Physics-informed neural networks: some applications and scalability

Dr. Khemraj Shukla

Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some instances, the objective is to discover part of the hidden physics from the available data, and PIML has been shown to be particularly effective for such problems for which conventional methods may fail. Unlike commercial machine learning where training of deep neural networks requires big data, in PIML big data are not available. Instead, we can train such networks from additional information obtained by employing the physical laws and evaluating them at random points in the space-time domain. Such physics-informed machine learning integrates multimodality and multi-fidelity data with mathematical models, and implements them using neural networks or graph networks. Here, we review some of the prevailing trends in embedding physics into machine learning, using physics-informed neural networks (PINNs) based primarily on feed-forward neural networks and automatic differentiation. In this I will discuss the application PIML for non-destructive evaluation using ultrasound data along with scalability of PIML using domain decomposition over MPI+X type of heterogeneous architectures.

SHORT BIO

Dr. Khemraj Shukla (khemraj_shukla@brown.edu) received his Ph.D. degree in computational geophysics. In his Ph.D., he studied high-order numerical methods for hyperbolic systems and finished his research work with GMIG Group of Rice University. He is an Assistant Professor in the Division of Applied Mathematics at Brown University, Providence, Rhode Island, 02906, USA."