Fractional modeling of viscoelasticity in 3D cerebral arteries and aneurysms. - Yue Yu; Paris Perdikaris; George E. Karniadakis (J. Comput. Phys., 2016)

Visualizing multiphysics, fluid-structure interaction phenomena in intracranial aneurysms. - Paris Perdikaris; Joseph A. Insley; Leopold Grinberg; Yue Yu; Michael E. Papka; George E. Karniadakis (Parallel Comput., 2016)

Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets. - Paris Perdikaris; Daniele Venturi 002; George E. Karniadakis (SIAM J. Sci. Comput., 2016)

Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations. - Maziar Raissi; Paris Perdikaris; George E. Karniadakis (CoRR, 2017)

Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations. - Maziar Raissi; Paris Perdikaris; George E. Karniadakis (CoRR, 2017)

Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations. - Maziar Raissi; Paris Perdikaris; George E. Karniadakis (CoRR, 2017)

Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization. - Guofei Pang; Paris Perdikaris; Wei Cai 003; George E. Karniadakis (J. Comput. Phys., 2017)

Multi-fidelity Gaussian process regression for prediction of random fields. - Lucia Parussini; Daniele Venturi 002; Paris Perdikaris; George E. Karniadakis (J. Comput. Phys., 2017)

Inferring solutions of differential equations using noisy multi-fidelity data. - Maziar Raissi; Paris Perdikaris; George E. Karniadakis (J. Comput. Phys., 2017)

Machine learning of linear differential equations using Gaussian processes. - Maziar Raissi; Paris Perdikaris; George E. Karniadakis (J. Comput. Phys., 2017)

Physics-informed deep generative models. - Yibo Yang; Paris Perdikaris (CoRR, 2018)

Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations. - Maziar Raissi; Paris Perdikaris; George E. Karniadakis (SIAM J. Sci. Comput., 2018)

Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems. - Yibo Yang; Paris Perdikaris (CoRR, 2019)

A comparative study of physics-informed neural network models for learning unknown dynamics and constitutive relations. - Ramakrishna Tipireddy; Paris Perdikaris; Panos Stinis; Alexandre M. Tartakovsky (CoRR, 2019)

Multi-fidelity classification using Gaussian processes: accelerating the prediction of large-scale computational models. - Francisco Sahli Costabal; Paris Perdikaris; Ellen Kuhl; Daniel E. Hurtado (CoRR, 2019)

Machine learning in cardiovascular flows modeling: Predicting pulse wave propagation from non-invasive clinical measurements using physics-informed deep learning. - Georgios Kissas; Yibo Yang; Eileen Hwuang; Walter R. Witschey; John A. Detre; Paris Perdikaris (CoRR, 2019)

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. - Maziar Raissi; Paris Perdikaris; George E. Karniadakis (J. Comput. Phys., 2019)

Adversarial uncertainty quantification in physics-informed neural networks. - Yibo Yang; Paris Perdikaris (J. Comput. Phys., 2019)

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data. - Yinhao Zhu; Nicholas Zabaras; Phaedon-Stelios Koutsourelakis; Paris Perdikaris (J. Comput. Phys., 2019)

Integrating machine learning and multiscale modeling - perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences. - Mark S. Alber; Adrian Buganza Tepole; William R. Cannon; Suvranu De; Salvador Dura-Bernal; Krishna C. Garikipati; George E. Karniadakis; William W. Lytton; Paris Perdikaris; Linda R. Petzold; Ellen Kuhl (npj Digit. Medicine, 2019)

Machine Learning of Space-Fractional Differential Equations. - Mamikon A. Gulian; Maziar Raissi; Paris Perdikaris; George E. Karniadakis (SIAM J. Sci. Comput., 2019)

Understanding and mitigating gradient pathologies in physics-informed neural networks. - Sifan Wang; Yujun Teng; Paris Perdikaris (CoRR, 2020)

Exact artificial boundary conditions of 1D semi-discretized peridynamics. - Songsong Ji; Gang Pang; Jiwei Zhang 002; Yibo Yang; Paris Perdikaris (CoRR, 2020)

Bayesian differential programming for robust systems identification under uncertainty. - Yibo Yang; Mohamed Aziz Bhouri; Paris Perdikaris (CoRR, 2020)

Learning Unknown Physics of non-Newtonian Fluids. - Brandon Reyes; Amanda A. Howard; Paris Perdikaris; Alexandre M. Tartakovsky (CoRR, 2020)

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks. - Sifan Wang; Hanwen Wang; Paris Perdikaris (CoRR, 2020)

