TY - INPR A1 - Alphonse, Amal A1 - Hintermüller, Michael A1 - Kister, Alexander A1 - Lun, Chin Hang A1 - Sirotenko, Clemens T1 - A neural network approach to learning solutions of a class of elliptic variational inequalities N2 - We develop a weak adversarial approach to solving obstacle problems using neural networks. By employing (generalised) regularised gap functions and their properties we rewrite the obstacle problem (which is an elliptic variational inequality) as a minmax problem, providing a natural formulation amenable to learning. Our approach, in contrast to much of the literature, does not require the elliptic operator to be symmetric. We provide an error analysis for suitable discretisations of the continuous problem, estimating in particular the approximation and statistical errors. Parametrising the solution and test function as neural networks, we apply a modified gradient descent ascent algorithm to treat the problem and conclude the paper with various examples and experiments. Our solution algorithm is in particular able to easily handle obstacle problems that feature biactivity (or lack of strict complementarity), a situation that poses difficulty for traditional numerical methods. KW - Obstacle Problems KW - Numerical Analysis KW - Optimization and Control KW - Simulation PY - 2024 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-622160 DO - https://doi.org/10.48550/arXiv.2411.18565 SP - 1 EP - 38 AN - OPUS4-62216 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -