CoDBench: A Critical Evaluation of Data-driven Models for Continuous Dynamical Systems
This provides a critical resource for the scientific machine learning community to guide model selection and development, though it is incremental as it focuses on benchmarking rather than introducing new methods.
The authors tackled the lack of comprehensive evaluation of data-driven models for continuous dynamical systems by introducing CoDBench, a benchmarking suite that tests 11 state-of-the-art models across 8 benchmark datasets, finding that current models struggle with newer mechanics datasets.
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.