Title: Interpretable data-driven model discovery with global optimization: dynamical systems, reduced-order models, and operator learning.
Abstract: Lack of interpretability and generalization are among the key challenges in applying deep learning to physics-based systems. In this talk, we leverage some of the building blocks of neural networks, such as ADAM optimization and the PyTorch language, to discover dynamical systems models, interpretable nonlinear reduced-order models (ROMs) for spatiotemporal fluid flow, and interpretable latent spaces with operator learning. I first introduce ADAM-SINDy, a sparse identification framework that uses ADAM optimization for data-driven discovery of nonlinear dynamical systems. Unlike traditional sparse identification of nonlinear dynamics (SINDy), which often depends on prior knowledge of nonlinear parameters, ADAM-SINDy efficiently and accurately identifies them through a flexible global optimization scheme. I discuss how the sparse regression optimization task could be modified to achieve machine-precision accuracy. Building on this foundation, we introduce Decomposed Sparse Modal Optimization (DESMO) as an interpretable nonlinear ROM for spatiotemporal fluid flow data. Our method enhances proper orthogonal decomposition (POD) with nonlinear, data-driven corrections identified through ADAM optimization. We utilize unsteady fluid flow data to show that our approach can reduce the number of modes required for representing unsteady flows while maintaining interpretability and accuracy. Finally, I will present our recent work demonstrating how similar ideas could be utilized in the context of operator learning and differentiable and interpretable latent space model discovery.
Bio: Dr. Amirhossein (Amir) Arzani is a tenured Associate Professor at the University of Utah (Scientific Computing and Imaging Institute and Mechanical Engineering Department). He obtained his BSc, MSc, and PhD degrees in mechanical engineering from Isfahan University of Technology, Illinois Institute of Technology, and UC Berkeley, respectively. He is the director of the Computational Biomechanics Group at Utah and a recipient of the NSF CAREER and NIH Trailblazer awards. He has received the prestigious Presidential Early Career Award for Scientists and Engineers (PECASE) from President Biden. He is also the 2026 recipient of the ASME Y. C. Fung Early Career Medal. His research develops various computational mathematics and scientific machine learning techniques for different applications, with a particular focus on biomedical flows and dynamical systems.