Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processes

TL;DR

This paper introduces a Gaussian Process framework that ensures physical consistency and energy conservation in learning Lagrangian systems, using novel kernels and requiring minimal measurements.

Contribution

It presents a new GP formulation with energy-aware kernels and Cholesky-based positive definiteness preservation for modeling Lagrangian dynamics.

Findings

Successfully preserves physical properties in simulations

Handles noisy measurements in system identification

Demonstrates effectiveness in numerical experiments

Abstract

This paper proposes a physically consistent Gaussian Process (GP) enabling the identification of uncertain Lagrangian systems. The function space is tailored according to the energy components of the Lagrangian and the differential equation structure, analytically guaranteeing physical and mathematical properties such as energy conservation and quadratic form. The novel formulation of Cholesky decomposed matrix kernels allow the probabilistic preservation of positive definiteness. Only differential input-to-output measurements of the function map are required while Gaussian noise is permitted in torques, velocities, and accelerations. We demonstrate the effectiveness of the approach in numerical simulation.