Neural Time Integrator with Stage Correction

Yifan Zhang, Hong Zhang

Keywords: dynamical system, hybrid ML, error correction, time integrator

Abstract:

Numerical simulation of dynamical systems requires time integration solvers that
balance accuracy and computational efficiency. Recent work indicates that neural
integrators, a hybrid of classical numerical integration and machine learning, can
achieve significant performance gains. Building upon this idea, we propose a new
type of neural integrator that introduces stage corrections inspired by the fact that
traditional time integration schemes such as Runge-Kutta exhibit different error
characteristics at each stage. Specifically, our method corrects numerical errors
immediately after each stage evaluation by using a neural network, mitigating
error propagation across stages. This enables the use of larger time steps while
preserving stability and accuracy. We demonstrate that our approach is at least
one order of magnitude more accurate than existing hybrid methods for complex
nonlinear dynamical systems when integrated with the same step size.

Primary Area: learning on time series and dynamical systems

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Submission Number: 12524