Next generation reservoir computing based on nonlinear vector autoregression (NVAR) is applied to emulate simple dynamical system models and compared to numerical integration schemes such as Euler and the $2^\text{nd}$ order Runge-Kutta. It is shown that the NVAR emulator can be interpreted as a data-driven method used to recover the numerical integration scheme that produced the data. It is also shown that the approach can be extended to produce high-order numerical schemes directly from data. The impacts of the presence of noise and temporal sparsity in the training set is further examined to gauge the potential use of this method for more realistic applications.
翻译:基于非线性矢量自动递减(NVAR)的下一代储油层计算,用于模仿简单的动态系统模型,并与Euler和$2 ⁇ text{nd}$sord Runge-Kutta等数字集成方案进行比较,显示NVAR模拟器可被解释为一种数据驱动方法,用于恢复生成数据的数字集成计划,还显示该方法可以扩展,直接从数据中产生高分数计划,进一步审查培训组中噪音和时空宽度的影响,以衡量这一方法在更现实应用方面的潜在用途。