George Em Karniadakis

263 papers B 1Journal 257Unranked 5

Year	Rank	Type	Title / Venue / Authors
2026	J	`jnl`	A digital twin for diesel engines: Operator-infused physics-informed neural networks with transfer learning for engine health monitoring. Eng. Appl. Artif. Intell. Kamaljyoti Nath, Varun Kumar, Daniel J. Smith, George Em Karniadakis
2026	J	`jnl`	An AI-enabled tool for quantifying overlapping red blood cell sickling dynamics in microfluidic assays. CoRR Nikhil Kadivar, Guansheng Li, Jianlu Zheng, John M. Higgins, Ming Dao, George Em Karniadakis, Mengjia Xu
2026	J	`jnl`	Fusion-DeepONet: A data-efficient neural operator for geometry-dependent hypersonic and supersonic flows. J. Comput. Phys. Ahmad Peyvan, Varun Kumar, George Em Karniadakis
2026	J	`jnl`	Learning in PINNs: Phase transition, diffusion equilibrium, and generalization. Neural Networks Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, George Em Karniadakis
2026	J	`jnl`	Mitigating spectral bias in neural operators via high-frequency scaling for physical systems. Neural Networks Siavash Khodakarami, Vivek Oommen, Aniruddha Bora, George Em Karniadakis
2026	J	`jnl`	Nonlinear parametrization solver for fractional Burgers equations. CoRR Haojun Qin, Zhiwei Gao, Jinye Shen, George Em Karniadakis
2026	J	`jnl`	Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations. CoRR Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi
2026	J	`jnl`	Representation meets optimization: Training PINNs and PIKANs for gray-box discovery in systems pharmacology. Comput. Biol. Medicine Nazanin Ahmadi Daryakenari, Khemraj Shukla, George Em Karniadakis
2026	J	`jnl`	Spectral bias in physics-informed and operator learning: Analysis and mitigation guidelines. CoRR Siavash Khodakarami, Vivek Oommen, Nazanin Ahmadi Daryakenari, Maxim Beekenkamp, George Em Karniadakis
2026	J	`jnl`	State-space models are accurate and efficient neural operators for dynamical systems. Neural Networks Zheyuan Hu, Nazanin Ahmadi Daryakenari, Qianli Shen, Kenji Kawaguchi, George Em Karniadakis
2025	J	`jnl`	A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers. CoRR Youngkyu Lee, Shanqing Liu, Jérôme Darbon, George Em Karniadakis
2025	J	`jnl`	A Time-Dependent Symplectic Network for Nonconvex Path Planning Problems with Linear and Nonlinear Dynamics. SIAM J. Sci. Comput. Zhen Zhang, Chenye Wang, Shanqing Liu, Jérôme Darbon, George Em Karniadakis
2025	J	`jnl`	A Variational Framework for Residual-Based Adaptivity in Neural PDE Solvers and Operator Learning. CoRR Juan Diego Toscano, Daniel T. Chen, Vivek Oommen, Jérôme Darbon, George Em Karniadakis
2025	J	`jnl`	AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kinetics. CoRR Kamaljyoti Nath, Additi Pandey, Bryan T. Susi, Hessam Babaee, George Em Karniadakis
2025	J	`jnl`	ATHENA: Agentic Team for Hierarchical Evolutionary Numerical Algorithms. CoRR Juan Diego Toscano, Daniel T. Chen, George Em Karniadakis
2025	J	`jnl`	Artificial to Spiking Neural Networks Conversion with Calibration in Scientific Machine Learning. SIAM J. Sci. Comput. Qian Zhang, Chenxi Wu, Adar Kahana, George Em Karniadakis, Youngeun Kim, Yuhang Li, Priyadarshini Panda
2025	J	`jnl`	Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs. CoRR Youngkyu Lee, Shanqing Liu, Jérôme Darbon, George Em Karniadakis
2025	J	`jnl`	Automatic selection of the best neural architecture for time series forecasting via multi-objective optimization and Pareto optimality conditions. CoRR Qianying Cao, Shanqing Liu, Alan John Varghese, Jérôme Darbon, Michael S. Triantafyllou, George Em Karniadakis
2025	J	`jnl`	CMINNs: Compartment model informed neural networks - Unlocking drug dynamics. Comput. Biol. Medicine Nazanin Ahmadi Daryakenari, Shupeng Wang, George Em Karniadakis
2025	J	`jnl`	Connecting the geometry and dynamics of many-body complex systems with message passing neural operators. CoRR Nicholas A. Gabriel, Neil F. Johnson, George Em Karniadakis
2025	J	`jnl`	Crack Path Prediction with Operator Learning using Discrete Particle System data Generation. CoRR Elham Kiyani, Venkatesh Ananchaperumal, Ahmad Peyvan, Mahendaran Uchimali, Gang Li, George Em Karniadakis
2025	J	`jnl`	DeepOMamba: State-space model for spatio-temporal PDE neural operator learning. J. Comput. Phys. Zheyuan Hu, Qianying Cao, Kenji Kawaguchi, George Em Karniadakis
2025	J	`jnl`	DeepONet Based Preconditioning Strategies for Solving Parametric Linear Systems of Equations. SIAM J. Sci. Comput. Alena Kopanicáková, George Em Karniadakis
2025	J	`jnl`	DeepSeek vs. ChatGPT: A Comparative Study for Scientific Computing and Scientific Machine Learning Tasks. CoRR Qile Jiang, Zhiwei Gao, George Em Karniadakis
2025	J	`jnl`	DeepVIVONet: Using deep neural operators to optimize sensor locations with application to vortex-induced vibrations. CoRR Ruyin Wan, Ehsan Kharazmi, Michael S. Triantafyllou, George Em Karniadakis
2025	J	`jnl`	FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor design. CoRR Chenxi Wu, Juan Diego Toscano, Khemraj Shukla, Yingjie Chen, Ali Shahmohammadi, Edward Raymond, Thomas Toupy, Neda Nazemifard, Charles Papageorgiou, George Em Karniadakis
2025	J	`jnl`	From LIF to QIF: Toward Differentiable Spiking Neurons for Scientific Machine Learning. CoRR Ruyin Wan, George Em Karniadakis, Panos Stinis
2025	J	`jnl`	GIMLET: Generalizable and Interpretable Model Learning through Embedded Thermodynamics. CoRR Suguru Shiratori, Elham Kiyani, Khemraj Shukla, George Em Karniadakis
2025	J	`jnl`	Hybrid Iterative Solvers with Geometry-Aware Neural Preconditioners for Parametric PDEs. CoRR Youngkyu Lee, Francesc Levrero-Florencio, Jay Pathak, George Em Karniadakis
