Neural DDEs with Learnable Delays for Partially Observed Dynamical Systems
Abstract: Many successful methods to learn dynamical systems from data have recently been introduced. Such methods often rely on the availability of the system's full state. However, this underlying hypothesis is rather restrictive as it is typically not confirmed in practice, leaving us with partially observed systems. Utilizing the Mori-Zwanzig (MZ) formalism from statistical physics, we demonstrate that Constant Lag Neural Delay Differential Equations (NDDEs) naturally serve as suitable models for partially observed states. In empirical evaluation, we show that such models outperform existing methods on both synthetic and experimental data. Code is available at \href{https://anonymous.4open.science/r/DynamicalSysDDE-F86C/}{https://anonymous.4open.science/r/DynamicalSysDDE-F86C/}
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Adam_Arany1
Submission Number: 3395
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