Deep Ray

Deep Ray is an Assistant Professor of Mathematics holding a joint position at the Department of Mathematics and the Institute for Physical Science and Technology at the University of Maryland, College Park. His research lies at the interface of conventional numerical analysis and machine learning, with a focus on developing computational methods that combine physics-based modeling with deep learning techniques.

Dr. Ray's primary research interests include scientific machine learning and hyperbolic conservation laws. In scientific machine learning, he develops deep learning tools to overcome computational bottlenecks in existing numerical methods, with applications in shock-capturing algorithms for conservation laws, reduced order modeling for flow problems, acceleration of Monte-Carlo algorithms using deep surrogates, PDE constrained optimization, physics-based deep Bayesian inference, and operator learning for surrogate modeling. His work in hyperbolic conservation laws focuses on developing numerical methods that satisfy important physical model properties such as entropy stability and kinetic energy preservation, including high-order entropy-stable finite volume schemes for compressible Euler equations.

His recent publications (2021-2024) demonstrate a strong focus on applying generative models, particularly GANs and related techniques, to solve physics-based inverse problems, medical imaging applications, and conservation laws. There's a clear trend toward developing physics-informed machine learning approaches that maintain the physical properties of the underlying systems while leveraging the representational power of deep learning. His work spans computational physics, fluid dynamics, medical imaging, and wildfire modeling.

Dr. Ray has developed several computational tools including TENSUM (a parallelized finite volume solver for compressible flows) and DGANN (a MATLAB-based DG-solver for conservation laws that uses neural networks for troubled-cell detection and artificial viscosity estimation). His research represents a significant contribution to the emerging field of scientific machine learning, bridging traditional numerical analysis with modern deep learning techniques.