Ensemble SINDy and PDE-FIND

This repository contains Matlab code to reproduce the results of the paper:

Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Urban Fasel, J. Nathan Kutz, Bingni W. Brunton, Steven L. Brunton.

https://arxiv.org/pdf/2111.10992.pdf

Ensemble-SINDy

Lorenz system: Comparing different ensemble-SINDy methods

SINDy/main_runEnsembleSINDy_heatmap.m

• compare different ensemble SINDy methods in terms of model error (error of SINDy coefficients) and success rate (rate of identifying the correct non-zero and zero terms in the library) over a range of noise levels and data length
• plot heatmap

Lorenz system: UQ and ensemble forecasting

SINDy/main_runEnsembleSINDy_UQ.m

• for one particular noise level and data length, run Enesmble-SINDy and get plots of:
  • SINDy coefficient uncertainties and inclusion probabilities
  • ensemble dynamics reconstruction and forecast

Lotka Volterra: Lynx and Hare polpulation data 1900-1920 Hudson Bay Company

SINDy/main_runLotkaVolterra.m

• SINDy coefficient uncertainties and inclusion probabilities
• ensemble dynamics reconstruction

Ensemble-PDE-FIND

Here, we use the weak formulation code from Messenger and Bortz as a baseline.

PDE-FIND/main_weakEnsemblePDE.m

• run comparison (model error and success rate) between weak PDE-FIND and weak-ensemble PDE-FIND to identify five different PDEs from very noisy data

PDE-FIND/main_get_FiguresTable.m

• plot figures shown in table below

PDE-FIND/main_weakEnsemblePDE_success09.m

• compare noise levels for different PDEs where weak PDE-FIND and weak-ensemble PDE-FIND success rate drops below 0.90.

Active E-SINDy

Active_and_control/Active/main_activePlot1and2.m

• plots active E-SINDy left and center figure

Active_and_control/Active/main_activePlot3.m

• plots active E-SINDy right figure

MPC E-SINDy

Active_and_control/MPC/main_MPC.m

• compare SINDy with E-SINDy for model predictive control