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Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

SIAM journal on scientific computing, 2021-01, Vol.43 (5), p.A3055-A3081

2021

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Machine learning of linear differential equations using Gaussian processes

Journal of computational physics, 2017-11, Vol.348, p.683-693

2017

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Inferring solutions of differential equations using noisy multi-fidelity data

Journal of computational physics, 2017-04, Vol.335, p.736-746

2017

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Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations

SIAM journal on scientific computing, 2018-01, Vol.40 (1), p.A172-A198

2018

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Fractional-Order Viscoelasticity in One-Dimensional Blood Flow Models

Annals of biomedical engineering, 2014-05, Vol.42 (5), p.1012-1023

2014

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Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences

NPJ digital medicine, 2019-11, Vol.2 (1), p.115-115, Article 115

2019

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Machine Learning of Space-Fractional Differential Equations

SIAM journal on scientific computing, 2019-01, Vol.41 (4), p.A2485-A2509

2019

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Physics-Informed Neural Networks for Cardiac Activation Mapping

Frontiers in physics, 2020-02, Vol.8

2020

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Discovering variable fractional orders of advection–dispersion equations from field data using multi-fidelity Bayesian optimization

Journal of computational physics, 2017-11, Vol.348, p.694-714

2017

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Adaptive behavior and different thermal experiences of real people: A Bayesian neural network approach to thermal preference prediction and classification

Building and environment, 2021-07, Vol.198 (C), p.107875, Article 107875

2021

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Adversarial uncertainty quantification in physics-informed neural networks

Journal of computational physics, 2019-10, Vol.394 (C), p.136-152

2019

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Multiscale Modeling Meets Machine Learning: What Can We Learn?

Archives of computational methods in engineering, 2021-05, Vol.28 (3), p.1017-1037

2021

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Deep learning of free boundary and Stefan problems

Journal of computational physics, 2021-03, Vol.428 (C), p.109914, Article 109914

2021

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Long-time integration of parametric evolution equations with physics-informed DeepONets

Journal of computational physics, 2023-02, Vol.475, p.111855, Article 111855

2023

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When and why PINNs fail to train: A neural tangent kernel perspective

Journal of computational physics, 2022-01, Vol.449, p.110768, Article 110768

2022

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PPDONet: Deep Operator Networks for Fast Prediction of Steady-state Solutions in Disk–Planet Systems

Astrophysical journal. Letters, 2023-06, Vol.950 (2), p.L12

2023

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Fast Characterization of Inducible Regions of Atrial Fibrillation Models With Multi-Fidelity Gaussian Process Classification

Frontiers in physiology, 2022-03, Vol.13, p.757159-757159

2022

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Mechanistic Machine Learning: Theory, Methods, and Applications

Theoretical and applied mechanics letters, 2020-03, Vol.10 (3), p.141-142

2020

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On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

Computer methods in applied mechanics and engineering, 2021-10, Vol.384 (C), p.113938, Article 113938

2021

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Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems

Computational mechanics, 2019-08, Vol.64 (2), p.417-434

2019

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Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Science advances, 2021-10, Vol.7 (40), p.eabi8605-eabi8605

2021

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Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond

Journal of the Royal Society interface, 2016-05, Vol.13 (118)

2016

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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

Journal of computational physics, 2019-10, Vol.394, p.56-81

2019

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Deep learning of free boundary and Stefan problems

Journal of computational physics, 2020-10, Vol.428 (C)

2020

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Physics-Informed Neural Networks for Heat Transfer Problems

Journal of heat transfer, 2021-06, Vol.143 (6)

2021

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Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

Machine learning of linear differential equations using Gaussian processes

Inferring solutions of differential equations using noisy multi-fidelity data

Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations

Fractional-Order Viscoelasticity in One-Dimensional Blood Flow Models

Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences

Machine Learning of Space-Fractional Differential Equations

Physics-Informed Neural Networks for Cardiac Activation Mapping

Discovering variable fractional orders of advection–dispersion equations from field data using multi-fidelity Bayesian optimization

Adaptive behavior and different thermal experiences of real people: A Bayesian neural network approach to thermal preference prediction and classification

Adversarial uncertainty quantification in physics-informed neural networks

Multiscale Modeling Meets Machine Learning: What Can We Learn?

Deep learning of free boundary and Stefan problems

Long-time integration of parametric evolution equations with physics-informed DeepONets

When and why PINNs fail to train: A neural tangent kernel perspective

PPDONet: Deep Operator Networks for Fast Prediction of Steady-state Solutions in Disk–Planet Systems

Fast Characterization of Inducible Regions of Atrial Fibrillation Models With Multi-Fidelity Gaussian Process Classification

Mechanistic Machine Learning: Theory, Methods, and Applications

On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Model inversion via multi-fidelity Bayesian optimization: a new paradigm for parameter estimation in haemodynamics, and beyond

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

Deep learning of free boundary and Stefan problems

Physics-Informed Neural Networks for Heat Transfer Problems

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