2025	J	`jnl`	In silico biophysics and rheology of blood and red blood cells in Gaucher Disease. PLoS Comput. Biol. Zhaojie Chai, Guansheng Li, Papa Alioune Ndour, Philippe Connes, Pierre A. Buffet, Mélanie Franco, George Em Karniadakis
2025	J	`jnl`	KKANs: Kurková-Kolmogorov-Arnold networks and their learning dynamics. Neural Networks Juan Diego Toscano, Li-Lian Wang, George Em Karniadakis
2025	J	`jnl`	Kinetic-Mamba: Mamba-Assisted Predictions of Stiff Chemical Kinetics. CoRR Additi Pandey, Liang Wei, Hessam Babaee, George Em Karniadakis
2025	J	`jnl`	Learning Nonlinear Responses in PET Bottle Buckling with a Hybrid DeepONet-Transolver Framework. CoRR Varun Kumar, Jing Bi, Cyril Ngo Ngoc, Victor Oancea, George Em Karniadakis
2025	J	`jnl`	Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction. CoRR Vivek Oommen, Siavash Khodakarami, Aniruddha Bora, Zhicheng Wang, George Em Karniadakis
2025	J	`jnl`	Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble. CoRR Zongren Zou, Zhicheng Wang, George Em Karniadakis
2025	J	`jnl`	Leveraging Operator Learning to Accelerate Convergence of the Preconditioned Conjugate Gradient Method. CoRR Alena Kopanicáková, Youngkyu Lee, George Em Karniadakis
2025	J	`jnl`	Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systems. CoRR Siavash Khodakarami, Vivek Oommen, Aniruddha Bora, George Em Karniadakis
2025	J	`jnl`	Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification. J. Comput. Phys. Zongren Zou, George Em Karniadakis
2025	J	`jnl`	Multi-resolution learning with DeepONets and long short-term memory neural networks. Neurocomputing Katarzyna Michalowska, Somdatta Goswami, George Em Karniadakis, Signe Riemer-Sørensen
2025	J	`jnl`	Operator Learning for Reconstructing Flow Fields from Sparse Measurements: an Energy Transformer Approach. CoRR Qian Zhang, Dmitry Krotov, George Em Karniadakis
2025	J	`jnl`	Operator learning for reconstructing flow fields from sparse measurements: An energy transformer approach. J. Comput. Phys. Qian Zhang, Dmitry Krotov, George Em Karniadakis
2025	J	`jnl`	Physics-Informed Machine Learning in Biomedical Science and Engineering. CoRR Nazanin Ahmadi, Qianying Cao, Jay D. Humphrey, George Em Karniadakis
2025	J	`jnl`	Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures. CoRR Elham Kiyani, Manav Manav, Nikhil Kadivar, Laura De Lorenzis, George Em Karniadakis
2025	J	`jnl`	Probabilistic Predictions of Process-Induced Deformation in Carbon/Epoxy Composites Using a Deep Operator Network. CoRR Elham Kiyani, Amit Makarand Deshpande, Madhura Limaye, Zhiwei Gao, Sai Aditya Pradeep, Srikanth Pilla, Gang Li, Zhen Li, George Em Karniadakis
2025	J	`jnl`	Process-Informed Forecasting of Complex Thermal Dynamics in Pharmaceutical Manufacturing. CoRR Ramona Rubini, Siavash Khodakarami, Aniruddha Bora, George Em Karniadakis, Michele Dassisti
2025	J	`jnl`	Representation Meets Optimization: Training PINNs and PIKANs for Gray-Box Discovery in Systems Pharmacology. CoRR Nazanin Ahmadi Daryakenari, Khemraj Shukla, George Em Karniadakis
2025	J	`jnl`	Safe Physics-Informed Machine Learning for Optimal Predefined-Time Stabilization: A Lyapunov-Based Approach. IEEE Trans. Neural Networks Learn. Syst. Nick-Marios T. Kokolakis, Zhen Zhang, Shanqing Liu, Kyriakos G. Vamvoudakis, Jérôme Darbon, George Em Karniadakis
2025	J	`jnl`	Safe cross-entropy-based importance sampling for rare event simulations. CoRR Zhiwei Gao, George Em Karniadakis
2025	J	`jnl`	Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks. CoRR Zhiwei Gao, George Em Karniadakis
2025	J	`jnl`	Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks. SIAM/ASA J. Uncertain. Quantification Zhiwei Gao, George Em Karniadakis
2025	J	`jnl`	SympGNNs: Symplectic Graph Neural Networks for identifying high-dimensional Hamiltonian systems and node classification. Neural Networks Alan John Varghese, Zhen Zhang, George Em Karniadakis
2025	J	`jnl`	Synergistic learning with multi-task DeepONet for efficient PDE problem solving. Neural Networks Varun Kumar, Somdatta Goswami, Katiana Kontolati, Michael D. Shields, George Em Karniadakis
2025	J	`jnl`	Tensor neural networks for high-dimensional Fokker-Planck equations. Neural Networks Taorui Wang, Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang, George Em Karniadakis
2025	J	`jnl`	Toward Autonomous Engineering Design: A Knowledge-Guided Multi-Agent Framework. CoRR Varun Kumar, George Em Karniadakis
2025	J	`jnl`	Which Optimizer Works Best for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks? CoRR Elham Kiyani, Khemraj Shukla, Jorge F. Urbán, Jérôme Darbon, George Em Karniadakis
2024	J	`jnl`	A Digital twin for Diesel Engines: Operator-infused PINNs with Transfer Learning for Engine Health Monitoring. CoRR Kamaljyoti Nath, Varun Kumar, Daniel J. Smith, George Em Karniadakis
2024	J	`jnl`	A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks. CoRR Khemraj Shukla, Juan Diego Toscano, Zhicheng Wang, Zongren Zou, George Em Karniadakis
2024	J	`jnl`	AI-Aristotle: A physics-informed framework for systems biology gray-box identification. PLoS Comput. Biol. Nazanin Ahmadi Daryakenari, Mario De Florio, Khemraj Shukla, George Em Karniadakis
2024	J	`jnl`	Analysis of biologically plausible neuron models for regression with spiking neural networks. CoRR Mario De Florio, Adar Kahana, George Em Karniadakis
2024	J	`jnl`	Automatic discovery of optimal meta-solvers via multi-objective optimization. CoRR Youngkyu Lee, Shanqing Liu, Jérôme Darbon, George Em Karniadakis
2024	J	`jnl`	Blending neural operators and relaxation methods in PDE numerical solvers. Nat. Mac. Intell. Enrui Zhang, Adar Kahana, Alena Kopanicáková, Eli Turkel, Rishikesh Ranade, Jay Pathak, George Em Karniadakis
