Merge pull request #144 from dynamicslab/pde_optimization

PDE and weak form in arbitrary dimensions now functional!
dynamicslab · Jan 6, 2022 · 6d908c3 · 6d908c3
2 parents dfcdb37 + fd4befd
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diff --git a/README.rst b/README.rst
@@ -215,7 +215,7 @@ If you use PySINDy in your work, please cite it using the following two referenc
 
 Brian M. de Silva, Kathleen Champion, Markus Quade, Jean-Christophe Loiseau, J. Nathan Kutz, and Steven L. Brunton., (2020). *PySINDy: A Python package for the sparse identification of nonlinear dynamical systems from data.* Journal of Open Source Software, 5(49), 2104, https://doi.org/10.21105/joss.02104
 
-Alan A. Kaptanoglu, Brian M. de Silva, Urban Fasel, Kadierdan Kaheman, Jared L. Callaham,   Charles  B.  Delahunt,   Kathleen  Champion,   Jean-Christophe  Loiseau,J. Nathan Kutz, and Steven L. Brunton. *PySINDy:  A comprehensive Python packagefor robust sparse system identification.* arXiv preprint arXiv:2111.08481, 2021.
+Alan A. Kaptanoglu, Brian M. de Silva, Urban Fasel, Kadierdan Kaheman, Jared L. Callaham,   Charles  B.  Delahunt,   Zachary G. Nicolaou,   Kathleen  Champion,   Jean-Christophe  Loiseau,J. Nathan Kutz, and Steven L. Brunton. *PySINDy:  A comprehensive Python packagefor robust sparse system identification.* arXiv preprint arXiv:2111.08481, 2021.
 
 Bibtex:
 
@@ -240,7 +240,7 @@ Bibtex:
 
       @article{kaptanoglu2021pysindy,
       title={PySINDy: A comprehensive Python package for robust sparse system identification},
-      author={Alan A. Kaptanoglu and Brian M. de Silva and Urban Fasel and Kadierdan Kaheman and Jared L. Callaham and Charles B. Delahunt and Kathleen Champion and Jean-Christophe Loiseau and J. Nathan Kutz and Steven L. Brunton},
+      author={Alan A. Kaptanoglu and Brian M. de Silva and Urban Fasel and Kadierdan Kaheman and Jared L. Callaham and Charles B. Delahunt and Zachary G. Nicolaou and Kathleen Champion and Jean-Christophe Loiseau and J. Nathan Kutz and Steven L. Brunton},
       year={2021},
 	  Journal = {arXiv preprint arXiv:2111.08481},
       }
@@ -254,8 +254,8 @@ References
    `[arXiv] <https://arxiv.org/abs/2004.08424>`__
 
 -  Kaptanoglu, Alan A., Brian M. de Silva, Urban Fasel, Kadierdan Kaheman,
-   Jared L. Callaham, Charles B. Delahunt, Kathleen Champion, Jean-Christophe Loiseau,
-   J. Nathan Kutz, and Steven L. Brunton.
+   Jared L. Callaham, Charles B. Delahunt, Zachary G. Nicolaou, Kathleen Champion, 
+   Jean-Christophe Loiseau, J. Nathan Kutz, and Steven L. Brunton.
    *PySINDy: A comprehensive Python package for robust sparse system identification.*
    arXiv preprint arXiv:2111.08481 (2021).
    `[arXiv] <https://arxiv.org/abs/2111.08481>`__

diff --git a/docs/JOSS2/paper.md b/docs/JOSS2/paper.md
@@ -20,6 +20,8 @@ authors:
     affiliation: 3
   - name: Charles B. Delahunt
     affiliation: 2
+  - name: Zachary G. Nicolaou
+    affiliation: 2
   - name: Kathleen Champion
     affiliation: 2
   - name: Jean-Christophe Loiseau
@@ -81,7 +83,7 @@ Recent variants of the SINDy method are available that address systems with cont
 In order to incorporate these new developments and accommodate the wide variety of possible dynamical systems, we have extended `PySINDy` to a more general setting and added significant new functionality. Our code\footnote{\url{https://github.com/dynamicslab/pysindy}} is thoroughly documented, contains extensive examples, and integrates a wide range of functionality, some of which may be found in a number of other local SINDy implementations\footnote{\url{https://github.com/snagcliffs/PDE-FIND}, \url{https://github.com/eurika-kaiser/SINDY-MPC},\\ \url{https://github.com/dynamicslab/SINDy-PI}, \url{https://github.com/SchatzLabGT/SymbolicRegression},\\ \url{https://github.com/dynamicslab/databook_python}, \url{https://github.com/sheadan/SINDy-BVP},\\ \url{https://github.com/sethhirsh/BayesianSindy}, \url{https://github.com/racdale/sindyr},\\ \url{https://github.com/SciML/DataDrivenDiffEq.jl}, \url{https://github.com/MathBioCU/WSINDy_PDE},\\ \url{https://github.com/pakreinbold/PDE_Discovery_Weak_Formulation}, \url{https://github.com/ZIB-IOL/CINDy}}. In contrast to some of these existing implementations, `PySINDy` is completely open-source, professionally-maintained (for instance, providing unit tests and adhering to PEP8 stylistic standards), and minimally dependent on non-standard Python packages.
 
 # New features
-Given spatiotemporal data $\mathbf{Q}(\mathbf{x}, t) \in \mathbb{R}^{m\times n}$, and optional control inputs $\mathbf{u} \in \mathbb{R}^{m \times r}$ (note $m$ has been redefined here to be the product of the number of spatial measurements and the number of time samples), `PySINDy` can now approximate algebraic systems of PDEs (and corresponding weak forms) in up to 3 spatial dimensions. Assuming the system is described by a function $\mathbf{g}$, we have
+Given spatiotemporal data $\mathbf{Q}(\mathbf{x}, t) \in \mathbb{R}^{m\times n}$, and optional control inputs $\mathbf{u} \in \mathbb{R}^{m \times r}$ (note $m$ has been redefined here to be the product of the number of spatial measurements and the number of time samples), `PySINDy` can now approximate algebraic systems of PDEs (and corresponding weak forms) in an arbitrary number of spatial dimensions. Assuming the system is described by a function $\mathbf{g}$, we have
 \begin{equation}\label{eq:pysindy_eq}
     \mathbf{g}(\mathbf{q},\mathbf q_t, \mathbf q_x, \mathbf q_y, \mathbf q_{xx}, ..., \mathbf{u}) = 0.
 \end{equation}

