【114/2/20】15:20-16:10 Colloquium：Dr. Lu, Bing-Ze (Department of Matihmatics, NCKU)
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| Date | 2025-2-20 15:20-16:10 |
| Place | Mathtmatics Building 1F Classroom 3173 |
| Speaker | Dr. Lu, Bing-Ze (Department of Matihmatics, NCKU) |
| Title | Numerical Effects on Dynamic Learning Problems Using Neural ODE Architecture |
| Abstract | In this presentation, I will introduce Neural ODE, a framework that leverages conventional numerical methods as part of its loss function design. One key application of Neural ODE is identifying the underlying dynamical system from snapshots of observable data. Specifically, for an autonomous differential system dx/dt = f(x), ODEnet employs a trainable neural network to approximate the unknown function f(x), minimizing the discrepancy between numerically predicted system states and the observed data at a fixed sampling interval. My focus will be on the special case of learning linear dynamical systems, whether they are conservative or dissipative. The first part of my talk examines structural concerns—such as rotational components and long-term trends—when using one-step or multi-step schemes. Despite the possibility of achieving a near-zero loss, the resulting learned system may not accurately mirror the true dynamics. I will present our observations and conclude this section by proposing guidelines for choosing numerical integrators that preserve the intrinsic structure of the unknown system. In the second part, I will discuss how noisy data influences learning outcomes. By comparing results derived from noisy observations with those obtained under noise-free conditions, I will illustrate how varying noise levels can distort the inferred dynamical system. |
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