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math.OC2024★ 1 cited
Optimal control of partial differential equations in PyTorch using automatic differentiation and neural network surrogates
Denis Khimin, Julian Roth, Alexander Henkes +1
The take-home message of this paper is that solving optimal control problems can be computationally straightforward, provided that differentiable partial differential equation (PDE…
math.OC2023
Analysis of a space-time phase-field fracture complementarity model and its optimal control formulation
Denis Khimin, Johannes Lankeit, Marc C. Steinbach +1
The purpose of this work is the formulation of optimality conditions for phase-field optimal control problems. The forward problem is first stated as an abstract nonlinear optimiza…