Theoretical and Applied Complex Systems Lab

The Theoretical and Applied Complex Systems (TACS) Lab is hosted in the department of applied mathematics at the University of California, Santa Cruz, led by Ashesh Chattopadhyay. We work on several aspects of complex systems including deep learning theory, scientific machine learning (SciML), and their applications in nonlinear dynamical systems focusing on atmospheric, oceanic, and engineering turbulence. Our work is generously funded by the National Science Foundation, Defense Advanced Research Projects Agency, National Research Foundation in Korea, and we work closely with industries in Silicon Valley. We are interested in several interesting questions at the intersection of physics and deep learning. Some of the recent ones have been in understanding:

• Inherent limit of predictability with deep learning models on multi-scale flows

• Data assimilation with SciML

• Understanding biases and failure modes in SciML

• Random matrix theory and their implications in understanding SciML

• High-performance computing, reduced-order modeling,... for large-scale systems and hopefully with data-driven approaches.