W24-05 Scientific Machine Learning: Application to Computational Mechanics

Instructor(s):  Rajeev Jaiman,  University of British Columbia; Romit Maulik, Pennsylvania State University; Gianmarco Menglado, National University of Singapore


Advances in high-performance computing (HPC) have empowered us to perform large-scale simulations for billions of variables in coupled fluid-structure systems involving complex geometries and multiphase flows. These high-fidelity simulations via coupled nonlinear partial differential equations (PDE) have been providing invaluable physical insight for the development of new designs and devices in engineering applications. Despite efficient numerical methods and powerful supercomputers, state-of-the-art computational mechanics simulations still lead to prohibitive costs for many-query problems such as optimization and control. In this short course, we will cover some of our recent developments to integrate and to complement the HPC-based high-fidelity computations with the emerging field of data science and machine learning.

The primary focus of this short course is to (i) develop simple and efficient reduced-order models for accelerating the computation of systems with very large degrees of freedom, and (ii) to explore state-of-the-art deep learning technologies that can dramatically accelerate computational simulations with reasonable accuracy. In the former, we will introduce projection-based reduced-order modeling which leverages dimensionality reduction through linear and nonlinear autoencoders. In the latter, we will introduce deep learning models based on various architectures such as convolutional and graph neural networks for learning high-dimensional surrogates. A series of academic and industry test cases will be covered to elucidate the integration of standard CFD and fluid-structure interaction solvers (using finite element & finite volume methods) with model reduction and deep learning techniques. Finally, this course will conclude with demonstrations of how scientific computing and deep learning workloads can be coupled and deployed for realistic problems using the PythonFOAM and in-house SimflowAI frameworks, which embed machine learning algorithms developed in Pytorch and TensorFlow within OpenFOAM (finite-volume open-source solver) and Simflow (finite-element based multiphysics package).