2024	J	`jnl`	CMINNs: Compartment Model Informed Neural Networks - Unlocking Drug Dynamics. CoRR Nazanin Ahmadi Daryakenari, Shupeng Wang, George Em Karniadakis
2024	J	`jnl`	Correcting model misspecification in physics-informed neural networks (PINNs). J. Comput. Phys. Zongren Zou, Xuhui Meng, George Em Karniadakis
2024	J	`jnl`	Deep neural operators as accurate surrogates for shape optimization. Eng. Appl. Artif. Intell. Khemraj Shukla, Vivek Oommen, Ahmad Peyvan, Michael Penwarden, Nicholas Plewacki, Luis Bravo, Anindya Ghoshal, Robert M. Kirby, George Em Karniadakis
2024	J	`jnl`	DeepOnet Based Preconditioning Strategies For Solving Parametric Linear Systems of Equations. CoRR Alena Kopanicáková, George Em Karniadakis
2024	J	`jnl`	DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs. IEEE Trans. Neural Networks Learn. Syst. Mengjia Xu, Apoorva Vikram Singh, George Em Karniadakis
2024	J	`jnl`	From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning. CoRR Juan Diego Toscano, Vivek Oommen, Alan John Varghese, Zongren Zou, Nazanin Ahmadi Daryakenari, Chenxi Wu, George Em Karniadakis
2024	J	`jnl`	GMC-PINNs: A new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains. CoRR Shupeng Wang, George Em Karniadakis
2024	J	`jnl`	HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models. CoRR Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis
2024	J	`jnl`	Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks. CoRR Juan Diego Toscano, Theo Käufer, Zhibo Wang, Martin Maxey, Christian Cierpka, George Em Karniadakis
2024	J	`jnl`	Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling. CoRR Vivek Oommen, Aniruddha Bora, Zhen Zhang, George Em Karniadakis
2024	J	`jnl`	KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics. CoRR Juan Diego Toscano, Li-Lian Wang, George Em Karniadakis
2024	J	`jnl`	Laplace neural operator for solving differential equations. Nat. Mac. Intell. Qianying Cao, Somdatta Goswami, George Em Karniadakis
2024	J	`jnl`	Large scale scattering using fast solvers based on neural operators. CoRR Zongren Zou, Adar Kahana, Enrui Zhang, Eli Turkel, Rishikesh Ranade, Jay Pathak, George Em Karniadakis
2024	J	`jnl`	Learning characteristic parameters and dynamics of centrifugal pumps under multiphase flow using physics-informed neural networks. Eng. Appl. Artif. Intell. Felipe de Castro Teixeira Carvalho, Kamaljyoti Nath, Alberto Luiz Serpa, George Em Karniadakis
2024	J	`jnl`	Learning in PINNs: Phase transition, total diffusion, and generalization. CoRR Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, George Em Karniadakis
2024	J	`jnl`	Learning thermoacoustic interactions in combustors using a physics-informed neural network. Eng. Appl. Artif. Intell. Sathesh Mariappan, Kamaljyoti Nath, George Em Karniadakis
2024	—	`conf`	Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning. L4DC Paula X. Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis
2024	J	`jnl`	Leveraging Multitime Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems. SIAM J. Sci. Comput. Paula X. Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis
2024	J	`jnl`	Leveraging Viscous Hamilton-Jacobi PDEs for Uncertainty Quantification in Scientific Machine Learning. SIAM/ASA J. Uncertain. Quantification Zongren Zou, Tingwei Meng, Paula X. Chen, Jérôme Darbon, George Em Karniadakis
2024	J	`jnl`	Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning. CoRR Zongren Zou, Tingwei Meng, Paula X. Chen, Jérôme Darbon, George Em Karniadakis
2024	B	`conf`	Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks. IJCNN Katarzyna Michalowska, Somdatta Goswami, George Em Karniadakis, Signe Riemer-Sørensen
2024	J	`jnl`	NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements. CoRR Khemraj Shukla, Zongren Zou, Chi Hin Chan, Additi Pandey, Zhicheng Wang, George Em Karniadakis
2024	J	`jnl`	Physics-Informed Neural Networks Enhanced Particle Tracking Velocimetry: An Example for Turbulent Jet Flow. IEEE Trans. Instrum. Meas. Shengze Cai, Callum Gray, George Em Karniadakis
2024	J	`jnl`	Physics-Informed Neural Networks and Extensions. CoRR Maziar Raissi, Paris Perdikaris, Nazanin Ahmadi Daryakenari, George Em Karniadakis
2024	J	`jnl`	Quantification of total uncertainty in the physics-informed reconstruction of CVSim-6 physiology. CoRR Mario De Florio, Zongren Zou, Daniele E. Schiavazzi, George Em Karniadakis
2024	J	`jnl`	Randomized Forward Mode Gradient for Spiking Neural Networks in Scientific Machine Learning. CoRR Ruyin Wan, Qian Zhang, George Em Karniadakis
2024	J	`jnl`	Real-time prediction of gas flow dynamics in diesel engines using a deep neural operator framework. Appl. Intell. Varun Kumar, Somdatta Goswami, Daniel Smith, George Em Karniadakis
2024	J	`jnl`	Red blood cell passage through deformable interendothelial slits in the spleen: Insights into splenic filtration and hemodynamics. Comput. Biol. Medicine Guansheng Li, He Li, Papa Alioune Ndour, Mélanie Franco, Xuejin Li, Ian MacDonald, Ming Dao, Pierre A. Buffet, George Em Karniadakis
2024	J	`jnl`	RiemannONets: Interpretable Neural Operators for Riemann Problems. CoRR Ahmad Peyvan, Vivek Oommen, Ameya D. Jagtap, George Em Karniadakis
2024	J	`jnl`	Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck Equations. CoRR Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, Kenji Kawaguchi
2024	J	`jnl`	Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Levy Equations. CoRR Zheyuan Hu, Zhongqiang Zhang, George Em Karniadakis, Kenji Kawaguchi
2024	—	`conf`	Spiking Physics-Informed Neural Networks on Loihi 2. NICE Bradley H. Theilman, Qian Zhang, Adar Kahana, Eric C. Cyr, Nathaniel Trask, James B. Aimone, George Em Karniadakis
2024	J	`jnl`	State-space models are accurate and efficient neural operators for dynamical systems. CoRR Zheyuan Hu, Nazanin Ahmadi Daryakenari, Qianli Shen, Kenji Kawaguchi, George Em Karniadakis