diff --git a/examples/10_PDEFIND_examples.ipynb b/examples/10_PDEFIND_examples.ipynb
diff --git a/examples/11_SSR_FROLS_examples.ipynb b/examples/11_SSR_FROLS_examples.ipynb
diff --git a/examples/12_weakform_SINDy_examples.ipynb b/examples/12_weakform_SINDy_examples.ipynb
diff --git a/examples/13_ensembling.ipynb b/examples/13_ensembling.ipynb
diff --git a/examples/14_cavity_flow.ipynb b/examples/14_cavity_flow.ipynb
diff --git a/examples/15_pysindy_lectures.ipynb b/examples/15_pysindy_lectures.ipynb
diff --git a/examples/1_feature_overview.ipynb b/examples/1_feature_overview.ipynb
diff --git a/examples/2_introduction_to_sindy.ipynb b/examples/2_introduction_to_sindy.ipynb
diff --git a/examples/3_original_paper.ipynb b/examples/3_original_paper.ipynb
diff --git a/examples/4_scikit_learn_compatibility.ipynb b/examples/4_scikit_learn_compatibility.ipynb
@@ -74,13 +74,15 @@
     "t_train = np.arange(0, 10, dt)\n",
     "t_train_span = (t_train[0], t_train[-1])\n",
     "x0_train = [-8, 8, 27]\n",
-    "x_train = solve_ivp(lorenz, t_train_span, x0_train, t_eval=t_train, **integrator_keywords).y.T\n",
+    "x_train = solve_ivp(lorenz, t_train_span, x0_train, \n",
+    "                    t_eval=t_train, **integrator_keywords).y.T\n",
     "\n",
     "# Evolve the Lorenz equations in time using a different initial condition\n",
     "t_test = np.arange(0, 15, dt)\n",
     "t_test_span = (t_test[0], t_test[-1])\n",
     "x0_test = np.array([8, 7, 15])\n",
-    "x_test = solve_ivp(lorenz, t_test_span, x0_test, t_eval=t_test, **integrator_keywords).y.T"
+    "x_test = solve_ivp(lorenz, t_test_span, x0_test, \n",
+    "                   t_eval=t_test, **integrator_keywords).y.T"
    ]
   },
   {
@@ -117,10 +119,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Best parameters: {'differentiation_method__order': 2, 'feature_library': PolynomialLibrary(), 'optimizer__alpha': 0.01, 'optimizer__threshold': 0.01}\n",
-      "(x0)' = -9.999 x0 + 9.999 x1\n",
-      "(x1)' = 27.992 x0 + -0.999 x1 + -1.000 x0 x2\n",
-      "(x2)' = -2.666 x2 + 1.000 x0 x1\n"
+      "Best parameters: {'differentiation_method__order': 1, 'feature_library': PolynomialLibrary(), 'optimizer__alpha': 0.01, 'optimizer__threshold': 0.01}\n",
+      "(x0)' = -10.021 x0 + 9.993 x1\n",
+      "(x1)' = 0.227 1 + 27.601 x0 + -0.611 x1 + -0.983 x0 x2 + -0.020 x1 x2\n",
+      "(x2)' = 0.590 1 + 0.045 x0 + -0.018 x1 + -2.691 x2 + 0.965 x0 x1 + 0.026 x1^2\n"
      ]
     }
    ],
@@ -344,7 +346,9 @@
    "source": [
     "from sklearn.linear_model import ElasticNet\n",
     "\n",
-    "model = ps.SINDy(optimizer=ElasticNet(l1_ratio=0.9, fit_intercept=False), t_default=dt)\n",
+    "model = ps.SINDy(optimizer=ElasticNet(l1_ratio=0.9, \n",
+    "                                      fit_intercept=False), \n",
+    "                 t_default=dt)\n",
     "model.fit(x_train)\n",
     "model.print()"
    ]
@@ -373,7 +377,8 @@
     "from sklearn.linear_model import OrthogonalMatchingPursuit\n",
     "\n",
     "model = ps.SINDy(\n",
-    "    optimizer=OrthogonalMatchingPursuit(n_nonzero_coefs=8, fit_intercept=False),\n",
+    "    optimizer=OrthogonalMatchingPursuit(n_nonzero_coefs=8, \n",
+    "                                        fit_intercept=False),\n",
     "    t_default=dt\n",
     ")\n",
     "model.fit(x_train)\n",

diff --git a/examples/5_differentiation.ipynb b/examples/5_differentiation.ipynb
diff --git a/examples/6_deeptime_compatibility.ipynb b/examples/6_deeptime_compatibility.ipynb
diff --git a/examples/7_plasma_examples.ipynb b/examples/7_plasma_examples.ipynb
diff --git a/examples/8_trapping_sindy_paper_examples.ipynb b/examples/8_trapping_sindy_paper_examples.ipynb
diff --git a/examples/9_sindypi_with_sympy.ipynb b/examples/9_sindypi_with_sympy.ipynb
diff --git a/pysindy/__init__.py b/pysindy/__init__.py
@@ -14,6 +14,7 @@
 from .pysindy import SINDy
 from .differentiation import BaseDifferentiation
 from .differentiation import FiniteDifference
+from .differentiation import SpectralDerivative
 from .differentiation import SINDyDerivative
 from .differentiation import SmoothedFiniteDifference
 from .feature_library import ConcatLibrary
@@ -24,6 +25,7 @@
 from .feature_library import IdentityLibrary
 from .feature_library import PolynomialLibrary
 from .feature_library import PDELibrary
+from .feature_library import WeakPDELibrary
 from .feature_library import SINDyPILibrary
 from .optimizers import BaseOptimizer
 from .optimizers import ConstrainedSR3

diff --git a/pysindy/differentiation/__init__.py b/pysindy/differentiation/__init__.py
@@ -2,11 +2,13 @@
 from .finite_difference import FiniteDifference
 from .sindy_derivative import SINDyDerivative
 from .smoothed_finite_difference import SmoothedFiniteDifference
+from .spectral_derivative import SpectralDerivative
 
 
 __all__ = [
     "BaseDifferentiation",
     "FiniteDifference",
     "SINDyDerivative",
     "SmoothedFiniteDifference",
+    "SpectralDerivative",
 ]