论文标题
NYSALT：NYSTRöm-Type基于推理的方案适应大型时间步变
NySALT: Nyström-type inference-based schemes adaptive to large time-stepping
论文作者
论文摘要
大型时间步长对于有效的确定性和随机性哈密顿动力系统的长期模拟很重要。传统的传播结构积分器虽然成功地用于通用系统，但由于稳定性和准确性限制，对时间步长的容忍度有限。我们建议使用数据来创新经典集成商，以便它们可以适应大型时间步变，并针对每个特定系统量身定制。特别是，我们介绍了Nysalt，NyStröm-type基于推理的方案适应大型时间稳定。 NYSALT通过最小化单步预测误差从数据中学到的每个时间步骤都有最佳参数。因此，它是针对每个时间步长和特定系统量身定制的，以实现最佳性能并以自适应方式忍受大型时间步变。随着数据大小的增加，我们证明和数值验证估计器的收敛性。此外，对确定性和随机Fermi-Pasta-Ulam（FPU）模型的分析和数值测试表明，Nysalt扩大线性稳定性的最大可允许的步骤大小，并在维持精度相似的störmer--Verlet和BaoAb时的时间步长四倍。
Large time-stepping is important for efficient long-time simulations of deterministic and stochastic Hamiltonian dynamical systems. Conventional structure-preserving integrators, while being successful for generic systems, have limited tolerance to time step size due to stability and accuracy constraints. We propose to use data to innovate classical integrators so that they can be adaptive to large time-stepping and are tailored to each specific system. In particular, we introduce NySALT, Nyström-type inference-based schemes adaptive to large time-stepping. The NySALT has optimal parameters for each time step learnt from data by minimizing the one-step prediction error. Thus, it is tailored for each time step size and the specific system to achieve optimal performance and tolerate large time-stepping in an adaptive fashion. We prove and numerically verify the convergence of the estimators as data size increases. Furthermore, analysis and numerical tests on the deterministic and stochastic Fermi-Pasta-Ulam (FPU) models show that NySALT enlarges the maximal admissible step size of linear stability, and quadruples the time step size of the Störmer--Verlet and the BAOAB when maintaining similar levels of accuracy.
