Modeling the wave propagation in viscoacoustic media: An efficient spectral approach in time and space domain. - Khemraj Shukla; José M. Carcione; Reynam da Cruz Pestana; Priyank Jaiswal; Turgut Özdenvar (Comput. Geosci., 2019)

Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks. - Khemraj Shukla; Patricio Clark Di Leoni; James L. Blackshire; Daniel Sparkman; George Em Karniadakis (CoRR, 2020)

A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: Penalty fluxes and micro-heterogeneities. - Khemraj Shukla; Jesse Chan; Maarten V. de Hoop; Priyank Jaiswal (J. Comput. Phys., 2020)

A high order discontinuous Galerkin method for the symmetric form of the anisotropic viscoelastic wave equation. - Khemraj Shukla; Jesse Chan; Maarten V. de Hoop (Comput. Math. Appl., 2021)

Parallel physics-informed neural networks via domain decomposition. - Khemraj Shukla; Ameya D. Jagtap; George Em Karniadakis (J. Comput. Phys., 2021)

Learning two-phase microstructure evolution using neural operators and autoencoder architectures. - Vivek Oommen; Khemraj Shukla; Somdatta Goswami; Rémi Dingreville; George Em Karniadakis (CoRR, 2022)

Scalable algorithms for physics-informed neural and graph networks. - Khemraj Shukla; Mengjia Xu; Nathaniel Trask; George Em Karniadakis (CoRR, 2022)

A Physics-Informed Neural Network for Quantifying the Microstructural Properties of Polycrystalline Nickel Using Ultrasound Data: A promising approach for solving inverse problems. - Khemraj Shukla; Ameya D. Jagtap; James L. Blackshire; Daniel Sparkman; George Em Karniadakis (IEEE Signal Process. Mag., 2022)

Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils. - Khemraj Shukla; Vivek Oommen; Ahmad Peyvan; Michael Penwarden; Luis Bravo; Anindya Ghoshal; Robert M. Kirby; George Em Karniadakis (CoRR, 2023)

Learning bias corrections for climate models using deep neural operators. - Aniruddha Bora; Khemraj Shukla; Shixuan Zhang; Bryce Harrop; Ruby Leung; George Em Karniadakis (CoRR, 2023)

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; Mikko Karttunen (CoRR, 2023)

CrunchGPT: A chatGPT assisted framework for scientific machine learning. - Varun Kumar; Leonard Gleyzer; Adar Kahana; Khemraj Shukla; George Em Karniadakis (CoRR, 2023)

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; Rahul Babu Koneru; Zhen Li 003; Luis Bravo; Anindya Ghoshal; George Em Karniadakis; Mikko Karttunen (CoRR, 2023)

Randomized Forward Mode of Automatic Differentiation for Optimization Algorithms. - Khemraj Shukla; Yeonjong Shin (CoRR, 2023)

Rethinking materials simulations: Blending direct numerical simulations with neural operators. - Vivek Oommen; Khemraj Shukla; Saaketh Desai; Rémi Dingreville; George Em Karniadakis (CoRR, 2023)

High-order methods for hypersonic flows with strong shocks and real chemistry. - Ahmad Peyvan; Khemraj Shukla; Jesse Chan; George E. Karniadakis (J. Comput. Phys., 2023)

A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks. - Khemraj Shukla; Juan Diego Toscano; Zhicheng Wang; Zongren Zou; George Em Karniadakis (CoRR, 2024)

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements. - Khemraj Shukla; Zongren Zou; Chi Hin Chan; Additi Pandey; Zhicheng Wang; George Em Karniadakis (CoRR, 2024)

Deep neural operators as accurate surrogates for shape optimization. - Khemraj Shukla; Vivek Oommen; Ahmad Peyvan; Michael Penwarden; Nicholas Plewacki; Luis Bravo; Anindya Ghoshal; Robert M. Kirby; George Em Karniadakis (Eng. Appl. Artif. Intell., 2024)

High order entropy stable schemes for the quasi-one-dimensional shallow water and compressible Euler equations. - Jesse Chan; Khemraj Shukla; Xinhui Wu; Ruofeng Liu; Prani Nalluri (J. Comput. Phys., 2024)

Tackling the curse of dimensionality with physics-informed neural networks. - Zheyuan Hu 002; Khemraj Shukla; George Em Karniadakis; Kenji Kawaguchi (Neural Networks, 2024)

AI-Aristotle: A physics-informed framework for systems biology gray-box identification. - Nazanin Ahmadi Daryakenari; Mario De Florio; Khemraj Shukla; George Em Karniadakis (PLoS Comput. Biol., 2024)

Which Optimizer Works Best for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks? - Elham Kiyani; Khemraj Shukla; Jorge F. Urbán; Jérôme Darbon; George Em Karniadakis (CoRR, 2025)

A Neural Operator-Based Emulator for Regional Shallow Water Dynamics. - Peter Rivera-Casillas; Sourav Dutta; Shukai Cai; Mark Loveland; Kamaljyoti Nath; Khemraj Shukla; Corey Jason Trahan; Jonghyun Lee 005; Matthew W. Farthing; Clint Dawson 001 (CoRR, 2025)

Discovering Partially Known Ordinary Differential Equations: a Case Study on the Chemical Kinetics of Cellulose Degradation. - Federica Bragone; Kateryna Morozovska; Tor Laneryd; Khemraj Shukla; Stefano Markidis (CoRR, 2025)

Representation Meets Optimization: Training PINNs and PIKANs for Gray-Box Discovery in Systems Pharmacology. - Nazanin Ahmadi Daryakenari; Khemraj Shukla; George Em Karniadakis (CoRR, 2025)

Leveraging Deep Operator Networks (DeepONet) for Acoustic Full Waveform Inversion (FWI). - Kamaljyoti Nath; Khemraj Shukla; Victor C. Tsai; Umair bin Waheed; Christian Huber; Omer Alpak; Chuen-Song Chen; Ligang Lu; Amik St.-Cyr (CoRR, 2025)

$PINN - a Domain Decomposition Method for Bayesian Physics-Informed Neural Networks. - Júlia Vicens Figueres; Juliette Vanderhaeghen; Federica Bragone; Kateryna Morozovska; Khemraj Shukla (CoRR, 2025)

Deep Operator Neural Network Model Predictive Control. - Thomas Oliver de Jong; Khemraj Shukla; Mircea Lazar (CoRR, 2025)

FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor design. - Chenxi Wu; Juan Diego Toscano; Khemraj Shukla; Yingjie Chen; Ali Shahmohammadi; Edward Raymond; Thomas Toupy; Neda Nazemifard; Charles Papageorgiou; George Em Karniadakis (CoRR, 2025)