2024	J	`jnl`	SympGNNs: Symplectic Graph Neural Networks for identifiying high-dimensional Hamiltonian systems and node classification. CoRR Alan John Varghese, Zhen Zhang, George Em Karniadakis
2024	J	`jnl`	Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving. CoRR Varun Kumar, Somdatta Goswami, Katiana Kontolati, Michael D. Shields, George Em Karniadakis
2024	J	`jnl`	Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks. CoRR Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang, George Em Karniadakis
2024	J	`jnl`	Tackling the curse of dimensionality with physics-informed neural networks. Neural Networks Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, Kenji Kawaguchi
2024	J	`jnl`	Tensor neural networks for high-dimensional Fokker-Planck equations. CoRR Taorui Wang, Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang, George Em Karniadakis
2024	J	`jnl`	TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers. Neural Networks Alan John Varghese, Aniruddha Bora, Mengjia Xu, George Em Karniadakis
2024	J	`jnl`	Transformers as Neural Operators for Solutions of Differential Equations with Finite Regularity. CoRR Benjamin Shih, Ahmad Peyvan, Zhongqiang Zhang, George Em Karniadakis
2024	J	`jnl`	Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications. CoRR Youngkyu Lee, Alena Kopanicáková, George Em Karniadakis
2024	J	`jnl`	Two-scale Neural Networks for Partial Differential Equations with Small Parameters. CoRR Qiao Zhuang, Chris Ziyi Yao, Zhongqiang Zhang, George Em Karniadakis
2024	J	`jnl`	Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations. CoRR Jin Song, Ming Zhong, George Em Karniadakis, Zhenya Yan
2024	J	`jnl`	Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations. J. Comput. Phys. Jin Song, Ming Zhong, George Em Karniadakis, Zhenya Yan
2023	J	`jnl`	A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data. CoRR Elham Kiyani, Khemraj Shukla, George Em Karniadakis, Mikko Karttunen
2023	J	`jnl`	A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimes. CoRR Minglang Yin, Zongren Zou, Enrui Zhang, Cristina Cavinato, Jay D. Humphrey, George Em Karniadakis
2023	J	`jnl`	A Hybrid Deep Neural Operator/Finite Element Method for Ice-Sheet Modeling. CoRR Qizhi He, Mauro Perego, Amanda A. Howard, George Em Karniadakis, Panos Stinis
2023	J	`jnl`	A combined computational and experimental investigation of the filtration function of splenic macrophages in sickle cell disease. PLoS Comput. Biol. Guansheng Li, Yuhao Qiang, He Li, Xuejin Li, Pierre Buffet, Ming Dao, George Em Karniadakis
2023	J	`jnl`	A hybrid deep neural operator/finite element method for ice-sheet modeling. J. Comput. Phys. Qizhi He, Mauro Perego, Amanda A. Howard, George Em Karniadakis, Panos Stinis
2023	J	`jnl`	A novel deeponet model for learning moving-solution operators with applications to earthquake hypocenter localization. CoRR Ehsan Haghighat, Umair bin Waheed, George Em Karniadakis
2023	J	`jnl`	A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions. CoRR Michael Penwarden, Ameya D. Jagtap, Shandian Zhe, George Em Karniadakis, Robert M. Kirby
2023	J	`jnl`	A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions. J. Comput. Phys. Michael Penwarden, Ameya D. Jagtap, Shandian Zhe, George Em Karniadakis, Robert M. Kirby
2023	J	`jnl`	AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification. CoRR Nazanin Ahmadi Daryakenari, Mario De Florio, Khemraj Shukla, George Em Karniadakis
2023	J	`jnl`	AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression. CoRR Mario De Florio, Ioannis G. Kevrekidis, George Em Karniadakis
2023	J	`jnl`	Accelerating gradient descent and Adam via fractional gradients. Neural Networks Yeonjong Shin, Jérôme Darbon, George Em Karniadakis
2023	J	`jnl`	Artificial to Spiking Neural Networks Conversion for Scientific Machine Learning. CoRR Qian Zhang, Chenxi Wu, Adar Kahana, Youngeun Kim, Yuhang Li, George Em Karniadakis, Priyadarshini Panda
2023	J	`jnl`	Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology. Eng. Appl. Artif. Intell. Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi
2023	J	`jnl`	Bi-orthogonal fPINN: A physics-informed neural network method for solving time-dependent stochastic fractional PDEs. CoRR Lei Ma, Rong xin Li, Fanhai Zeng, Ling Guo, George Em Karniadakis
2023	J	`jnl`	Bias-Variance Trade-off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs. CoRR Zheyuan Hu, Zhouhao Yang, Yezhen Wang, George Em Karniadakis, Kenji Kawaguchi
2023	J	`jnl`	Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs. CoRR Elham Kiyani, Mahdi Kooshkbaghi, Khemraj Shukla, Rahul Babu Koneru, Zhen Li, Luis Bravo, Anindya Ghoshal, George Em Karniadakis, Mikko Karttunen
2023	J	`jnl`	Correcting model misspecification in physics-informed neural networks (PINNs). CoRR Zongren Zou, Xuhui Meng, George Em Karniadakis
2023	J	`jnl`	CrunchGPT: A chatGPT assisted framework for scientific machine learning. CoRR Varun Kumar, Leonard Gleyzer, Adar Kahana, Khemraj Shukla, George Em Karniadakis
2023	J	`jnl`	DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networks. CoRR Katarzyna Michalowska, Somdatta Goswami, George Em Karniadakis, Signe Riemer-Sørensen
2023	J	`jnl`	Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils. CoRR Khemraj Shukla, Vivek Oommen, Ahmad Peyvan, Michael Penwarden, Luis Bravo, Anindya Ghoshal, Robert M. Kirby, George Em Karniadakis
2023	J	`jnl`	DiTTO: Diffusion-inspired Temporal Transformer Operator. CoRR Oded Ovadia, Eli Turkel, Adar Kahana, George Em Karniadakis
2023	J	`jnl`	Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression. CoRR Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis
