10:00 - 11:00, November 21, 2025 (Friday) Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Qualitative Analysis with Neural ODEs: Numerical Stability, Artifacts, and Generalization Bing-Ze Lu (National Chung Cheng University)
Abstract
Learning dynamical systems directly from data has surged across disciplines, but trajectory fitting alone rarely guarantees that the learned model preserves the system's qualitative behavior. This talk first reviews data-driven approaches SINDy for inferring governing equations from trajectories and Neural ODEs (Chen et al., 2018), which parameterize the vector field and embed numerical integration into training. Because closed-form solutions at sampling times are unavailable, the numerical solver becomes part of the model, and its properties shape what we ultimately “learn.”
We demonstrate these issues on a damped pendulum case study by training with different integrators and step sizes. Even when the training error is within a small tolerance, long-horizon rollouts or finer-step interpolations can exhibit amplitude decay and phase drift that depend on the chosen scheme.
This talk addresses two questions:
Q1. How does the choice of numerical integrator—such as step size or order—affect the learned dynamics?
Q2. How well do these learned models generalize to initial conditions outside the training distribution?
We connect the answers to the stability regimes of the underlying schemes and present diagnostics (phase-portrait checks, invariant-set tests, local linearization probes) to audit models beyond fit. The takeaway is a recipe for structure-preserving learning with Neural ODEs: choosing solvers and step sizes that support reliable extrapolation and robust qualitative behavior.
