WSINDy for PDEs (Python)

A Python 3 implementation of the Weak-form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm for partial differential equations (PDEs).

Based on the JCP paper by D. A. Messenger, D. M. Bortz 2021.
See authors' original MatLab code repository (copyright 2020, all rights reserved by original authors).

For other existing implementations, see also PySINDy documentation.

Stable as of August, 2024.

Notebooks

WSINDy.ipynb

_{A template for running WSINDy on your own data. See the 'Usage' section below for details.
^{Stable as of August, 2024.}}
WSINDy_Tutorial.ipynb

_{This notebook serves as a walkthrough and introduction to the WSINDy algorithm. As an example, it shows how the Kuramoto-Sivashinksy equation can be recovered from data (see the picture above).
^{Stable as of July, 2024.}}
WSINDy_SH23.ipynb

_{The WSINDy algorithm applied to the Swift-Hohenberg (23) equation. Simulation data were obtained using MatLab's chebfun package; see sh23_simulation.m and chebfun.org (navigate to examples > Swift Hohenberg).
^{Stable as of July, 2024.}}
JHTDB_WSINDy.ipynb

_{Uses a numerical simulation of the ideal MHD equations, sourced from the Johns Hopkins Tubulence Database, as a dataset for WSINDy.
^{Stable as of August, 2024.}}

To access a dataset stored in Google Drive (e.g., `/content/drive/My Drive/WSINDy/dataset_name.txt`) while using Google Colab, use the following commands to change directories:

# Create directory if necessary
!mkdir -p "/content/drive/My Drive/WSINDy"

from google.colab import drive
drive.mount('/content/drive')

%cd /content/drive/My Drive/WSINDy

Python Files

wsindy.py

_{Returns sparse weights for candidate basis functions. See the 'Usage' section below for details.
^{Stable as of July, 2024.}}

Libraries

This algorithm uses the following dependencies:

import torch
import numpy as np
import matplotlib.pyplot as plt
import scipy
import symengine as sp
import itertools
import re

Optional dependencies based upon GPU/parallelism features are as follows:

import torch.nn.functional as nnF # GPU
from concurrent.futures import ProcessPoolExecutor, as_completed # Parallelism

Usage

For a dataset `U` (tensor), function library `fj` (dictionary), and derivative library `alpha` (tuple), the syntax is as follows:

w = wsindy(U, fj, alpha, **params)

Example algorithm hyperparameter specification:

# Grid parameters (should match dimension of dataset)
(Lx, Ly, T) = (30*np.pi, 30*np.pi, 20)
(dx, dy, dt) = (Lx/U.shape[0], Ly/U.shape[1], T/U.shape[-1])

# Function library
fields = 1 # Number of scalar fields
powers = 4 # Maximum monomial power
poly = get_poly(powers, fields)
trig = () # (Frequency, phase) pairs
fj = {'poly': poly, 'trig': trig}

# Derivative library
lhs = ((0,0,1),) # Evolution operator D^0
dimension = 2 # Spatial dimensions
pure_derivs = 4 # Include up to fourth order
cross_derivs = 2 # Include up to second order
rhs = get_alpha(dimension, pure_derivs, cross_derivs)
alpha = lhs + rhs

params = {
    # x = spatial domain(s)
    # dx = spatial discretization(s)
    # t = temporal domain
    # dt = temporal discretization
    # aux_fields = extra library variables
    # aux_scales = scaling factors for aux fields
    #--------------------------------------------
    'x' : [(0, Lx), (0, Ly)],
    'dx' : [dx, dy],
    't' : (0, T),
    'dt' : dt,

    # m = explicit (mx,...,mt) values
    # s = explicit (sx,...,st) values
    # lambdas = MSTLS threshold search space
    # threshold = known optimal threshold
    # p = explicit (px,...,pt) values
    # tau = test function tolerance
    # tau_hat = Fourier test function tolerance
    # scales = explicit (yu,yx,yt) scaling factors
    # M = explicit scaling matrix
    #---------------------------------------------

