CoDBench: A Critical Evaluation of Data-driven Models for Continuous
  Dynamical Systems
Priyanshu Burark Karn Tiwari Meer Mehran Rashid Prathosh A P N M Anoop Krishnan
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.