Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space. Recently, machine learning (ML) has emerged as a promising solution that can either serve as a surrogate for, accelerate or augment traditional numerical methods. Pioneering work has demonstrated that ML provides solutions to governing systems of equations with comparable accuracy to those obtained using direct numerical methods, but with significantly faster computational speed. These high-speed, high-fidelity estimations can facilitate the solving of complex multiscale systems by providing a better initial solution to traditional solvers. This paper provides a perspective on the opportunities and challenges of using ML for complex multiscale modeling and simulation. We first outline the current state-of-the-art ML approaches for simulating multiscale systems and highlight some of the landmark developments. Next, we discuss current challenges for ML in multiscale computational modeling, such as the data and discretization dependence, interpretability, and data sharing and collaborative platform development. Finally, we suggest several potential research directions for the future.

翻译：许多机械工程应用需要多尺度计算建模与仿真。然而，由于解空间的高维特性，求解复杂的多尺度系统在计算上仍然十分繁重。近年来，机器学习作为一种有前景的解决方案出现，它可以作为传统数值方法的替代、加速或增强手段。开创性研究已表明，机器学习提供的控制方程系统解，其精度可与直接数值方法相媲美，但计算速度显著更快。这些高速、高保真度的估计能够为传统求解器提供更好的初始解，从而有助于求解复杂的多尺度系统。本文对使用机器学习进行复杂多尺度建模与仿真的机遇和挑战进行了展望。我们首先概述了当前用于模拟多尺度系统的最先进的机器学习方法，并重点介绍了一些标志性进展。接着，我们讨论了当前机器学习在多尺度计算建模中面临的挑战，例如数据和离散化依赖性、可解释性以及数据共享与协作平台开发。最后，我们为未来提出了几个潜在的研究方向。