67 citations · 324 across the 36 of their papers we have counts for
4 papers · 1 filter
Optimal control of a kinetic equation
Aaron Pim, Tristan Pryer, Alex Trenam
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-pos…
A Deep Uzawa-Lagrange Multiplier Approach for Boundary Conditions in PINNs and Deep Ritz Methods
Charalambos G. Makridakis, Aaron Pim, Tristan Pryer
We introduce a deep learning-based framework for weakly enforcing boundary conditions in the numerical approximation of partial differential equations. Building on existing physics…
Deep Uzawa for PDE constrained optimisation
Charalambos G. Makridakis, Aaron Pim, Tristan Pryer
In this work, we present a numerical solver for optimal control problems constrained by linear and semi-linear second-order elliptic PDEs. The approach is based on recasting the pr…
A nodally bound-preserving discontinuous Galerkin method for the drift-diffusion equation
Gabriel R. Barrenechea, Tristan Pryer, Alex Trenam
In this work, we introduce and analyse discontinuous Galerkin (dG) methods for the drift-diffusion model. We explore two dG formulations: a classical interior penalty approach and…