199 citations · 302 across the 61 of their papers we have counts for
72 papers
Physics-informed Kolmogorov-Arnold networks (PIKANs) for noise-robust reconstruction of boiling heat flux from infrared measurements
Siavash Khodakarami, Parimala Vardhan Vydyula, Aniruddha Bora +2
Recovering a noise-amplified inverse quantity from corrupted boundary data is a recurring problem in physics-informed learning for real-world applications. Specifically, small pert…
Well-posedness of neural turbulence closures and tangent dissipation
Zhen Zhang, George Em Karniadakis
A neural turbulence closure defines a new boundary-value problem, , with a coupled Jacobian , where is the original mean-flow operator and $…
Site-scale, Multi-resolution WRF Wind Modeling with Observational Nudging for Methane Emission Monitoring in the Permian Basin
Ehsan Kharazmi, Erin Menezes, George Karniadakis +2
Accurate methane source localization and emission-rate estimation at oil and gas facilities require wind fields that resolve site-scale spatial and temporal variability, which cann…
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…
Quantifying reticulocyte biomechanics in health and disease
Zhaojie Chai, Jianlu Zheng, He Li +2
Red blood cell (RBC) populations are mechanically and morphologically heterogeneous, yet how this heterogeneity governs transport, splenic retention and blood rheology in confineme…
Generalizable turbulence closures across bluff-body shapes by PINN-based solver-agnostic training
Zhen Zhang, Theo Käufer, Louise Ronglan +2
Data-driven turbulence closures are commonly calibrated by embedding a CFD solver within an inverse procedure that requires a converged flow solution at every optimization iteratio…
Agents' Last Exam
Yiyou Sun, Xinyang Han, Weichen Zhang +355
Recent AI systems have achieved strong results on a wide range of benchmarks, yet these gains have not translated into economically meaningful deployment across many professional d…
Quantifying the biophysical properties of stomatocytes in health and disease
Zhaojie Chai, Jianlu Zheng, He Li +2
Hereditary stomatocytosis (HS) comprises red blood cell (RBC) disorders characterized by cup-shaped erythrocytes that respond oppositely to splenectomy: curative in overhydrated HS…
Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers
Jaemin Oh, Youngkyu Lee, Jerome Darbon +1
Neural operators are increasingly used to warm-start Newton solvers for nonlinear PDEs, on the premise that a low test error places the initial guess inside the basin of attraction…
Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems
Zhen Zhang, Alessandro Alla, George Em Karniadakis
Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-infor…
Spectral Audit of In-Context Operator Networks
Zhiwei Gao, Liu Yang, George Em Karniadakis
Existing evaluations of neural operators and in-context operator learning rely primarily on prediction error, but accurate output prediction does not guarantee the correct local dy…
Operator Learning for Reconstructing Flow Fields from Sparse Measurements: a Language Model Approach
Qian Zhang, George Em Karniadakis
Reconstructing flow fields from sparse measurements is a fundamental problem in fluid mechanics with broad implications for modeling, control, and design. In this work, we propose…
Proposal-Guided Greedy Surrogate Refinement for PDE-Driven High-Dimensional Rare-Event Estimation
Zhiwei Gao, George Karniadakis
Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate…
PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems
Alan John Varghese, Shanqing Liu, Paula Chen +3
Many real-life applications involve controlling high-dimensional multi-agent systems in real-time. Existing optimal control solvers often suffer from the curse-of-dimensionality an…
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…
NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces
Francesc Levrero-Florencio, Youngkyu Lee, Jay Pathak +1
The convergence of Krylov-based linear iterative solvers applied to parametric partial differential equations (PDEs) is often highly sensitive to the domain, its discretization, th…
Multi-fidelity surrogates for mechanics of composites: from co-kriging to multi-fidelity neural networks
Haizhou Wen, Elham Kiyani, Gang Li +3
Composite materials exhibit strongly hierarchical and anisotropic properties governed by coupled mechanisms spanning constituents, plies, laminates, structures, and manufacturing h…
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…
Agentic Risk-Aware Set-Based Engineering Design
Varun Kumar, George Em Karniadakis
This paper introduces a multi-agent framework guided by Large Language Models (LLMs) to assist in the early stages of engineering design, a phase often characterized by vast parame…
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…
PINNs in PDE Constrained Optimal Control Problems: Direct vs Indirect Methods
Zhen Zhang, Shanqing Liu, Alessandro Alla +2
We study physics-informed neural networks (PINNs) as numerical tools for the optimal control of semilinear partial differential equations. We first recall the classical direct and…
AI-enabled cardiac shape reconstruction from routine magnetic resonance imaging
Tanmay Mukherjee, Neil Gautam, Nikhil Kadivar +10
Computational models of cardiac structure and function are increasingly central to the development of subject-specific cardiac digital twins, enabling improved characterization of…
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…