用贝叶斯滤波从噪声数据中学习物理系统动力学
A Bayesian Filtering Approach for Learning Lagrangian Dynamics from Noisy Measurements
- 基于拉格朗日力学建模，神经网络拟合能量项
- 在噪声观测下实现状态与参数联合估计，精度优于传统LNN
- 适合含噪声、不完整数据的物理系统建模任务
本文提出一种基于贝叶斯滤波的方法，从部分、噪声测量中学习物理系统的动力学。采用拉格朗日力学形式建模，通过神经网络参数化动能和势能，将拉格朗日中的未知外力建模为白高斯噪声。由此导出连续时间随机状态空间模型（SSM），描述系统动力学。利用基于高斯近似的贝叶斯滤波，通过最大似然法联合学习神经网络参数与系统状态。在单摆和杜芬振子实例上验证了该方法的有效性，并与传统拉格朗日神经网络（LNNs）及已知模型下近似贝叶斯滤波进行对比。
原文摘要 · Abstract (English)
This paper proposes a Bayesian filtering-based approach for learning the dynamics of a physical system from partial, noisy measurements. We model the system dynamics using a Lagrangian mechanics formulation. As in Lagrangian neural networks (LNNs), we parameterize the kinetic and potential energies with neural networks. The unknown external forces in the Lagrangian formulation are modeled as white Gaussian noise. The corresponding Euler--Lagrange equations then yield a continuous-time stochastic state-space model (SSM) that describes the system dynamics. The neural network parameters and system states are then jointly learned via a maximum-likelihood method using Gaussian-approximation-based Bayesian filters. The effectiveness of the proposed method is demonstrated on pendulum and Duffing oscillator examples, and its performance is compared with conventional LNNs and with approximate Bayesian filters using known system models.
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