Modern design, control, and optimization often requires simulation of highly nonlinear models, leading to prohibitive computational costs. These costs can be amortized by evaluating a cheap surrogate of the full model. Here we present a general data-driven method, the continuous-time echo state network (CTESN), for generating surrogates of nonlinear ordinary differential equations with dynamics at widely separated timescales. We empirically demonstrate near-constant time performance using our CTESNs on a physically motivated scalable model of a heating system whose full execution time increases exponentially, while maintaining relative error of within 0.2 %. We also show that our model captures fast transients as well as slow dynamics effectively, while other techniques such as physics informed neural networks have difficulties trying to train and predict the highly nonlinear behavior of these models.

翻译：现代设计、控制和优化往往需要模拟高度非线性模型,从而导致令人望而生畏的计算成本。这些费用可以通过对全模型的廉价替代物进行评估来摊还。在这里,我们展示了一种一般数据驱动方法,即连续时回声状态网络(CTESN),用于产生非线性普通差异方程式的代孕,且具有高度分离的时标动态。我们的经验表明,利用我们的CTESN,在一个具有物理动机的、可缩放的供暖系统模型上,我们的CTESN,其完全执行时间急剧增加,同时保持0.2 % 的相对误差。我们还表明,我们的模型能够有效捕捉快速瞬态和缓慢的动态,而物理学知情神经网络等其他技术则难以培训和预测这些模型的高度非线性行为。