Learning from Imperfect Data: Robust Inference of Dynamic Systems Using Simulation-Based Generative Model

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) HyperPINN, and (2) W-GAN. We demonstrate that SiGMoID quantifies data noise, estimates system parameters, and infers unobserved system components. Its effectiveness is validated by analyzing examples based on realistic experiments, showcasing its broad applicability in various domains, from scientific research to engineered systems, and enabling the discovery of full system dynamics.