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07/23/2023
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks
The curse-of-dimensionality (CoD) taxes computational resources heavily ...
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07/18/2023
DiTTO: Diffusion-inspired Temporal Transformer Operator
Solving partial differential equations (PDEs) using a data-driven approa...
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02/28/2023
A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions
Physics-informed neural networks (PINNs) as a means of solving partial d...
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11/16/2022
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology
In this paper, we propose the augmented physics-informed neural network ...
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09/06/2022
How important are activation functions in regression and classification? A survey, performance comparison, and future directions
Inspired by biological neurons, the activation functions play an essenti...
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08/28/2022
A Hybrid Iterative Numerical Transferable Solver (HINTS) for PDEs Based on Deep Operator Network and Relaxation Methods
Iterative solvers of linear systems are a key component for the numerica...
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07/08/2022
Physics-Informed Deep Neural Operator Networks
Standard neural networks can approximate general nonlinear operators, re...
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05/17/2022
Function Regression using Spiking DeepONet
One of the main broad applications of deep learning is function regressi...
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05/20/2021
Physics-informed neural networks (PINNs) for fluid mechanics: A review
Despite the significant progress over the last 50 years in simulating fl...
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10/15/2020
Error estimates of residual minimization using neural networks for linear PDEs
We propose an abstract framework for analyzing the convergence of least-...
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04/03/2020
On the Convergence and generalization of Physics Informed Neural Networks
Physics informed neural networks (PINNs) are deep learning based techniq...
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03/13/2020
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
We propose a Bayesian physics-informed neural network (B-PINN) to solve ...
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10/08/2019
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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09/23/2019
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs
Physics-informed neural networks (PINNs) encode physical conservation la...
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05/03/2019
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
One of the open problems in scientific computing is the long-time integr...
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11/28/2017
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
We introduce physics informed neural networks -- neural networks that ar...
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11/28/2017
