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The large-scale simulation of dynamical systems is critical in numerousscientific and engineering disciplines. However, traditional numerical solversare limited by the choice of step sizes when estimating integration, resultingin a trade-off between accuracy and computational efficiency. To address thischallenge, we introduce a deep learning-based corrector called Neural Vector(NeurVec), which can compensate for integration errors and enable larger timestep sizes in simulations. Our extensive experiments on a variety of complexdynamical system benchmarks demonstrate that NeurVec exhibits remarkablegeneralization capability on a continuous phase space, even when trained usinglimited and discrete data. NeurVec significantly accelerates traditionalsolvers, achieving speeds tens to hundreds of times faster while maintaininghigh levels of accuracy and stability. Moreover, NeurVec's simple-yet-effectivedesign, combined with its ease of implementation, has the potential toestablish a new paradigm for fast-solving differential equations based on deeplearning.

On Fast Simulation of Dynamical System with Neural Vector Enhanced Numerical Solver