Yeonjong Shin, Brown University

Dongbin Xiu, The Ohio State University

Machine learning (ML) has achi eved unprecedented empirical success in diverse applications. It now has be en applied to solve scientific problems, which has become a new sub-field u nder the name of Scientific Machine Learning (SciML). Many ML techniques, h owever, are very sophisticated, requiring trial-and-error and numerous tric ks. These result in a lack of robustness and reliability, which are critica l factors for scientific applications.

< br />This talk centers around mathematical approaches for SciML to provide robustness and reliability. The first part will focus on the data-driven di scovery of dynamical systems. I will present a general framework of designi ng neural networks (NNs) for the GENERIC formalism, resulting in the GENERI C formalism informed NNs (GFINNs). The framework provides flexible ways of leveraging available physics information into NNs. Also, the universal appr oximation theorem for GFINNs is established. The second part will be on the Active Neuron Least Squares (ANLS), an efficient training algorithm for NN s. ANLS is designed from the insight gained from the analysis of gradient d escent training of NNs, particularly, the analysis of Plateau Phenomenon. T he performance of ANLS will be demonstrated and compared with existing popu lar methods in various learning tasks ranging from function approximation t o solving PDEs.