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

Hrishikesh Viswanath, Yue Chang, Julius Berner, Peter Yichen Chen, Aniket Bera

Keywords: Reduced order modeling, Neural Operator, lagrangian dynamics, neural field, discretization invariance

TL;DR: Solve Lagrangian dynamics on highly sparse graph inputs to significantly improve computation speed

Abstract: We propose accelerating the simulation of Lagrangian dynamics, such as fluid flows, granular flows, and elastoplasticity, with neural-operator-based reduced-order modeling. While full-order approaches simulate the physics of every particle within the system, incurring high computation time for dense inputs, we propose to simulate the physics on sparse graphs constructed by sampling from the spatially discretized system. Our discretization-invariant reduced-order framework trains on any spatial discretizations and computes temporal dynamics on any sparse sampling of these discretizations through neural operators. Our proposed approach is termed Graph Informed Optimized Reduced-Order Modeling or \textit{GIOROM}. Through reduced order modeling, we ensure lower computation time by sparsifying the system by 6.6-32.0$\times$, while ensuring high-fidelity full-order inference via neural fields. We show that our model generalizes to a range of initial conditions, resolutions, and materials.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 7991