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06/08/2023
Multilevel domain decomposition-based architectures for physics-informed neural networks
Physics-informed neural networks (PINNs) are a popular and powerful appr...
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06/06/2023
How does over-squashing affect the power of GNNs?
Graph Neural Networks (GNNs) are the state-of-the-art model for machine ...
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05/31/2023
Are Neural Operators Really Neural Operators? Frame Theory Meets Operator Learning
Recently, there has been significant interest in operator learning, i.e....
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05/15/2023
Neural Oscillators are Universal
Coupled oscillators are being increasingly used as the basis of machine ...
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03/29/2023
A Monte-Carlo ab-initio algorithm for the multiscale simulation of compressible multiphase flows
We propose a novel Monte-Carlo based ab-initio algorithm for directly co...
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03/20/2023
A Survey on Oversmoothing in Graph Neural Networks
Node features of graph neural networks (GNNs) tend to become more simila...
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02/07/2023
Multi-Scale Message Passing Neural PDE Solvers
We propose a novel multi-scale message passing neural network algorithm ...
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02/02/2023
Convolutional Neural Operators
Although very successfully used in machine learning, convolution based n...
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01/26/2023
Neural Inverse Operators for Solving PDE Inverse Problems
A large class of inverse problems for PDEs are only well-defined as mapp...
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11/10/2022
Finite basis physics-informed neural networks as a Schwarz domain decomposition method
Physics-informed neural networks (PINNs) [4, 10] are an approach for sol...
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10/03/2022
Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities
A large class of hyperbolic and advection-dominated PDEs can have soluti...
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10/02/2022
Gradient Gating for Deep Multi-Rate Learning on Graphs
We present Gradient Gating (G^2), a novel framework for improving the pe...
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07/18/2022
wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws
Physics informed neural networks (PINNs) require regularity of solutions...
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07/15/2022
Error analysis for deep neural network approximations of parametric hyperbolic conservation laws
We derive rigorous bounds on the error resulting from the approximation ...
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05/30/2022
Agnostic Physics-Driven Deep Learning
This work establishes that a physical system can perform statistical lea...
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05/23/2022
Variable-Input Deep Operator Networks
Existing architectures for operator learning require that the number and...
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05/23/2022
Generic bounds on the approximation error for physics-informed (and) operator learning
We propose a very general framework for deriving rigorous bounds on the ...
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04/03/2022
On the discrete equation model for compressible multiphase fluid flows
The modeling of multi-phase flow is very challenging, given the range of...
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03/17/2022
Error estimates for physics informed neural networks approximating the Navier-Stokes equations
We prove rigorous bounds on the errors resulting from the approximation ...
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02/04/2022
Graph-Coupled Oscillator Networks
We propose Graph-Coupled Oscillator Networks (GraphCON), a novel framewo...
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10/22/2021
A novel fourth-order WENO interpolation technique. A possible new tool designed for radiative transfer
Context. Several numerical problems require the interpolation of discret...
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07/20/2021
Well-posedness of Bayesian inverse problems for hyperbolic conservation laws
We study the well-posedness of the Bayesian inverse problem for scalar h...
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07/15/2021
On the well-posedness of Bayesian inversion for PDEs with ill-posed forward problems
We study the well-posedness of Bayesian inverse problems for PDEs, for w...
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07/15/2021
On universal approximation and error bounds for Fourier Neural Operators
Fourier neural operators (FNOs) have recently been proposed as an effect...
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06/28/2021
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs
Physics informed neural networks approximate solutions of PDEs by minimi...
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04/18/2021
On the approximation of functions by tanh neural networks
We derive bounds on the error, in high-order Sobolev norms, incurred in ...
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04/12/2021
Physics Informed Neural Networks (PINNs)for approximating nonlinear dispersive PDEs
We propose a novel algorithm, based on physics-informed neural networks ...
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03/09/2021
UnICORNN: A recurrent model for learning very long time dependencies
The design of recurrent neural networks (RNNs) to accurately process seq...
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02/18/2021
Error estimates for DeepOnets: A deep learning framework in infinite dimensions
DeepOnets have recently been proposed as a framework for learning nonlin...
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10/02/2020
Coupled Oscillatory Recurrent Neural Network (coRNN): An accurate and (gradient) stable architecture for learning long time dependencies
Circuits of biological neurons, such as in the functional parts of the b...
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09/25/2020
Physics Informed Neural Networks for Simulating Radiative Transfer
We propose a novel machine learning algorithm for simulating radiative t...
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08/13/2020
Iterative Surrogate Model Optimization (ISMO): An active learning algorithm for PDE constrained optimization with deep neural networks
We present a novel active learning algorithm, termed as iterative surrog...
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06/29/2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs II: A class of inverse problems
Physics informed neural networks (PINNs) have recently been very success...
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06/29/2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs
Physics informed neural networks (PINNs) have recently been widely used ...
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05/26/2020
Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences
We propose a deep supervised learning algorithm based on low-discrepancy...
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12/13/2019
On the approximation of rough functions with deep neural networks
Deep neural networks and the ENO procedure are both efficient frameworks...
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09/20/2019
A Multi-level procedure for enhancing accuracy of machine learning algorithms
We propose a multi-level method to increase the accuracy of machine lear...
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09/14/2019
Statistical solutions of the incompressible Euler equations
We propose and study the framework of dissipative statistical solutions ...
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03/07/2019