Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processes
This work addresses the challenge of learning conservative Lagrangian systems with physical consistency, which is incremental as it builds on existing GP methods by incorporating novel kernel formulations.
The paper tackles the problem of identifying uncertain Lagrangian systems by proposing a physically consistent Gaussian Process that analytically guarantees properties like energy conservation and quadratic form, demonstrating its effectiveness in numerical simulation.
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.