Learning Physics Informed Neural ODEs With Partial Measurements
This addresses a practical challenge in modeling physical systems with partial measurements, though it appears incremental as an extension of Physics Informed Neural ODEs.
The paper tackles the problem of learning dynamics governing physical systems when parts of the system's states are not measured, presenting a sequential optimization framework that learns dynamics for unmeasured processes. It demonstrates improved performance over baselines using numerical simulations and a real electro-mechanical positioning dataset.
Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when parts of the system's states are not measured, specifically when the dynamics generating the non-measured states are unknown. Inspired by state estimation theory and Physics Informed Neural ODEs, we present a sequential optimization framework in which dynamics governing unmeasured processes can be learned. We demonstrate the performance of the proposed approach leveraging numerical simulations and a real dataset extracted from an electro-mechanical positioning system. We show how the underlying equations fit into our formalism and demonstrate the improved performance of the proposed method when compared with baselines.