
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness
The accuracy of deep learning, i.e., deep neural networks, can be charac...
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DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
While it is widely known that neural networks are universal approximator...
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Locally adaptive activation functions with slope recovery term for deep and physicsinformed neural networks
We propose two approaches of locally adaptive activation functions namel...
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BPINNs: Bayesian PhysicsInformed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
We propose a Bayesian physicsinformed neural network (BPINN) to solve ...
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Physicsinformed neural network for ultrasound nondestructive quantification of surface breaking cracks
We introduce an optimized physicsinformed neural network (PINN) trained...
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Physicsinformed semantic inpainting: Application to geostatistical modeling
A fundamental problem in geostatistical modeling is to infer the heterog...
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PPINN: Parareal PhysicsInformed Neural Network for timedependent PDEs
Physicsinformed neural networks (PINNs) encode physical conservation la...
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hpVPINNs: Variational PhysicsInformed Neural Networks With Domain Decomposition
We formulate a general framework for hpvariational physicsinformed neu...
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Learning in Modal Space: Solving TimeDependent Stochastic PDEs Using PhysicsInformed Neural Networks
One of the open problems in scientific computing is the longtime integr...
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Symplectic networks: Intrinsic structurepreserving networks for identifying Hamiltonian systems
This work presents a framework of constructing the neural networks prese...
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Trainability and Datadependent Initialization of Overparameterized ReLU Neural Networks
A neural network is said to be overspecified if its representational po...
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Hidden Fluid Mechanics: A NavierStokes Informed Deep Learning Framework for Assimilating Flow Visualization Data
We present hidden fluid mechanics (HFM), a physics informed deep learnin...
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Potential Flow Generator with L_2 Optimal Transport Regularity for Generative Models
We propose a potential flow generator with L_2 optimal transport regular...
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Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
While there is currently a lot of enthusiasm about "big data", useful da...
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Machine Learning of Linear Differential Equations using Gaussian Processes
This work leverages recent advances in probabilistic machine learning to...
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Physics Informed Deep Learning (Part II): Datadriven Discovery of Nonlinear Partial Differential Equations
We introduce physics informed neural networks  neural networks that ar...
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Multistep Neural Networks for Datadriven Discovery of Nonlinear Dynamical Systems
The process of transforming observed data into predictive mathematical m...
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Numerical Gaussian Processes for Timedependent and Nonlinear Partial Differential Equations
We introduce the concept of numerical Gaussian processes, which we defin...
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Neuralnetinduced Gaussian process regression for function approximation and PDE solution
Neuralnetinduced Gaussian process (NNGP) regression inherits both the ...
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An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields
Molecular fingerprints, i.e. feature vectors describing atomistic neighb...
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Collapse of Deep and Narrow Neural Nets
Recent theoretical work has demonstrated that deep neural networks have ...
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Quantifying total uncertainty in physicsinformed neural networks for solving forward and inverse stochastic problems
Physicsinformed neural networks (PINNs) have recently emerged as an alt...
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Physics Informed Deep Learning (Part I): Datadriven Solutions of Nonlinear Partial Differential Equations
We introduce physics informed neural networks  neural networks that ar...
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Nonlocal flocking dynamics: Learning the fractional order of PDEs from particle simulations
Flocking refers to collective behavior of a large number of interacting ...
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PhysicsInformed Generative Adversarial Networks for Stochastic Differential Equations
We developed a new class of physicsinformed generative adversarial netw...
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Dying ReLU and Initialization: Theory and Numerical Examples
The dying ReLU refers to the problem when ReLU neurons become inactive a...
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Deep Learning of Vortex Induced Vibrations
Vortex induced vibrations of bluff bodies occur when the vortex shedding...
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Linking Gaussian Process regression with datadriven manifold embeddings for nonlinear data fusion
In statistical modeling with Gaussian Process regression, it has been sh...
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Learning and MetaLearning of Stochastic AdvectionDiffusionReaction Systems from Sparse Measurements
Physicsinformed neural networks (PINNs) were recently proposed in [1] a...
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Reinforcement Learning for Active Flow Control in Experiments
We demonstrate experimentally the feasibility of applying reinforcement ...
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On the Convergence and generalization of Physics Informed Neural Networks
Physics informed neural networks (PINNs) are deep learning based techniq...
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George Em Karniadakis
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Researcher at MIT Sea Grant, Professor at Brown University