Rapid evolution of sensor technology, advances in instrumentation, and progress in devising data-acquisition softwares/hardwares are providing vast amounts of data for various complex phenomena, ranging from those in atomospheric environment, to large-scale porous formations, and biological systems. The tremendous increase in the speed of scientific computing has also made it possible to emulate diverse high-dimensional, multiscale and multiphysics phenomena that contain elements of stochasticity, and to generate large volumes of numerical data for them in heterogeneous systems. The difficulty is, however, that often the governing equations for such phenomena are not known. A prime example is flow, transport, and deformation processes in macroscopically-heterogeneous materials and geomedia. In other cases, the governing equations are only partially known, in the sense that they either contain various coefficients that must be evaluated based on data, or that they require constitutive relations, such as the relationship between the stress tensor and the velocity gradients for non-Newtonian fluids in the momentum conservation equation, in order for them to be useful to the modeling. Several classes of approaches are emerging to address such problems that are based on machine learning, symbolic regression, the Mori-Zwanzig projection operator formulation, sparse identification of nonlinear dynamics, data assimilation, and stochastic optimization and analysis, or a combination of two or more of such approaches. This Perspective describes the latest developments in this highly important area, and discusses possible future directions.

翻译：传感器技术的快速演进、仪器设备的进步以及数据采集软硬件的发展，正为各类复杂现象（从大气环境到大规模多孔介质再到生物系统）提供海量数据。科学计算速度的极大提升也使得模拟包含随机性特征的高维、多尺度、多物理场现象成为可能，并能在非均匀系统中生成这些现象的大规模数值数据。然而，难点在于这类现象的控制方程往往未知。宏观非均匀材料与地质介质中的流动、输运及变形过程便是典型例证。另一些情况下，控制方程仅部分已知——要么包含需基于数据评估的各类系数，要么需要本构关系（如动量守恒方程中非牛顿流体的应力张量与速度梯度关系）方能用于建模。目前涌现出多类方法应对这类问题，包括基于机器学习、符号回归、Mori-Zwanzig投影算子公式化、非线性动力学稀疏辨识、数据同化、随机优化分析，或上述方法的组合。本文综述了该重要领域的最新进展，并探讨了未来可能的发展方向。