2023	J	`jnl`	Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies. CoRR Alena Kopanicáková, Hardik Kothari, George Em Karniadakis, Rolf Krause
2023	J	`jnl`	GPT vs Human for Scientific Reviews: A Dual Source Review on Applications of ChatGPT in Science. CoRR Chenxi Wu, Alan John Varghese, Vivek Oommen, George Em Karniadakis
2023	J	`jnl`	Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks. CoRR Zheyuan Hu, Zekun Shi, George Em Karniadakis, Kenji Kawaguchi
2023	J	`jnl`	Instability-wave prediction in hypersonic boundary layers with physics-informed neural operators. J. Comput. Sci. Yue Hao, Patricio Clark Di Leoni, Olaf Marxen, Charles Meneveau, George Em Karniadakis, Tamer A. Zaki
2023	J	`jnl`	L-HYDRA: Multi-Head Physics-Informed Neural Networks. CoRR Zongren Zou, George Em Karniadakis
2023	J	`jnl`	LNO: Laplace Neural Operator for Solving Differential Equations. CoRR Qianying Cao, Somdatta Goswami, George Em Karniadakis
2023	J	`jnl`	Learning Poisson Systems and Trajectories of Autonomous Systems via Poisson Neural Networks. IEEE Trans. Neural Networks Learn. Syst. Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis, George Em Karniadakis
2023	J	`jnl`	Learning bias corrections for climate models using deep neural operators. CoRR Aniruddha Bora, Khemraj Shukla, Shixuan Zhang, Bryce E. Harrop, L. Ruby Leung, George Em Karniadakis
2023	J	`jnl`	Learning characteristic parameters and dynamics of centrifugal pumps under multi-phase flow using physics-informed neural networks. CoRR Felipe de Castro Teixeira Carvalho, Kamaljyoti Nath, Alberto Luiz Serpa, George Em Karniadakis
2023	J	`jnl`	Learning in latent spaces improves the predictive accuracy of deep neural operators. CoRR Katiana Kontolati, Somdatta Goswami, George Em Karniadakis, Michael D. Shields
2023	J	`jnl`	Learning stiff chemical kinetics using extended deep neural operators. CoRR Somdatta Goswami, Ameya D. Jagtap, Hessam Babaee, Bryan T. Susi, George Em Karniadakis
2023	J	`jnl`	Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning. CoRR Paula X. Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis
2023	J	`jnl`	Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems. CoRR Paula X. Chen, Tingwei Meng, Zongren Zou, Jérôme Darbon, George Em Karniadakis
2023	J	`jnl`	Mechanical Characterization and Inverse Design of Stochastic Architected Metamaterials Using Neural Operators. CoRR Hanxun Jin, Enrui Zhang, Boyu Zhang, Sridhar Krishnaswamy, George Em Karniadakis, Horacio D. Espinosa
2023	J	`jnl`	Multifidelity deep operator networks for data-driven and physics-informed problems. J. Comput. Phys. Amanda A. Howard, Mauro Perego, George Em Karniadakis, Panos Stinis
2023	J	`jnl`	Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks. CoRR Katarzyna Michalowska, Somdatta Goswami, George Em Karniadakis, Signe Riemer-Sørensen
2023	J	`jnl`	Neural operator prediction of linear instability waves in high-speed boundary layers. J. Comput. Phys. Patricio Clark Di Leoni, Lu Lu, Charles Meneveau, George Em Karniadakis, Tamer A. Zaki
2023	J	`jnl`	On the influence of over-parameterization in manifold based surrogates and deep neural operators. J. Comput. Phys. Katiana Kontolati, Somdatta Goswami, Michael D. Shields, George Em Karniadakis
2023	J	`jnl`	Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions. CoRR Bin Lin, Zhiping Mao, Zhicheng Wang, George Em Karniadakis
2023	J	`jnl`	Physics-Informed Computer Vision: A Review and Perspectives. CoRR Chayan Banerjee, Kien Nguyen, Clinton Fookes, George Em Karniadakis
2023	J	`jnl`	Physics-informed neural networks for predicting gas flow dynamics and unknown parameters in diesel engines. CoRR Kamaljyoti Nath, Xuhui Meng, Daniel J. Smith, George Em Karniadakis
2023	J	`jnl`	Residual-based attention and connection to information bottleneck theory in PINNs. CoRR Sokratis J. Anagnostopoulos, Juan Diego Toscano, Nikolaos Stergiopulos, George Em Karniadakis
2023	J	`jnl`	Rethinking materials simulations: Blending direct numerical simulations with neural operators. CoRR Vivek Oommen, Khemraj Shukla, Saaketh Desai, Rémi Dingreville, George Em Karniadakis
2023	J	`jnl`	Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators. CoRR Nikolas Borrel-Jensen, Somdatta Goswami, Allan P. Engsig-Karup, George Em Karniadakis, Cheol-Ho Jeong
2023	J	`jnl`	Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models. CoRR Simin Shekarpaz, Fanhai Zeng, George Em Karniadakis
2023	J	`jnl`	Tackling the Curse of Dimensionality with Physics-Informed Neural Networks. CoRR Zheyuan Hu, Khemraj Shukla, George Em Karniadakis, Kenji Kawaguchi
2023	J	`jnl`	TransformerG2G: Adaptive time-stepping for learning temporal graph embeddings using transformers. CoRR Alan John Varghese, Aniruddha Bora, Mengjia Xu, George Em Karniadakis
2023	J	`jnl`	Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators. CoRR Zongren Zou, Xuhui Meng, George Em Karniadakis
2023	J	`jnl`	Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons. J. Comput. Phys. Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, George Em Karniadakis
2023	J	`jnl`	ViTO: Vision Transformer-Operator. CoRR Oded Ovadia, Adar Kahana, Panos Stinis, Eli Turkel, George Em Karniadakis
2022	J	`jnl`	A Hybrid Iterative Numerical Transferable Solver (HINTS) for PDEs Based on Deep Operator Network and Relaxation Methods. CoRR Enrui Zhang, Adar Kahana, Eli Turkel, Rishikesh Ranade, Jay Pathak, George Em Karniadakis
2022	J	`jnl`	A Physics-Informed Neural Network for Quantifying the Microstructural Properties of Polycrystalline Nickel Using Ultrasound Data: A promising approach for solving inverse problems. IEEE Signal Process. Mag. Khemraj Shukla, Ameya D. Jagtap, James L. Blackshire, Daniel Sparkman, George Em Karniadakis
