论文标题
加速使用连续时间回声状态网络对僵硬的非线性系统的模拟
Accelerating Simulation of Stiff Nonlinear Systems using Continuous-Time Echo State Networks
论文作者
论文摘要
现代设计，控制和优化通常需要模拟高度非线性模型，从而导致过度的计算成本。这些成本可以通过评估完整模型的廉价代理来摊销。在这里，我们提出了一种通用数据驱动的方法，即连续时间回波状态网络（CTESN），用于生成在广泛分开的时间标准下具有动力学的非线性普通微分方程的替代物。我们在经验上使用我们的CTESN在供暖系统的可扩展模型上进行了近似时间的表现，该模型的全部执行时间呈指数增长，同时将相对误差保持在0.2％以内。我们还表明，我们的模型可以有效地捕获快速瞬变和缓慢的动态，而其他技术（例如物理学知情的神经网络）却难以训练和预测这些模型的高度非线性行为。
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.