Learning Atrial Fiber Orientations and Conductivity Tensors from Intracardiac Maps Using Physics-Informed Neural Networks. - Thomas Grandits; Simone Pezzuto; Francisco Sahli Costabal; Paris Perdikaris; Thomas Pock; Gernot Plank; Rolf Krause (FIMH, 2021)

Physics-Guided AI for Large-Scale Spatiotemporal Data. - Rose Yu; Paris Perdikaris; Anuj Karpatne (KDD, 2021)

Output-Weighted Sampling for Multi-Armed Bandits with Extreme Payoffs. - Yibo Yang; Antoine Blanchard; Themistoklis P. Sapsis; Paris Perdikaris (CoRR, 2021)

Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data. - Mohamed Aziz Bhouri; Paris Perdikaris (CoRR, 2021)

Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. - Sifan Wang; Hanwen Wang; Paris Perdikaris (CoRR, 2021)

Fast PDE-constrained optimization via self-supervised operator learning. - Sifan Wang; Mohamed Aziz Bhouri; Paris Perdikaris (CoRR, 2021)

Fast characterization of inducible regions of atrial fibrillation models with multi-fidelity Gaussian process classification. - Lia Gander; Simone Pezzuto; Ali Gharaviri; Rolf Krause; Paris Perdikaris; Francisco Sahli Costabal (CoRR, 2021)

Deep learning of free boundary and Stefan problems. - Sifan Wang; Paris Perdikaris (J. Comput. Phys., 2021)

Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks. - Sifan Wang; Yujun Teng; Paris Perdikaris (SIAM J. Sci. Comput., 2021)

Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior. - Thomas Beckers 001; Jacob H. Seidman; Paris Perdikaris; George J. Pappas (CDC, 2022)

NOMAD: Nonlinear Manifold Decoders for Operator Learning. - Jacob H. Seidman; Georgios Kissas; Paris Perdikaris; George J. Pappas (NeurIPS, 2022)

Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors. - Yibo Yang; Georgios Kissas; Paris Perdikaris (CoRR, 2022)

Learning cardiac activation maps from 12-lead ECG with multi-fidelity Bayesian optimization on manifolds. - Simone Pezzuto; Paris Perdikaris; Francisco Sahli Costabal (CoRR, 2022)

Respecting causality is all you need for training physics-informed neural networks. - Sifan Wang; Shyam Sankaran; Paris Perdikaris (CoRR, 2022)

Rethinking the Importance of Sampling in Physics-informed Neural Networks. - Arka Daw; Jie Bu; Sifan Wang; Paris Perdikaris; Anuj Karpatne (CoRR, 2022)

Semi-supervised Invertible DeepONets for Bayesian Inverse Problems. - Sebastian Kaltenbach; Paris Perdikaris; Phaedon-Stelios Koutsourelakis (CoRR, 2022)

Random Weight Factorization Improves the Training of Continuous Neural Representations. - Sifan Wang; Hanwen Wang; Jacob H. Seidman; Paris Perdikaris (CoRR, 2022)

Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps. - Carlos Ruiz Herrera; Thomas Grandits; Gernot Plank; Paris Perdikaris; Francisco Sahli Costabal; Simone Pezzuto (Eng. Comput., 2022)

When and why PINNs fail to train: A neural tangent kernel perspective. - Sifan Wang; Xinling Yu; Paris Perdikaris (J. Comput. Phys., 2022)

Learning Operators with Coupled Attention. - Georgios Kissas; Jacob H. Seidman; Leonardo Ferreira Guilhoto; Victor M. Preciado; George J. Pappas; Paris Perdikaris (J. Mach. Learn. Res., 2022)

Improved Architectures and Training Algorithms for Deep Operator Networks. - Sifan Wang; Hanwen Wang; Paris Perdikaris (J. Sci. Comput., 2022)

Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling. - Arka Daw; Jie Bu; Sifan Wang; Paris Perdikaris; Anuj Karpatne (ICML, 2023)

Variational Autoencoding Neural Operators. - Jacob H. Seidman; Georgios Kissas; George J. Pappas; Paris Perdikaris (ICML, 2023)

PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers. - Phillip Lippe; Bas Veeling; Paris Perdikaris; Richard E. Turner; Johannes Brandstetter (NeurIPS, 2023)

Scalable Bayesian optimization with high-dimensional outputs using randomized prior networks. - Mohamed Aziz Bhouri; Michael Joly; Robert Yu; Soumalya Sarkar; Paris Perdikaris (CoRR, 2023)

Ensemble learning for Physics Informed Neural Networks: a Gradient Boosting approach. - Zhiwei Fang; Sifan Wang; Paris Perdikaris (CoRR, 2023)

