Learnable-Differentiable Finite Volume Solver for Accelerated Simulation of Flows
This addresses the problem of slow and data-dependent simulations for researchers in fields like meteorology and aerodynamics, though it is an incremental improvement combining existing methods.
The paper tackles the computational cost of fluid flow simulations by proposing LDSolver, a learnable and differentiable finite volume solver that accelerates simulations on coarse grids while maintaining high accuracy, achieving state-of-the-art performance with notable margins on various flow systems.
Simulation of fluid flows is crucial for modeling physical phenomena like meteorology, aerodynamics, and biomedicine. Classical numerical solvers often require fine spatiotemporal grids to satisfy stability, consistency, and convergence conditions, leading to substantial computational costs. Although machine learning has demonstrated better efficiency, they typically suffer from issues of interpretability, generalizability, and data dependency. Hence, we propose a learnable and differentiable finite volume solver, called LDSolver, designed for efficient and accurate simulation of fluid flows on spatiotemporal coarse grids. LDSolver comprises two key components: (1) a differentiable finite volume solver, and (2) an learnable module providing equivalent approximation for fluxes (derivatives and interpolations), and temporal error correction on coarse grids. Even with limited training data (e.g., only a few trajectories), our model could accelerate the simulation while maintaining a high accuracy with superior generalizability. Experiments on different flow systems (e.g., Burgers, decaying, forced and shear flows) show that LDSolver achieves state-of-the-art performance, surpassing baseline models with notable margins.