8 citations · 13 across the 3 of their papers we have counts for
4 papers
Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs
T. De Ryck, S. Mishra, Y. Shang +1
We present approximation results and numerical experiments for the use of randomized neural networks within physics-informed extreme learning machines to efficiently solve high-dim…
Variable-Input Deep Operator Networks
Michael Prasthofer, Tim De Ryck, Siddhartha Mishra
Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test…
Error estimates for physics informed neural networks approximating the Navier-Stokes equations
Tim De Ryck, Ameya D. Jagtap, Siddhartha Mishra
We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier-Stokes equations with (extended) physics informed neural networks. We show that…
On the approximation of rough functions with deep neural networks
Tim De Ryck, Siddhartha Mishra, Deep Ray
Deep neural networks and the ENO procedure are both efficient frameworks for approximating rough functions. We prove that at any order, the ENO interpolation procedure can be cast…