199 citations · 302 across the 61 of their papers we have counts for
28 papers · 1 filter
Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces
Khemraj Shukla, George Em Karniadakis
Deep Operator Networks (DeepONets; arXiv:1910.03193) typically encode an input function through point values on a fixed discretization. Building on the Topological DeepONet framewo…
UFO: A Domain-Unification-Free Operator Framework for Generalized Operator Learning
Hanli Qiao, George Em Karniadakis, Muhammad Muniruzzaman
Neural operators have become an effective framework for learning mappings between function spaces, yet most existing architectures realize operators within a single representationa…
GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms
Juan Diego Toscano, Zhaojie Chai, George Em Karniadakis
Language-model agents plan, execute, and evaluate scientific workflows. However, the problem--method relationships guiding their choices remain implicit, so plausible outputs can v…
Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles
Khemraj Shukla, Zongren Zou, Theo Kaeufer +2
Physics-informed neural networks (PINNs) have emerged as a promising framework for solving inverse problems governed by partial differential equations (PDEs), including the reconst…
Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks
Anas Jnini, Elham Kiyani, Khemraj Shukla +5
Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy -- faithfully capturing co…
Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelines
Siavash Khodakarami, Vivek Oommen, Nazanin Ahmadi Daryakenari +2
Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed…
Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations
Heechang Kim, Qianying Cao, Hyomin Shin +3
Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training da…
Hybrid Iterative Solvers with Geometry-Aware Neural Preconditioners for Parametric PDEs
Youngkyu Lee, Francesc Levrero Florencio, Jay Pathak +1
The convergence behavior of classical iterative solvers for parametric partial differential equations (PDEs) is often highly sensitive to the domain and specific discretization of…
Retrofitting Earth System Models with Cadence-Limited Neural Operator Updates
Aniruddha Bora, Shixuan Zhang, Khemraj Shukla +3
Coarse resolution, imperfect parameterizations, and uncertain initial states and forcings limit Earth-system model (ESM) predictions. Traditional bias correction via data assimilat…
Kinetic-Mamba: Mamba-Assisted Predictions of Stiff Chemical Kinetics
Additi Pandey, Liang Wei, Hessam Babaee +1
Accurate chemical kinetics modeling is essential for combustion simulations, as it governs the evolution of complex reaction pathways and thermochemical states. In this work, we in…
ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms
Juan Diego Toscano, Daniel T. Chen, George Em Karniadakis
Progress in computational science depends on complex numerical workflows that must faithfully encode physical laws, yet translating conceptual insight into reliable code remains a…
Importance of localized dilatation and distensibility in identifying determinants of thoracic aortic aneurysm with neural operators
David S. Li, Somdatta Goswami, Qianying Cao +4
Thoracic aortic aneurysms (TAAs) arise from diverse mechanical and mechanobiological disruptions to the aortic wall that increase the risk of dissection or rupture. Evidence links…
A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning
Juan Diego Toscano, Daniel T. Chen, Vivek Oommen +2
Residual-based adaptive strategies are widely used in scientific machine learning but remain largely heuristic. We introduce a unifying variational framework that formalizes these…
Learning Nonlinear Responses in PET Bottle Buckling with a Hybrid DeepONet-Transolver Framework
Varun Kumar, Jing Bi, Cyril Ngo Ngoc +2
Neural surrogates and operator networks for solving partial differential equation (PDE) problems have attracted significant research interest in recent years. However, most existin…
Process-Informed Forecasting of Complex Thermal Dynamics in Pharmaceutical Manufacturing
Ramona Rubini, Siavash Khodakarami, Aniruddha Bora +2
Accurate time-series forecasting for complex physical systems is the backbone of modern industrial monitoring and control, yet deep learning models often lack the physical consiste…
Crack Path Prediction with Operator Learning using Discrete Particle System data Generation
Elham Kiyani, Venkatesh Ananchaperumal, Ahmad Peyvan +3
Accurately modeling crack propagation is critical for predicting failure in engineering materials and structures, where small cracks can rapidly evolve and cause catastrophic damag…
FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor design
Chenxi Wu, Juan Diego Toscano, Khemraj Shukla +7
We propose FMEnets, a physics-informed machine learning framework for the design and analysis of non-ideal plug flow reactors. FMEnets integrates the fundamental governing equation…
Equilibrium Conserving Neural Operators for Super-Resolution Learning
Vivek Oommen, Andreas E. Robertson, Daniel Diaz +5
Neural surrogate solvers can estimate solutions to partial differential equations in physical problems more efficiently than standard numerical methods, but require extensive high-…
Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems
Siavash Khodakarami, Vivek Oommen, Aniruddha Bora +1
Neural operators have emerged as powerful surrogates for modeling complex physical problems. However, they suffer from spectral bias making them oblivious to high-frequency modes,…
XAI4Extremes: An interpretable machine learning framework for understanding extreme-weather precursors under climate change
Jiawen Wei, Aniruddha Bora, Vivek Oommen +7
Extreme weather events are increasing in frequency and intensity due to climate change. This, in turn, is exacting a significant toll in communities worldwide. While prediction ski…
Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble
Zongren Zou, Zhicheng Wang, George Em Karniadakis
We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs),…
Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks
Elham Kiyani, Khemraj Shukla, Jorge F. Urbán +2
Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network's trainin…
Automatic selection of the best neural architecture for time series forecasting
Qianying Cao, Shanqing Liu, Alan John Varghese +3
Time series forecasting plays a pivotal role in a wide range of applications, including weather prediction, healthcare, structural health monitoring, predictive maintenance, energy…
From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning
Juan Diego Toscano, Vivek Oommen, Alan John Varghese +4
Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and…