北京雁栖湖应用数学研究院

熊繁升 , 杨武岳 , 雍稳安 , 朱毅

Ameya D. Jagtap

2022年10月13日 09:00 至 10:00

1129B

Zoom 537 192 5549 (BIMSA)

Traditional approaches for scientific computation have undergone remarkable progress but they still operate under stringent requirements such as they need precise knowledge of underlying physical laws, precise knowledge of boundary and/or initial conditions, and often need time-consuming workflows such as mesh generation and long time simulation. On top of these limitations, high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, seamlessly incorporating noisy data is still a challenge for solving inverse problems efficiently. Physics-Informed Machine learning (PIML) has emerged as a promising alternative for solving above-mentioned problems. In this talk, we will discuss a particular type of PIML method namely, Physics-Informed Neural Networks (PINNs). We review some of the current capabilities and limitations of PINNs and discuss diverse applications where PINN is proved to be very effective compared to traditional approaches. We also discuss the extensions of the current PINN method such as Conservative PINNs (cPINNs) and eXtended PINNs (XPINNs) for big data and/or large models. To this end, we will also discuss various adaptive activation functions that can accelerate the convergence of deep and physics-informed neural networks.

Dr. Ameya D. Jagtap is an Assistant Professor of Applied Mathematics (Research) at Brown University, USA. He received his PhD degree in Aerospace Engineering from the Indian Institute of Science (IISc), India. Later, he went to Brown University to pursue his postdoctoral research in the division of applied mathematics. Due to his interdisciplinary background in mechanical /aerospace engineering, applied mathematics and computation, a key focus of his research work is to develop data and physics-driven scientific machine learning algorithms applicable to a wide range of problems in computational physics. His expertise lies in the field of Scientific Machine Learning, Deep Learning, Data/Physics-driven deep learning techniques with multi-fidelity data, Uncertainty Quantification/Propagation, Multi-scale & Multi- physics simulations, Computational Continuum Mechanics (Solids, Fluids, and Acoustics), Spectral/Finite Element Methods, WENO/DG schemes, Domain decomposition techniques, etc. He is also interested in the development of novel artificial neural network architectures, which give faster convergence.