    # verbosity = report info and create plots? (0 or 1)
    # init_guess = [x0, y0, m1, m2], for (kx,kt) curve fit
    # max_its = specify maximum number of MSTLS iterations
    # sigma_NR = noise ratio of artifical gaussian noise
    # sparsify = use 'original' or 'scaled' data in MSTLS
    #-----------------------------------------------------
    'verbosity' : 1,
    'sigma_NR' : 0.0,
    'sparsify' : 'original'}

sethminor / pywsindy-for-pdes Goto Github PK

pywsindy-for-pdes's Introduction

WSINDy for PDEs (Python)

A Python 3 implementation of the Weak-form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm for partial differential equations (PDEs).

Based on the JCP paper by D. A. Messenger, D. M. Bortz 2021. See authors' original MatLab code repository (copyright 2020, all rights reserved by original authors).

For other existing implementations, see also PySINDy documentation.

Stable as of August, 2024.

Notebooks

WSINDy.ipynb A template for running WSINDy on your own data. See the 'Usage' section below for details. Stable as of August, 2024.

WSINDy_Tutorial.ipynb This notebook serves as a walkthrough and introduction to the WSINDy algorithm. As an example, it shows how the Kuramoto-Sivashinksy equation can be recovered from data (see the picture above). Stable as of July, 2024.

WSINDy_SH23.ipynb The WSINDy algorithm applied to the Swift-Hohenberg (23) equation. Simulation data were obtained using MatLab's chebfun package; see sh23_simulation.m and chebfun.org (navigate to examples > Swift Hohenberg). Stable as of July, 2024.

JHTDB_WSINDy.ipynb Uses a numerical simulation of the ideal MHD equations, sourced from the Johns Hopkins Tubulence Database, as a dataset for WSINDy. Stable as of August, 2024.

To access a dataset stored in Google Drive (e.g., /content/drive/My Drive/WSINDy/dataset_name.txt) while using Google Colab, use the following commands to change directories:

Python Files

wsindy.py Returns sparse weights for candidate basis functions. See the 'Usage' section below for details. Stable as of July, 2024.

Libraries

This algorithm uses the following dependencies:

Optional dependencies based upon GPU/parallelism features are as follows:

Usage

For a dataset U (tensor), function library fj (dictionary), and derivative library alpha (tuple), the syntax is as follows:

Example algorithm hyperparameter specification:

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Based on the JCP paper by D. A. Messenger, D. M. Bortz 2021.
See authors' original MatLab code repository (copyright 2020, all rights reserved by original authors).

`WSINDy.ipynb`

_{A template for running WSINDy on your own data. See the 'Usage' section below for details.
^{Stable as of August, 2024.}}

`WSINDy_Tutorial.ipynb`

_{This notebook serves as a walkthrough and introduction to the WSINDy algorithm. As an example, it shows how the Kuramoto-Sivashinksy equation can be recovered from data (see the picture above).
^{Stable as of July, 2024.}}

`WSINDy_SH23.ipynb`

_{The WSINDy algorithm applied to the Swift-Hohenberg (23) equation. Simulation data were obtained using MatLab's chebfun package; see sh23_simulation.m and chebfun.org (navigate to examples > Swift Hohenberg).
^{Stable as of July, 2024.}}

`JHTDB_WSINDy.ipynb`

_{Uses a numerical simulation of the ideal MHD equations, sourced from the Johns Hopkins Tubulence Database, as a dataset for WSINDy.
^{Stable as of August, 2024.}}

To access a dataset stored in Google Drive (e.g., `/content/drive/My Drive/WSINDy/dataset_name.txt`) while using Google Colab, use the following commands to change directories:

`wsindy.py`

_{Returns sparse weights for candidate basis functions. See the 'Usage' section below for details.
^{Stable as of July, 2024.}}

For a dataset `U` (tensor), function library `fj` (dictionary), and derivative library `alpha` (tuple), the syntax is as follows: