We propose a novel surrogate modelling approach to efficiently and accurately approximate the response of complex dynamical systems driven by time-varying exogenous excitations over extended time periods. Our approach, namely manifold nonlinear autoregressive modelling with exogenous input (mNARX), involves constructing a problem-specific exogenous input manifold that is optimal for constructing autoregressive surrogates. The manifold, which forms the core of mNARX, is constructed incrementally by incorporating the physics of the system, as well as prior expert- and domain- knowledge. Because mNARX decomposes the full problem into a series of smaller sub-problems, each with a lower complexity than the original, it scales well with the complexity of the problem, both in terms of training and evaluation costs of the final surrogate. Furthermore, mNARX synergizes well with traditional dimensionality reduction techniques, making it highly suitable for modelling dynamical systems with high-dimensional exogenous inputs, a class of problems that is typically challenging to solve. Since domain knowledge is particularly abundant in physical systems, such as those found in civil and mechanical engineering, mNARX is well suited for these applications. We demonstrate that mNARX outperforms traditional autoregressive surrogates in predicting the response of a classical coupled spring-mass system excited by a one-dimensional random excitation. Additionally, we show that mNARX is well suited for emulating very high-dimensional time- and state-dependent systems, even when affected by active controllers, by surrogating the dynamics of a realistic aero-servo-elastic onshore wind turbine simulator. In general, our results demonstrate that mNARX offers promising prospects for modelling complex dynamical systems, in terms of accuracy and efficiency.

翻译：我们提出了一种新颖的代理建模方法，以高效且精确地近似复杂动态系统在长时间内受时变外生激励驱动的响应。该方法即流形非线性自回归外生输入建模（mNARX），其核心在于构建一个针对问题特化的外生输入流形，该流形专为构建自回归代理而优化。作为mNARX核心的流形采用增量方式构建，融合了系统物理机制及现有专家知识与领域知识。由于mNARX将完整问题分解为一系列复杂度低于原始问题的子问题，其在训练和最终代理评估成本方面均能随问题复杂度良好扩展。此外，mNARX与传统降维技术具有协同效应，尤其适用于建模高维外生输入动态系统——这类问题通常难以求解。鉴于物理系统（如土木与机械工程领域）中领域知识尤为丰富，mNARX在这些应用中具有显著优势。我们证明，在预测受一维随机激励驱动的经典耦合弹簧-质量系统响应时，mNARX优于传统自回归代理。同时，通过为真实气动-伺服-弹性陆上风力发电机仿真器建立动力学代理，我们展示了mNARX即使在高维时间及状态相关系统（含主动控制器影响）中仍具有卓越的模拟能力。总体而言，我们的结果表明mNARX在精度与效率方面为复杂动态系统建模提供了有前景的方案。