Machine learning helps choose simpler boundary conditions for faster simulations
Selective boundary condition reduction via learned error gating
Machine Learning
Summary
Simulating physical problems often requires tricky boundary rules that change how accurate and slow the solution is. The authors created a method where a neural network learns when a simpler rule can replace a more complicated one without losing too much accuracy. Their approach checks predictions on the error before deciding which rule to use, saving time when possible. They tested this on problems like corrosion and other steady and changing conditions and found it works well.
parametric PDEsboundary conditionsneural networkserror estimationRobin boundary conditionDirichlet boundary conditiongalvanic corrosionsingular limitscomputational costnonlinear evolution problems
Authors
Daniel Fernández, Dominik Penk, Dominik Riedelbauch
Abstract
Parametric PDEs can admit different boundary conditions with different accuracy and computational cost. We introduce a framework for learning when one reduced boundary condition can replace another: paired solutions train a neural network to estimate the resulting domain and boundary errors, and the simpler condition is used only when both predicted errors meet prescribed tolerances. We focus on singular limits in applications, in which a stiff Robin or nonlinear boundary law is replaced by its limiting Dirichlet form. We evaluate the method on a galvanic corrosion problem and other nonlinear stationary and evolution problems.