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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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05/23/2022
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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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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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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08/21/2020
Change Point Detection in Time Series Data using Autoencoders with a Time-Invariant Representation
Change point detection (CPD) aims to locate abrupt property changes in t...
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12/13/2019