Neural network guided adjoint computations in dual weighted residual error estimation

Abstract In this work, we are concerned with neural network guided goal-oriented a posteriori error estimation and adaptivity using the dual weighted residual method. The primal problem is solved classical Galerkin finite elements. adjoint in strong form feedforward two or three hidden layers. main objective of our approach to explore alternatives for solving greater potential numerical cost reduction. proposed algorithm based on general theorem including both linear nonlinear stationary partial differential equations goal functionals. Our developments substantiated some experiments that include comparisons computed adjoints element solutions adjoints. programming software, open-source library deal.II successfully coupled LibTorch, PyTorch C++ application interface. Article Highlights Adjoint approximation dual-weighted estimation. Side-by-side accuracy computational computations. Numerical problems yielding excellent effectivity indices.