论文标题
在使用神经矢量增强的数值求解器的动态系统快速模拟上
On Fast Simulation of Dynamical System with Neural Vector Enhanced Numerical Solver
论文作者
论文摘要
在众多科学和工程学科中，动态系统的大规模模拟至关重要。但是，传统的数值求解器受到估计集成时步进大小的选择的限制，从而导致准确性和计算效率之间的权衡。为了应对这一挑战，我们引入了一个名为Neural Vector（Neurvec）的深度学习校正器，该校正器可以弥补集成错误并在模拟中实现更大的时间步长。我们对各种复杂动力学系统基准的广泛实验表明，即使使用有限和离散数据训练，Neurvec在连续相空间上也表现出显着的概括能力。 Neurvec显着加速了传统的求解器，在保持较高的准确性和稳定性的同时，达到了数十倍至数百倍。此外，Neurvec的简单效果设计，结合其易于实施，有可能建立一个基于深度学习的快速溶解微分方程的新范式。
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.
