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

2025-07-14

AI Summary

Modeling highly noisy, sparse, and partially observable nonlinear dynamical systems—governed by ordinary differential equations (ODEs)—remains challenging due to insufficient data, measurement uncertainty, and lack of full state observability. Method: We propose SiGMoID, a simulation-based generative model that integrates physics-informed neural networks (PINNs) with hypernetworks to construct a differentiable ODE solver, embedded within a Wasserstein generative adversarial network (WGAN) framework to explicitly characterize observational noise distributions. SiGMoID jointly performs parameter estimation, latent-state inference, and uncertainty quantification. Contribution/Results: Unlike conventional methods, SiGMoID requires no strong prior assumptions or dense sampling, ensuring both physical consistency and data-driven robustness. Evaluated on diverse real-world experimental systems—including biological, chemical, and engineering dynamical processes—SiGMoID accurately recovers underlying dynamics and significantly improves system identification under partial observability. It establishes a novel paradigm for scientific discovery and complex system modeling.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Mixture of Experts (MoE)
• Intelligent Robots: State Estimation

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation

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.

Problem

• Robust inference of nonlinear dynamic systems with imperfect data
• Estimating ODE parameters from noisy, sparse, or partial observations
• Inferring unobserved system components and quantifying data noise

Innovation

• Physics-informed neural networks with hyper-networks
• Wasserstein generative adversarial networks
• Simulation-based Generative Model for Imperfect Data