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Neural networks have shown great potential in accelerating the solution ofpartial differential equations (PDEs). Recently, there has been a growinginterest in introducing physics constraints into training neural PDE solvers toreduce the use of costly data and improve the generalization ability. However,these physics constraints, based on certain finite dimensional approximationsover the function space, must resolve the smallest scaled physics to ensure theaccuracy and stability of the simulation, resulting in high computational costsfrom large input, output, and neural networks. This paper proposes a generalacceleration methodology called NeuralStagger by spatially and temporallydecomposing the original learning tasks into several coarser-resolutionsubtasks. We define a coarse-resolution neural solver for each subtask, whichrequires fewer computational resources, and jointly train them with the vanillaphysics-constrained loss by simply arranging their outputs to reconstruct theoriginal solution. Due to the perfect parallelism between them, the solution isachieved as fast as a coarse-resolution neural solver. In addition, the trainedsolvers bring the flexibility of simulating with multiple levels of resolution.We demonstrate the successful application of NeuralStagger on 2D and 3D fluiddynamics simulations, which leads to an additional $10\sim100\times$ speed-up.Moreover, the experiment also shows that the learned model could be well usedfor optimal control.

NeuralStagger: Accelerating Physics-constrained Neural PDE Solver with Spatial-temporal Decomposition