Artifacts of Numerical Integration in Learning Dynamical Systems
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Abstract (arXiv)
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the optimization procedure, prediction data from generic dynamics requires a numerical integrator to assess the mismatch with the observed data. This paper reveals potentially serious effects of a chosen numerical scheme on the learning outcome. Specifically, the analysis demonstrates that a damped oscillatory system may be incorrectly identified as having "anti-damping" and exhibiting a reversed oscillation direction, even though it adequately fits the given data points. This paper shows that the stability region of the selected integrator will distort the nature of the learned dynamics. Crucially, reducing the step size or raising the order of an explicit integrator does not, in general, remedy this artifact, because higher-order explicit methods have stability regions that extend further into the right half complex plane. Furthermore, it is shown that the implicit midpoint method can preserve either conservative or dissipative properties from discrete data, offering a principled integrator choice even when the only prior knowledge is that the system is autonomous.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 15 of its 40 references that are in the map. First posted on arXiv 19 Jul 2025.
Builds on
15 of 40 references.
References · 15
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3 more
- 2020Revealing hidden dynamics from time-series data by ODENetcited by 17
- 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
- 2023Explainable Deep Learning for Tumor Dynamic Modeling and Overall Survival Prediction using Neural-ODEcited by 5
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Citing papers per year: 2025: 1.
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