ODE Parameter Identification: An Integral Matching Approach
Keywords: ODEs, System Identification, Collocation
TL;DR: A highly parallel and noise robust method to identify parameters of Ordinary Differential Equations from time series data.
Abstract: We present a novel method to identify parameter of nonlinear Ordinary Differential Equations (ODEs) using time series data. Our approach fits parameters by matching a collocation-based estimate of the integral of the learned derivative to an interpolation of the trajectory, thus avoiding the computational cost of ODE solvers in adjoint methods and the sensitivity to noise of derivative estimates in gradient matching methods. By employing batching strategies based on time subintervals and state components, our method achieves linear complexity in relation to system dimensions and dataset sizes. The method is highly parallel enabling fast gradient evaluations and a faster convergence than adjoint methods. For fully observed systems, we demonstrate the method on canonical dynamical systems, where the method achieves speed-ups of three orders of magnitude over adjoint methods and an increased robustness against observational noise. We provide an extension to partially observed systems and demonstrate the method on the Lorenz63 attractor.
Primary Area: learning on time series and dynamical systems
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Submission Number: 12659
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