440 citations · 851 across the 27 of their papers we have counts for
9 papers · 1 filter
Rethinking materials simulations: Blending direct numerical simulations with neural operators
Vivek Oommen, Khemraj Shukla, Saaketh Desai +2
Direct numerical simulations (DNS) are accurate but computationally expensive for predicting materials evolution across timescales, due to the complexity of the underlying evolutio…
AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification
Nazanin Ahmadi Daryakenari, Mario De Florio, Khemraj Shukla +1
Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research. We present a new physics-inform…
MyCrunchGPT: A chatGPT assisted framework for scientific machine learning
Varun Kumar, Leonard Gleyzer, Adar Kahana +2
Scientific Machine Learning (SciML) has advanced recently across many different areas in computational science and engineering. The objective is to integrate data and physics seaml…
Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs
Elham Kiyani, Mahdi Kooshkbaghi, Khemraj Shukla +6
The molten sand, a mixture of calcia, magnesia, alumina, and silicate, known as CMAS, is characterized by its high viscosity, density, and surface tension. The unique properties of…
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks
Zheyuan Hu, Khemraj Shukla, George Em Karniadakis +1
The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solvin…
High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations
Jesse Chan, Khemraj Shukla, Xinhui Wu +2
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes add…
A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data
Elham Kiyani, Khemraj Shukla, George Em Karniadakis +1
We propose a framework and an algorithm to uncover the unknown parts of nonlinear equations directly from data. The framework is based on eXtended Physics-Informed Neural Networks…
Learning bias corrections for climate models using deep neural operators
Aniruddha Bora, Khemraj Shukla, Shixuan Zhang +3
Numerical simulation for climate modeling resolving all important scales is a computationally taxing process. Therefore, to circumvent this issue a low resolution simulation is per…
Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils
Khemraj Shukla, Vivek Oommen, Ahmad Peyvan +5
Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving…