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

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 hypernetworks 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.