Gaussian process learning with flow map refinement for parameter estimation in dynamical systems

2026-08-23

AI Summary

本文针对动力系统参数估计问题，提出了一种结合高斯过程学习与流映射精炼的两阶段方法，以提高在稀疏和噪声观测下的参数估计精度。

Abstract

Parameter estimation is a central task in data-driven learning of dynamical systems. It aims to recover the underlying physical parameters from observed time-series data, thereby providing interpretable insights into the physical mechanisms governing the system. Gradient/derivative matching methods based on Gaussian process provide an efficient way to perform parameter estimation. Those methods avoid repeated numerical integration and enforce local derivative consistency. However, such local matching may result in global inconsistency with the governing flow map, particularly under scarce and noisy observations. To address this limitation, we propose a framework based on Gaussian process learning with flow map refinement (GPL-FMR), a two-stage parameter estimation framework. The first stage is based on Gaussian process learning algorithm and the posterior obtained from which is transferred as an informative prior to the second stage based on flow-map refinement. The second stage further improves the parameter estimation via optimisation based on global dynamical constraints. We demonstrate and analyse its performance on multiple numerical examples, including the Van der Pol oscillator, the Lotka-Volterra model, and the Lorenz-63 system. The results show that the proposed framework consistently improves parameter estimation accuracy, particularly under scarce and noisy observations.

Problem

• Parameter estimation
• Gaussian process
• Dynamical systems
• Flow map refinement

Innovation

• Gaussian process learning
• flow map refinement
• parameter estimation
• dynamical systems
• global dynamical constraints