@
     "plt.figure(figsize=(10, 6))\n",
     "\n",
     "# plot the results\n",
+    "plt.plot(*true_trajectory.states.T, linewidth=2, label='Ground Truth')\n",
     "plt.plot(*trajectory.states.T, label='Weighted Trajectory Prediction')\n",
     "plt.plot(*trajectory_uw.states.T, label='Trajectory Prediction')\n",
-    "plt.plot(*true_trajectory.states.T, label='Ground Truth')\n",
+    "\n",
     "\n",
     "plt.xlabel(\"$x_1$\")\n",
     "plt.ylabel(\"$x_2$\")\n",