Reduced-Order Neural Operators: Learning Lagrangian Dynamics on Highly Sparse Graphs

• DOI: 10.48550/arxiv.2407.03925
• Publication Date: 2024-07-04
• Authors: Hrishikesh Viswanath; Chang Yue; Julius Berner; Peter Yichen Chen; Aniket Bera
• Keywords: Dynamics

We present a neural operator architecture to simulate Lagrangian dynamics, such as fluid flow, granular flows, and elastoplasticity. Traditional numerical methods, the finite element method (FEM), suffer from long run times large memory consumption. On other hand, approaches based on graph networks are faster but still computation dense graphs, which often required for high-fidelity simulations. Our model, GIOROM or Graph Interaction Operator Reduced-Order Modeling, learns temporal dynamics within reduced-order setting, capturing spatial features highly sparse representation of input generalizing arbitrary locations during inference. The model is geometry-aware discretization-agnostic can generalize different initial conditions, velocities, geometries after training. show that point clouds order 100,000 points be inferred graphs with $\sim$1000 points, negligible change in time. empirically evaluate our elastic solids, Newtonian fluids, Non-Newtonian Drucker-Prager von Mises these benchmarks, approach results 25$\times$ speedup compared network-based physics simulators while delivering predictions complex physical systems showing better performance most benchmarks. code demos provided at https://github.com/HrishikeshVish/GIOROM.