Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model

TL;DR

This paper introduces SiGMoID, a robust simulation-based generative model that accurately infers parameters and unobserved components of nonlinear dynamic systems from noisy, sparse, or partial data using neural networks and adversarial training.

Contribution

It presents a novel integration of physics-informed neural networks and Wasserstein GANs for robust inference of ODE-based dynamic systems from imperfect data.

Findings

Effective noise quantification and parameter estimation demonstrated

Accurate inference of unobserved system components achieved

Validated across diverse experimental scenarios

Abstract

System inference for nonlinear dynamic models, represented by ordinary differential equations (ODEs), remains a significant challenge in many fields, particularly when the data are noisy, sparse, or partially observable. In this paper, we propose a Simulation-based Generative Model for Imperfect Data (SiGMoID) that enables precise and robust inference for dynamic systems. The proposed approach integrates two key methods: (1) physics-informed neural networks with hyper-networks that constructs an ODE solver, and (2) Wasserstein generative adversarial networks that estimates ODE parameters by effectively capturing noisy data distributions. We demonstrate that SiGMoID quantifies data noise, estimates system parameters, and infers unobserved system components. Its effectiveness is validated validated through realistic experimental examples, showcasing its broad applicability in various domains, from scientific research to engineered systems, and enabling the discovery of full system dynamics.