7 citations · 14 across the 3 of their papers we have counts for
3 papers
math.NA2025★ 2 cited
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…
math.NA2022★ 5 cited
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…
math.NA2022★ 7 cited
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…