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math.NA2024
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…
math.NA2024
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…