2022	J	`jnl`	A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition. J. Comput. Phys. Yue Zhao, Zhiping Mao, Ling Guo, Yifa Tang, George Em Karniadakis
2022	J	`jnl`	Approximation rates of DeepONets for learning operators arising from advection-diffusion equations. Neural Networks Beichuan Deng, Yeonjong Shin, Lu Lu, Zhongqiang Zhang, George Em Karniadakis
2022	J	`jnl`	Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology. CoRR Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi
2022	J	`jnl`	Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems. CoRR Kevin Linka, Amelie Schäfer, Xuhui Meng, Zongren Zou, George Em Karniadakis, Ellen Kuhl
2022	J	`jnl`	Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions. Neurocomputing Ameya D. Jagtap, Yeonjong Shin, Kenji Kawaguchi, George Em Karniadakis
2022	J	`jnl`	Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre-Green-Naghdi equations. CoRR Ameya D. Jagtap, Dimitrios Mitsotakis, George Em Karniadakis
2022	J	`jnl`	Deep transfer learning for partial differential equations under conditional shift with DeepONet. CoRR Somdatta Goswami, Katiana Kontolati, Michael D. Shields, George Em Karniadakis
2022	J	`jnl`	Deep transfer operator learning for partial differential equations under conditional shift. Nat. Mac. Intell. Somdatta Goswami, Katiana Kontolati, Michael D. Shields, George Em Karniadakis
2022	J	`jnl`	Discovering and forecasting extreme events via active learning in neural operators. CoRR Ethan Pickering, George Em Karniadakis, Themistoklis P. Sapsis
2022	J	`jnl`	Discovering and forecasting extreme events via active learning in neural operators. Nat. Comput. Sci. Ethan Pickering, Stephen Guth, George Em Karniadakis, Themistoklis P. Sapsis
2022	J	`jnl`	Fractional SEIR Model and Data-Driven Predictions of COVID-19 Dynamics of Omicron Variant. CoRR Min Cai, George Em Karniadakis, Changpin Li
2022	J	`jnl`	Function Regression using Spiking DeepONet. CoRR Adar Kahana, Qian Zhang, Leonard Gleyzer, George Em Karniadakis
2022	J	`jnl`	G2Φnet: Relating Genotype and Biomechanical Phenotype of Tissues with Deep Learning. CoRR Enrui Zhang, Bart Spronck, Jay D. Humphrey, George Em Karniadakis
2022	J	`jnl`	G2Φnet: Relating genotype and biomechanical phenotype of tissues with deep learning. PLoS Comput. Biol. Enrui Zhang, Bart Spronck, Jay D. Humphrey, George Em Karniadakis
2022	J	`jnl`	High-Order Methods for Hypersonic Flows with Strong Shocks and Real Chemistry. CoRR Ahmad Peyvan, Khemraj Shukla, Jesse Chan, George Em Karniadakis
2022	J	`jnl`	How important are activation functions in regression and classification? A survey, performance comparison, and future directions. CoRR Ameya D. Jagtap, George Em Karniadakis
2022	J	`jnl`	Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems. CoRR Minglang Yin, Enrui Zhang, Yue Yu, George Em Karniadakis
2022	J	`jnl`	Learning functional priors and posteriors from data and physics. J. Comput. Phys. Xuhui Meng, Liu Yang, Zhiping Mao, José del Águila Ferrandis, George Em Karniadakis
2022	J	`jnl`	Learning two-phase microstructure evolution using neural operators and autoencoder architectures. CoRR Vivek Oommen, Khemraj Shukla, Somdatta Goswami, Rémi Dingreville, George Em Karniadakis
2022	J	`jnl`	Machine Learning in Heterogeneous Porous Materials. CoRR Marta D'Elia, Hang Deng, Cedric G. Fraces, Krishna C. Garikipati, Lori Graham-Brady, Amanda A. Howard, George Em Karniadakis, Vahid Keshavarzzadeh, Robert M. Kirby, J. Nathan Kutz, Chunhui Li, Xing Liu, Hannah Lu, Pania Newell, Daniel O'Malley, Masa Prodanovic, Gowri Srinivasan, Alexandre M. Tartakovsky, Daniel M. Tartakovsky, Hamdi A. Tchelepi, Bozo Vazic, Hari S. Viswanathan, Hongkyu Yoon, Piotr Zarzycki
2022	J	`jnl`	Meta-learning PINN loss functions. J. Comput. Phys. Apostolos F. Psaros, Kenji Kawaguchi, George Em Karniadakis
2022	J	`jnl`	Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms. CoRR Somdatta Goswami, David S. Li, Bruno V. Rego, Marcos Latorre, Jay D. Humphrey, George Em Karniadakis
2022	J	`jnl`	NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators. CoRR Zongren Zou, Xuhui Meng, Apostolos F. Psaros, George Em Karniadakis
2022	J	`jnl`	On the Geometry Transferability of the Hybrid Iterative Numerical Solver for Differential Equations. CoRR Adar Kahana, Enrui Zhang, Somdatta Goswami, George Em Karniadakis, Rishikesh Ranade, Jay Pathak
2022	J	`jnl`	On the influence of over-parameterization in manifold based surrogates and deep neural operators. CoRR Katiana Kontolati, Somdatta Goswami, Michael D. Shields, George Em Karniadakis
2022	J	`jnl`	Physics-Informed Deep Neural Operator Networks. CoRR Somdatta Goswami, Aniruddha Bora, Yue Yu, George Em Karniadakis
2022	J	`jnl`	Physics-informed neural networks for inverse problems in supersonic flows. CoRR Ameya D. Jagtap, Zhiping Mao, Nikolaus A. Adams, George Em Karniadakis
2022	J	`jnl`	Physics-informed neural networks for inverse problems in supersonic flows. J. Comput. Phys. Ameya D. Jagtap, Zhiping Mao, Nikolaus A. Adams, George Em Karniadakis
2022	J	`jnl`	Potential Flow Generator With L IEEE Trans. Neural Networks Learn. Syst. Liu Yang, George Em Karniadakis
2022	J	`jnl`	Reliable extrapolation of deep neural operators informed by physics or sparse observations. CoRR Min Zhu, Handi Zhang, Anran Jiao, George Em Karniadakis, Lu Lu
2022	J	`jnl`	SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations. CoRR Qian Zhang, Adar Kahana, George Em Karniadakis, Panos Stinis
2022	J	`jnl`	Scalable algorithms for physics-informed neural and graph networks. CoRR Khemraj Shukla, Mengjia Xu, Nathaniel Trask, George Em Karniadakis
2022	J	`jnl`	SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems. CoRR Tingwei Meng, Zhen Zhang, Jérôme Darbon, George Em Karniadakis
