Mathematical Approaches for Effective and Robust Scientific Machine Learning
Prof. Yeonjong Shin
, North Carolina State University
Abstract:
Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific and engineering problems, which has become an emerging field, Scientific Machine Learning (SciML). Many ML techniques, however, are very complex and sophisticated, commonly requiring many trial-and-error and tricks. These result in a lack of robustness and interpretability, which are critical factors for scientific applications. This talk centers around mathematical approaches for SciML, promoting trustworthiness. The first part will present recent efforts advancing the predictive power of physics-informed machine learning through robust training methods. This includes an effective training method for multivariate neural networks (NNs), namely, Active Neuron Least Squares (ANLS) and a two-step training method for deep operator networks. The second part is about how to embed the first principles of physics into neural networks. Prof. Yeonjong will present a general framework for designing NNs that obey the first and second laws of thermodynamics. The framework not only provides flexible ways of leveraging available physics information but also results in expressive NN architectures. Yeonjong will also present an intriguing phenomenon of this framework when it is applied in the context of latent space dynamics identification where an intriguing correlation is observed between an entropy related quantity in the latent space and the behaviors of the full-state solution.
Speaker’s Bio:
Prof. Yeonjong Shin is an Assistant Professor of Mathematics in Department of Mathematics at North Carolina State University. He completed his Ph.D. in Mathematics from The Ohio State University. Before joining NC State, he was an Assistant Professor in the Department of Mathematical Sciences at Korea Advanced Institute of Science & Technology. Before that, he was a Prager Assistant Professor in the Division of Applied Mathematics at Brown University. He is a recipient of the Sangsan Young Mathematician Award from KMS and a founding member of the Center for Mathematical Machine Learning and its Applications (CM2LA), which was established as a Science Research Center (SRC) supported by the Korean Ministry of Science and ICT in 2023.
