USACM Math Methods TTA Asia-US Seminar Series - Qianxiao Li and Oliver Schmidt

December 2, 2025

Dr. Qianxiao Li, National University of Singapore

Constructing Macroscopic Dynamics Using Deep Learning

We discuss some recent work on constructing stable and interpretable macroscopic dynamics from trajectory data using deep learning. We adopt a modelling approach: instead of generic neural networks as functional approximators, we use a model-based ansatz for the dynamics following a suitable generalisation of the classical Onsager principle for non-equilibrium systems. This allows the construction of macroscopic dynamics that are physically motivated and can be readily used for subsequent analysis and control. We discuss applications in the analysis of polymer stretching in elongational flow. Moreover, we will also discuss some algorithmic challenges associated with learning (macroscopic) dynamics for scientific applications.

Dr. Oliver Schmidt, University of California San Diego

Data-Driven Forecasting of High-Dimensional Transient and Stationary Processes via Space-Time Projection

In this talk, I present Space-Time Projection (STP), a data-driven forecasting method tailored for high-dimensional, transient datasets. STP builds on space-time Proper Orthogonal Decomposition (POD) to derive orthogonal modes capturing both past (hindcast) and future (forecast) dynamics. Forecasting involves projecting new observations onto these modes, exploiting their inherent spatiotemporal correlations. The method combines dimensionality reduction and time-delay embedding, requiring only the truncation rank as a tunable parameter. Hindcast performance reliably predicts short-term forecasting accuracy, setting a practical lower bound on expected errors. I illustrate STP’s effectiveness using two cases: simulations of anisotropic turbulence from supernova explosions and experimental velocity measurements of a turbulent, high-subsonic flow. In comparisons with standard Long Short-Term Memory (LSTM) neural networks and classical Dynamic Mode Decomposition (DMD), STP consistently delivers better or comparable forecasting accuracy.