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.

翻译：动力系统的大规模仿真在众多科学与工程领域中具有关键作用。然而，传统数值求解器在积分估计中受限于步长选择，导致计算精度与效率之间存在权衡。针对这一挑战，我们提出了一种基于深度学习的修正器——神经向量（NeurVec），通过补偿积分误差实现仿真中更大时间步长的应用。在多种复杂动力系统基准测试上的大量实验表明，即使仅使用有限且离散的数据进行训练，NeurVec在连续相空间上仍展现出显著的泛化能力。该修正器可将传统求解器的运算速度提升数十至数百倍，同时保持高精度与稳定性。此外，NeurVec兼具简洁有效的设计理念与易于实现的特性，有望为基于深度学习的高速微分方程求解建立新范式。