2022	J	`jnl`	Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks. CoRR Mitchell Daneker, Zhen Zhang, George Em Karniadakis, Lu Lu
2022	J	`jnl`	Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons. CoRR Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, George Em Karniadakis
2022	J	`jnl`	When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization? SIAM J. Sci. Comput. Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi
2021	J	`jnl`	A Caputo fractional derivative-based algorithm for optimization. CoRR Yeonjong Shin, Jérôme Darbon, George Em Karniadakis
2021	J	`jnl`	A phase-field method for boiling heat transfer. J. Comput. Phys. Zhicheng Wang, Xiaoning Zheng, Chryssostomos Chryssostomidis, George Em Karniadakis
2021	J	`jnl`	AOSLO-net: A deep learning-based method for automatic segmentation of retinal microaneurysms from adaptive optics scanning laser ophthalmoscope images. CoRR Qian Zhang, Konstantina Sampani, Mengjia Xu, Shengze Cai, Yixiang Deng, He Li, Jennifer K. Sun, George Em Karniadakis
2021	J	`jnl`	Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows. J. Comput. Phys. Lifei Zhao, Zhen Li, Zhicheng Wang, Bruce Caswell, Jie Ouyang, George Em Karniadakis
2021	J	`jnl`	An open-source parallel code for computing the spectral fractional Laplacian on 3D complex geometry domains. Comput. Phys. Commun. Max Carlson, Xiaoning Zheng, Hari Sundar, George Em Karniadakis, Robert M. Kirby
2021	J	`jnl`	B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data. J. Comput. Phys. Liu Yang, Xuhui Meng, George Em Karniadakis
2021	J	`jnl`	Convergence rate of DeepONets for learning operators arising from advection-diffusion equations. CoRR Beichuan Deng, Yeonjong Shin, Lu Lu, Zhongqiang Zhang, George Em Karniadakis
2021	J	`jnl`	Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions. CoRR Ameya D. Jagtap, Yeonjong Shin, Kenji Kawaguchi, George Em Karniadakis
2021	J	`jnl`	Deep transfer learning and data augmentation improve glucose levels prediction in type 2 diabetes patients. npj Digit. Medicine Yixiang Deng, Lu Lu, Laura Aponte, Angeliki M. Angelidi, Vera Novak, George Em Karniadakis, Christos S. Mantzoros
2021	J	`jnl`	DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators. J. Comput. Phys. Zhiping Mao, Lu Lu, Olaf Marxen, Tamer A. Zaki, George Em Karniadakis
2021	J	`jnl`	DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks. J. Comput. Phys. Shengze Cai, Zhicheng Wang, Lu Lu, Tamer A. Zaki, George Em Karniadakis
2021	J	`jnl`	DeepXDE: A Deep Learning Library for Solving Differential Equations. SIAM Rev. Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis
2021	J	`jnl`	DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs. CoRR Mengjia Xu, Apoorva Vikram Singh, George Em Karniadakis
2021	J	`jnl`	Error estimates for DeepOnets: A deep learning framework in infinite dimensions. CoRR Samuel Lanthaler, Siddhartha Mishra, George Em Karniadakis
2021	J	`jnl`	Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation. CoRR Min Cai, Ehsan Kharazmi, Changpin Li, George Em Karniadakis
2021	J	`jnl`	GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems. CoRR Zhen Zhang, Yeonjong Shin, George Em Karniadakis
2021	J	`jnl`	Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. CoRR Jeremy Yu, Lu Lu, Xuhui Meng, George Em Karniadakis
2021	J	`jnl`	How the spleen reshapes and retains young and old red blood cells: A computational investigation. PLoS Comput. Biol. He Li, Zixiang Leonardo Liu, Lu Lu, Pierre Buffet, George Em Karniadakis
2021	J	`jnl`	Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks. Nat. Comput. Sci. Ehsan Kharazmi, Min Cai, Xiaoning Zheng, Zhen Zhang, Guang Lin, George Em Karniadakis
2021	J	`jnl`	Learning Functional Priors and Posteriors from Data and Physics. CoRR Xuhui Meng, Liu Yang, Zhiping Mao, José del Águila Ferrandis, George Em Karniadakis
2021	J	`jnl`	Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nat. Mach. Intell. Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, George Em Karniadakis
2021	J	`jnl`	Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates. CoRR Liu Yang, Tingwei Meng, George Em Karniadakis
2021	J	`jnl`	Meta-learning PINN loss functions. CoRR Apostolos F. Psaros, Kenji Kawaguchi, George Em Karniadakis
2021	J	`jnl`	Multi-fidelity Bayesian neural networks: Algorithms and applications. J. Comput. Phys. Xuhui Meng, Hessam Babaee, George Em Karniadakis
2021	J	`jnl`	NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations. J. Comput. Phys. Xiaowei Jin, Shengze Cai, Hui Li, George Em Karniadakis
2021	J	`jnl`	Parallel Physics-Informed Neural Networks via Domain Decomposition. CoRR Khemraj Shukla, Ameya D. Jagtap, George Em Karniadakis
2021	J	`jnl`	Parallel physics-informed neural networks via domain decomposition. J. Comput. Phys. Khemraj Shukla, Ameya D. Jagtap, George Em Karniadakis
2021	J	`jnl`	Physics-informed neural networks (PINNs) for fluid mechanics: A review. CoRR Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin, George Em Karniadakis
2021	J	`jnl`	Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation. J. Comput. Phys. Qin Lou, Xuhui Meng, George Em Karniadakis
2021	J	`jnl`	Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural network. CoRR Minglang Yin, Ehsan Ban, Bruno V. Rego, Enrui Zhang, Cristina Cavinato, Jay D. Humphrey, George Em Karniadakis
2021	J	`jnl`	Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-Informed Neural Networks. SIAM J. Sci. Comput. Xiaoli Chen, Liu Yang, Jinqiao Duan, George Em Karniadakis
2021	J	`jnl`	Variable-Order Fractional Models for Wall-Bounded Turbulent Flows. Entropy Fangying Song, George Em Karniadakis
