RECURSIVE NEURAL ORDINARY DIFFERENTIAL EQUATIONS FOR PARTIALLY OBSERVED SYSTEM

Paul Ghanem, ahmet demirkaya, Zachary Danziger, Alireza Ramezani, Tales Imbiriba, Deniz Erdogmus

Keywords: NODE, Second Order Newton Method, Learning from partial observations

Abstract: Identifying spatiotemporal dynamics is a difficult task, especially in scenarios where latent states are partially observed and/or represent physical quantities. In this context, first-principle ordinary differential equation (ODE) systems are often designed to describe the system's dynamics. In this work, we address the problem of learning parts of the spatiotemporal dynamics with neural networks when only partial information about the system's state is available. Taking inspiration from recursive state estimation and Neural ODEs, we outline a general framework in which complex dynamics generated by differential equations with distinguishable states can be learned in a principled way. We demonstrate the performance of the proposed approach leveraging both 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 standard baselines.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 6444