1 citations · 2 across the 3 of their papers we have counts for
4 papers
Feature tracking in physics-informed neural networks via joint optimization of nonlinear deformation manifolds: application to shocks
Akshay Thakur, Matthew Zahr
Physics-informed neural networks (PINNs) often converge to inaccurate solutions for conservation laws with shocks, because uniformly distributed collocation points undersample loca…
Scalable h-adaptive probabilistic solver for time-independent and time-dependent systems
Akshay Thakur, Sawan Kumar, Matthew Zahr +1
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discreti…
Neural network-based Godunov corrections for approximate Riemann solvers using bi-fidelity learning
Akshay Thakur, Matthew J. Zahr
The Riemann problem is fundamental in the computational modeling of hyperbolic partial differential equations, enabling the development of stable and accurate upwind schemes. While…
MD-NOMAD: Mixture density nonlinear manifold decoder for emulating stochastic differential equations and uncertainty propagation
Akshay Thakur, Souvik Chakraborty
We propose a neural operator framework, termed mixture density nonlinear manifold decoder (MD-NOMAD), for stochastic simulators. Our approach leverages an amalgamation of the point…