2021	J	`jnl`	When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization? CoRR Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis, Kenji Kawaguchi
2020	J	`jnl`	A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems. J. Comput. Phys. Xuhui Meng, George Em Karniadakis
2020	J	`jnl`	A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations. J. Comput. Phys. Hui Zhang, Xiaoyun Jiang, Fanhai Zeng, George Em Karniadakis
2020	J	`jnl`	Adaptive activation functions accelerate convergence in deep and physics-informed neural networks. J. Comput. Phys. Ameya D. Jagtap, Kenji Kawaguchi, George Em Karniadakis
2020	J	`jnl`	B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data. CoRR Liu Yang, Xuhui Meng, George Em Karniadakis
2020	J	`jnl`	Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations. CoRR Hui Zhang, Fanhai Zeng, Xiaoyun Jiang, George Em Karniadakis
2020	—	`conf`	DeepXDE: A Deep Learning Library for Solving Differential Equations. AAAI Spring Symposium: MLPS Lu Lu, Xuhui Meng, Zhiping Mao, George Em Karniadakis
2020	J	`jnl`	Error estimates of residual minimization using neural networks for linear PDEs. CoRR Yeonjong Shin, Zhongqiang Zhang, George Em Karniadakis
2020	J	`jnl`	Generative Ensemble-Regression: Learning Stochastic Dynamics from Discrete Particle Ensemble Observations. CoRR Liu Yang, Constantinos Daskalakis, George Em Karniadakis
2020	J	`jnl`	Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks. CoRR Pengzhan Jin, Zhen Zhang, Ioannis G. Kevrekidis, George Em Karniadakis
2020	J	`jnl`	Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks. SIAM J. Sci. Comput. Dongkun Zhang, Ling Guo, George Em Karniadakis
2020	J	`jnl`	Multi-fidelity Bayesian Neural Networks: Algorithms and Applications. CoRR Xuhui Meng, Hessam Babaee, George Em Karniadakis
2020	J	`jnl`	On the Convergence and generalization of Physics Informed Neural Networks. CoRR Yeonjong Shin, Jérôme Darbon, George Em Karniadakis
2020	J	`jnl`	Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations. SIAM J. Sci. Comput. Liu Yang, Dongkun Zhang, George Em Karniadakis
2020	J	`jnl`	Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging. CoRR Enrui Zhang, Minglang Yin, George Em Karniadakis
2020	J	`jnl`	Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks. CoRR Khemraj Shukla, Patricio Clark Di Leoni, James L. Blackshire, Daniel Sparkman, George Em Karniadakis
2020	J	`jnl`	Physics-informed semantic inpainting: Application to geostatistical modeling. J. Comput. Phys. Qiang Zheng, Lingzao Zeng, George Em Karniadakis
2020	J	`jnl`	Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness. Neural Networks Pengzhan Jin, Lu Lu, Yifa Tang, George Em Karniadakis
2020	J	`jnl`	Reinforcement Learning for Active Flow Control in Experiments. CoRR Dixia Fan, Liu Yang, Michael S. Triantafyllou, George Em Karniadakis
2020	J	`jnl`	Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks. CoRR Xiaoli Chen, Liu Yang, Jinqiao Duan, George Em Karniadakis
2020	J	`jnl`	SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems. Neural Networks Pengzhan Jin, Zhen Zhang, Aiqing Zhu, Yifa Tang, George Em Karniadakis
2020	J	`jnl`	Symplectic networks: Intrinsic structure-preserving networks for identifying Hamiltonian systems. CoRR Pengzhan Jin, Aiqing Zhu, George Em Karniadakis, Yifa Tang
2020	J	`jnl`	Systems biology informed deep learning for inferring parameters and hidden dynamics. PLoS Comput. Biol. Alireza Yazdani, Lu Lu, Maziar Raissi, George Em Karniadakis
2020	J	`jnl`	What is the fractional Laplacian? A comparative review with new results. J. Comput. Phys. Anna Lischke, Guofei Pang, Mamikon A. Gulian, Fangying Song, Christian Glusa, Xiaoning Zheng, Zhiping Mao, Wei Cai, Mark M. Meerschaert, Mark Ainsworth, George Em Karniadakis
2020	J	`jnl`	hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition. CoRR Ehsan Kharazmi, Zhongqiang Zhang, George Em Karniadakis
2019	J	`jnl`	A stabilized phase-field method for two-phase flow at high Reynolds number and large density/viscosity ratio. J. Comput. Phys. Zhicheng Wang, Suchuan Dong, Michael S. Triantafyllou, Yiannis Constantinides, George Em Karniadakis
2019	J	`jnl`	DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. CoRR Lu Lu, Pengzhan Jin, George Em Karniadakis
2019	J	`jnl`	Efficient Multistep Methods for Tempered Fractional Calculus: Algorithms and Simulations. SIAM J. Sci. Comput. Ling Guo, Fanhai Zeng, Ian W. Turner, Kevin Burrage, George Em Karniadakis
2019	J	`jnl`	Learning and Meta-Learning of Stochastic Advection-Diffusion-Reaction Systems from Sparse Measurements. CoRR Xiaoli Chen, Jinqiao Duan, George Em Karniadakis
2019	J	`jnl`	Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states. CoRR José del Águila Ferrandis, Michael S. Triantafyllou, Chryssostomos Chryssostomidis, George Em Karniadakis
2019	J	`jnl`	PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs. CoRR Xuhui Meng, Zhen Li, Dongkun Zhang, George Em Karniadakis
2019	J	`jnl`	Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems. J. Comput. Phys. Dongkun Zhang, Lu Lu, Ling Guo, George Em Karniadakis
2019	J	`jnl`	Variational Physics-Informed Neural Networks For Solving Partial Differential Equations. CoRR Ehsan Kharazmi, Zhongqiang Zhang, George Em Karniadakis
2019	J	`jnl`	fPINNs: Fractional Physics-Informed Neural Networks. SIAM J. Sci. Comput. Guofei Pang, Lu Lu, George Em Karniadakis
2012	—	`conf`	Multiscale simulations of blood-flow: from a platelet to an artery. XSEDE Leopold Grinberg, Mingge Deng, Huan Lei, Joseph A. Insley, George Em Karniadakis
1997	—	`conf`	hpDevelopment of a Parallel Unstructured Spectral/ Method for Unsteady Fluid Dynamics. Parallel CFD Spencer J. Sherwin, Constantinos Evangelinos, H. Tufo, George Em Karniadakis