Mechanics Simulation with Implicit Neural Representations of Complex Geometries

Abstract: Implicit Neural Representations (INRs), characterized by neural network-encoded signed distance fields, provide a powerful means to represent complex geometries continuously and efficiently. While successful in computer vision and generative modeling, integrating INRs into computational analysis workflows, such as finite element simulations, remains underdeveloped. In this work, we propose a computational framework that seamlessly combines INRs with the Shifted Boundary Method (SBM) for high-fidelity linear elasticity simulations without explicit geometry transformations. By directly querying the neural implicit geometry, we obtain the surrogate boundaries and distance vectors essential for SBM, effectively eliminating the meshing step. We demonstrate the efficacy and robustness of our approach through elasticity simulations on complex geometries (Stanford Bunny, Eiffel Tower, gyroids) sourced from triangle soups and point clouds. Our method showcases significant computational advantages and accuracy, underscoring its potential in biomedical, geophysical, and advanced manufacturing applications.