mlsanityData to 7 Oct 2026

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

arXiv 2208.03680 ↗First posted 7 Aug 2022cs.CE cs.AI cs.LGcited by 9

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Abstract (arXiv)

The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a trade-off between accuracy and computational efficiency. To address this challenge, we introduce a deep learning-based corrector called Neural Vector (NeurVec), which can compensate for integration errors and enable larger time step sizes in simulations. Our extensive experiments on a variety of complex dynamical system benchmarks demonstrate that NeurVec exhibits remarkable generalization capability on a continuous phase space, even when trained using limited and discrete data. NeurVec significantly accelerates traditional solvers, achieving speeds tens to hundreds of times faster while maintaining high levels of accuracy and stability. Moreover, NeurVec's simple-yet-effective design, combined with its ease of implementation, has the potential to establish a new paradigm for fast-solving differential equations based on deep learning.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 32 of its 83 references that are in the map. First posted on arXiv 7 Aug 2022.

Builds on

32 of 83 references.

References · 32

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20 more
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