Continuous dynamical systems, characterized by differential equations, are ubiquitously used to model several important problems: plasma dynamics, flow through porous media, weather forecasting, and epidemic dynamics. Recently, a wide range of data-driven models has been used successfully to model these systems. However, in contrast to established fields like computer vision, limited studies are available analyzing the strengths and potential applications of different classes of these models that could steer decision-making in scientific machine learning. Here, we introduce CodBench, an exhaustive benchmarking suite comprising 11 state-of-the-art data-driven models for solving differential equations. Specifically, we comprehensively evaluate 4 distinct categories of models, viz., feed forward neural networks, deep operator regression models, frequency-based neural operators, and transformer architectures against 8 widely applicable benchmark datasets encompassing challenges from fluid and solid mechanics. We conduct extensive experiments, assessing the operators' capabilities in learning, zero-shot super-resolution, data efficiency, robustness to noise, and computational efficiency. Interestingly, our findings highlight that current operators struggle with the newer mechanics datasets, motivating the need for more robust neural operators. All the datasets and codes will be shared in an easy-to-use fashion for the scientific community. We hope this resource will be an impetus for accelerated progress and exploration in modeling dynamical systems.

连续动力系统建模方法研究了数据驱动模型在解决微分方程方面的表现，通过CodBench进行了四类不同模型的全面评估并揭示了神经算子对新型力学数据集的困难，为建模动力系统的加速进展和探索提供了动力学研究资源。

CoDBench：对连续动力系统的数据驱动模型进行的关键评估