用生成模型从噪声、稀疏数据中精准推断动态系统演化规律
Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model
- 结合物理信息神经网络与变分生成对抗网络构建求解器
- 可量化噪声水平，准确估计参数并补全缺失状态变量
- 适合科研与工程中数据不完整时的系统建模需求
非线性动态系统通常由常微分方程（ODE）描述，但在实际应用中，数据常存在噪声大、采样稀疏或观测不全的问题。本文提出一种面向不完美数据的仿真生成模型（SiGMoID），通过融合物理信息神经网络与超网络构造的ODE求解器，以及利用Wasserstein生成对抗网络捕捉噪声数据分布的参数估计方法，实现对系统参数的精准估计和未观测状态的推断。实验验证表明，该方法能有效量化数据噪声，还原完整系统动态，适用于科学发现与工程系统建模等多个领域。
原文摘要 · Abstract (English)
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.
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