Strain-energy-based training of super-resolution for deformation simulation

Abstract Supervised super-resolution methods estimate high-resolution simulation results from low-resolution inputs. These methods typically train the neural networks using pairs of high-resolution data and their downsampled low-resolution counterparts, implicitly assuming the global similarity between the low- and high-resolution models. This assumption, however, often fails as the low-resolution models usually exhibit stiffer behaviour than high-resolution models due to numerical stiffening. This paper proposes a novel supervised super-resolution method to mitigate this problem for linear deformable object simulation. The method constructs training data pairs by matching low- and high-resolution simulation snapshots based on the similarity of the normalized strain energy, the normalized temporal change rate of strain energy, and the modal contributions to the overall strain energy. The loss function also incorporates the equation residuals derived from the finite-element method. The time-integration scheme is selected by examining the eigenvalue distributions of the neural tangent kernel associated with the finite-element residuals. Compared with previous downsampling methods, the proposed method reduces the maximum relative displacement error by 25%, 54%, and 38% for the beam, elephant, and armadillo models, respectively.