Events
DMS Applied and Computational Mathematics Seminar |
| Time: Mar 21, 2025 (02:00 PM) |
| Location: 328 Parker Hall |
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Details:  Speaker: Qi Tang (Georgia Tech)
Title: Structure-preserving machine learning for learning dynamical systems
Abstract: I will present our recent work on structure-preserving machine learning (ML) for dynamical systems. First, I introduce a structure-preserving neural ODE framework that accurately captures chaotic dynamics in dissipative systems. Inspired by the inertial manifold theorem, our model learns the ODE’s right-hand side by combining a linear and a nonlinear term, enabling long-term stability on the attractor for the Kuramoto-Sivashinsky equation. This framework is further enhanced with exponential integrators. Next, I discuss ML for singularly perturbed systems, leveraging the Fenichel normal form to simplify fast dynamics near slow manifolds. A fast-slow neural network is proposed that enforces the existence of a trainable, attractive invariant slow manifold as a hard constraint.
ACM seminar’s website: https://auburn.edu/cosam/mathseminar/index.htm
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