PPDONet: Deep Operator Networks for Fast Prediction of Steady-State Solutions in Disk-Planet Systems. - Shunyuan Mao; Ruobing Dong; Lu Lu; Kwang Moo Yi; Sifan Wang; Paris Perdikaris (CoRR, 2023)

An Expert's Guide to Training Physics-informed Neural Networks. - Sifan Wang; Shyam Sankaran; Hanwen Wang; Paris Perdikaris (CoRR, 2023)

Long-time integration of parametric evolution equations with physics-informed DeepONets. - Sifan Wang; Paris Perdikaris (J. Comput. Phys., 2023)

On conditional diffusion models for PDE simulations. - Aliaksandra Shysheya; Cristiana Diaconu; Federico Bergamin; Paris Perdikaris; José Miguel Hernández-Lobato; Richard E. Turner; Emile Mathieu (NeurIPS, 2024)

PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks. - Sifan Wang; Bowen Li; Yuhan Chen; Paris Perdikaris (CoRR, 2024)

Composite Bayesian Optimization In Function Spaces Using NEON - Neural Epistemic Operator Networks. - Leonardo Ferreira Guilhoto; Paris Perdikaris (CoRR, 2024)

Aurora: A Foundation Model of the Atmosphere. - Cristian Bodnar; Wessel P. Bruinsma; Ana Lucic; Megan Stanley; Johannes Brandstetter; Patrick Garvan; Maik Riechert; Jonathan A. Weyn; Haiyu Dong; Anna Vaughan; Jayesh K. Gupta; Kit Thambiratnam; et al. (CoRR, 2024)

Bridging Operator Learning and Conditioned Neural Fields: A Unifying Perspective. - Sifan Wang; Jacob H. Seidman; Shyam Sankaran; Hanwen Wang; George J. Pappas; Paris Perdikaris (CoRR, 2024)

Physics-Informed Neural Networks and Extensions. - Maziar Raissi; Paris Perdikaris; Nazanin Ahmadi Daryakenari; George Em Karniadakis (CoRR, 2024)

Disk2Planet: A Robust and Automated Machine Learning Tool for Parameter Inference in Disk-Planet Systems. - Shunyuan Mao; Ruobing Dong; Kwang Moo Yi; Lu Lu; Sifan Wang; Paris Perdikaris (CoRR, 2024)

Micrometer: Micromechanics Transformer for Predicting Mechanical Responses of Heterogeneous Materials. - Sifan Wang; Tong-Rui Liu; Shyam Sankaran; Paris Perdikaris (CoRR, 2024)

Score Neural Operator: A Generative Model for Learning and Generalizing Across Multiple Probability Distributions. - Xinyu Liao; Aoyang Qin; Jacob H. Seidman; Junqi Wang; Wei Wang; Paris Perdikaris (CoRR, 2024)

Δ-PINNs: Physics-informed neural networks on complex geometries. - Francisco Sahli Costabal; Simone Pezzuto; Paris Perdikaris (Eng. Appl. Artif. Intell., 2024)

Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries. - Zhiwei Fang; Sifan Wang; Paris Perdikaris (Neural Comput., 2024)

Deep Learning Alternatives Of The Kolmogorov Superposition Theorem. - Leonardo Ferreira Guilhoto; Paris Perdikaris (ICLR, 2025)

CViT: Continuous Vision Transformer for Operator Learning. - Sifan Wang; Jacob H. Seidman; Shyam Sankaran; Hanwen Wang; George J. Pappas; Paris Perdikaris (ICLR, 2025)

A foundation model for the Earth system. - Cristian Bodnar; Wessel P. Bruinsma; Ana Lucic; Megan Stanley; Anna Allen; Johannes Brandstetter; Patrick Garvan; Maik Riechert; Jonathan A. Weyn; Haiyu Dong; Jayesh K. Gupta; Kit Thambiratnam; et al. (Nat., 2025)

Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective. - Sifan Wang; Ananyae Kumar Bhartari; Bowen Li; Paris Perdikaris (CoRR, 2025)

Active Learning Design: Modeling Force Output for Axisymmetric Soft Pneumatic Actuators. - Gregory M. Campbell; Gentian Muhaxheri; Leonardo Ferreira Guilhoto; Christian D. Santangelo; Paris Perdikaris; James H. Pikul; Mark Yim (CoRR, 2025)

PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulations. - Xinquan Huang; Paris Perdikaris (CoRR, 2025)

Simulating Three-dimensional Turbulence with Physics-informed Neural Networks. - Sifan Wang; Shyam Sankaran; Panos Stinis; Paris Perdikaris (CoRR, 2025)