Deep Learning and Computational Physics

The main objective of this book is to introduce a student who is familiar with elementary math concepts to select topics in deep learning. It exploits strong connections between deep learning algorithms and the techniques of computational physics to achieve two important goals. First, it uses concepts from computational physics to develop an understanding of deep learning algorithms. Second, it describes several novel deep learning algorithms for solving challenging problems in computational physics, thereby offering someone who is interested in modeling physical phenomena with a complementary set of tools. It is intended for senior undergraduate and graduate students in science and engineering programs. It is used as a textbook for a course (or a course sequence) for senior-level undergraduate or graduate-level students.

Introduces a graduate student with linear algebra and partial differential equations to select topics in deep learning Exploits the connections between deep learning algorithms and the more conventional techniques of computational physics Uses concepts from computational physics to develop an understanding of deep learning algorithms

Autorentext

Assad Oberai is the Hughes Professor of Aerospace and Mechanical Engineering in the Viterbi School of Engineering. He earned a Bachelor of Engineering degree from Osmania University, an MS from the University of Colorado, and a PhD from Stanford University all in Mechanical Engineering. He has held academic appointments at Boston University, Rensselaer Polytechnic Institute, and the University of Southern California. Assad leads a group that designs, implements, and applies data- and physics-based models and algorithms to solve problems in engineering and science. Problems such as better detection, diagnosis, and care of diseases like cancer, understanding the role of mechanics and physics in medicine and biology, modeling the evolution of multi-physics and multiscale systems, and reduced-order models for aerospace and mechanical systems. Assad is a Fellow of the American Academy of Mechanics, American Society of Mechanical Engineers, the American Institute of Medical and Biological Engineering, and the United States Association of Computational Mechanics.

Deep Ray is an Assistant Professor of Mathematics at the University of Maryland. He earned his Bachelor of Mathematics from University of Delhi, followed by a Masters and PhD in Mathematics from Tata Institute of Fundamental Research - Center for Applicable Mathematics. He has held research positions at ETH Zurich, EPFL, Rice University and University of Southern California. Deep's research lies at the interface of conventional numerical analysis and machine learning. He focuses on identifying computational bottlenecks in existing numerical algorithms and resolving them by the careful integration of machine learning tools. He has used such techniques to design efficient shock-capturing methods, build deep learning-based surrogate models to solve partial differential equations, develop differentiable models for constrained optimization, and solve Bayesian inference problems arising in real-world applications.

Orazio Pinti is a Research Scientist at Pasteur Labs, working in the field of scientific machine learning and computational physics. He holds a BSc and MSc from the Polytechnic University of Turin, and a PhD from the University of Southern California, all in Aerospace Engineering. His interests include applied mathematics, machine learning, and computational science, with a focus on reduced-order and multi-fidelity modeling.

Inhalt

Introduction.- Introduction to deep neural networks.- Residual neural networks.- Convolutional Neural Networks.- Solving PDEs with Neural Networks.- Operator Networks.- Generative Deep Learning.