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USACM UQ Virtual Seminar
Thursday, October 07, 2021, 2:00 PM - 3:00 PM CDT
Category: Events

USACM UQ Virtual Seminar

Mathematical approaches for robustness and reliability in scientific machine learning


Yeonjong Shin, Brown University


Dongbin Xiu, The Ohio State University



Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific problems, which has become a new sub-field under the name of Scientific Machine Learning (SciML). Many ML techniques, however, are very sophisticated, requiring trial-and-error and numerous tricks. These result in a lack of robustness and reliability, which are critical factors for scientific applications.
This talk centers around mathematical approaches for SciML to provide robustness and reliability. The first part will focus on the data-driven discovery of dynamical systems. I will present a general framework of designing neural networks (NNs) for the GENERIC formalism, resulting in the GENERIC formalism informed NNs (GFINNs). The framework provides flexible ways of leveraging available physics information into NNs. Also, the universal approximation theorem for GFINNs is established. The second part will be on the Active Neuron Least Squares (ANLS), an efficient training algorithm for NNs. ANLS is designed from the insight gained from the analysis of gradient descent training of NNs, particularly, the analysis of Plateau Phenomenon. The performance of ANLS will be demonstrated and compared with existing popular methods in various learning tasks ranging from function approximation to solving PDEs.