swMATH ID: 
43337

Software Authors: 
Messenger, Daniel A.; Bortz, David M.

Description: 
Learning meanfield equations from particle data using WSINDy. We develop a weakform sparse identification method for interacting particle systems (IPS) with the primary goals of reducing computational complexity for large particle number (N) and offering robustness to either intrinsic or extrinsic noise. In particular, we use concepts from meanfield theory of IPS in combination with the weakform sparse identification of nonlinear dynamics algorithm (WSINDy) to provide a fast and reliable system identification scheme for recovering the governing stochastic differential equations for an IPS when the number of particles per experiment (N) is on the order of several thousands and the number of experiments (M) is less than 100. This is in contrast to existing work showing that system identification for (N) less than 100 and (M) on the order of several thousand is feasible using strongform methods. We prove that under some standard regularity assumptions the scheme converges with rate (mathcal{O}(N^{1/2})) in the ordinary least squares setting and we demonstrate the convergence rate numerically on several systems in one and two spatial dimensions. Our examples include a canonical problem from homogenization theory (as a first step towards learning coarsegrained models), the dynamics of an attractiverepulsive swarm, and the IPS description of the parabolicelliptic KellerSegel model for chemotaxis. Code is available at url{https://github.com/MathBioCU/WSINDy_IPS}. 
Homepage: 
https://arxiv.org/abs/2110.07756

Source Code: 
https://github.com/MathBioCU/WSINDy_IPS

Dependencies: 
Matlab 
Keywords: 
datadriven modeling;
interacting particle systems;
weak form;
meanfield limit;
sparse regression

Related Software: 
GitHub

Cited in: 
1 Publication
