82 citations · 241 across the 8 of their papers we have counts for
8 papers
Numerical analysis of physics-informed neural networks and related models in physics-informed machine learning
Tim De Ryck, Siddhartha Mishra
Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems f…
An operator preconditioning perspective on training in physics-informed machine learning
Tim De Ryck, Florent Bonnet, Siddhartha Mishra +1
In this paper, we investigate the behavior of gradient descent algorithms in physics-informed machine learning methods like PINNs, which minimize residuals connected to partial dif…
Convolutional Neural Operators for robust and accurate learning of PDEs
Bogdan Raonić, Roberto Molinaro, Tim De Ryck +5
Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been large…
wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws
Tim De Ryck, Siddhartha Mishra, Roberto Molinaro
Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation. Consequently, they may fail at approximating dis…
Error analysis for deep neural network approximations of parametric hyperbolic conservation laws
Tim De Ryck, Siddhartha Mishra
We derive rigorous bounds on the error resulting from the approximation of the solution of parametric hyperbolic scalar conservation laws with ReLU neural networks. We show that th…
Generic bounds on the approximation error for physics-informed (and) operator learning
Tim De Ryck, Siddhartha Mishra
We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as…
On the approximation of functions by tanh neural networks
Tim De Ryck, Samuel Lanthaler, Siddhartha Mishra
We derive bounds on the error, in high-order Sobolev norms, incurred in the approximation of Sobolev-regular as well as analytic functions by neural networks with the hyperbolic ta…
Change Point Detection in Time Series Data using Autoencoders with a Time-Invariant Representation
Tim De Ryck, Maarten De Vos, Alexander Bertrand
Change point detection (CPD) aims to locate abrupt property changes in time series data. Recent CPD methods demonstrated the potential of using deep learning techniques, but often…