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math.OC2024
An Analysis of Constraint-Relaxation in PDE-Based Inverse Problems
Tristan van Leeuwen, Yunan Yang
Inverse problems are ubiquitous in science and engineering. Many of these are naturally formulated as a PDE-constrained optimization problem. These non-linear, large-scale, constra…
math.NA2024
Adjoint Monte Carlo Method
Russel Caflisch, Yunan Yang
This survey explores the development of adjoint Monte Carlo methods for solving optimization problems governed by kinetic equations, a common challenge in areas such as plasma cont…