The development of machine learning (ML) models for scientific applications has long been hindered by the lack of suitable datasets that capture the complexity and diversity of physical systems. Many existing datasets are limited, often covering only small classes of physical behaviors. This lack of comprehensive data makes it challenging to develop effective surrogate models for real-world scientific phenomena. Moreover, numerical methods for solving partial differential equations (PDEs) can be computationally expensive, particularly when high accuracy is required, making surrogate models a practical alternative. Despite advances in machine learning, there remains a significant gap between the datasets currently used and the complex problems of practical interest. PolymathicAI’s “The Well” aims to address this issue.
PolymathicAI Releases ‘The Well’: 15TB of Datasets for Spatiotemporal Physical Systems
PolymathicAI has released “The Well,” a large-scale collection of machine learning datasets containing numerical simulations of a wide variety of spatiotemporal physical systems. With 15 terabytes of data spanning 16 unique datasets, “The Well” includes simulations from fields such as biological systems, fluid dynamics, acoustic scattering, and magneto-hydrodynamic (MHD) simulations involving supernova explosions. Each dataset is curated to present challenging learning tasks suitable for surrogate model development, a critical area in computational physics and engineering. To facilitate ease of use, a unified PyTorch interface is provided for training and evaluating models, along with example baselines to guide researchers.
Technical Details
“The Well” features a variety of datasets organized into 15TB of data, encompassing 16 distinct scenarios, ranging from the evolution of biological systems to the turbulent behaviors of interstellar matter. Each dataset comprises temporally coarsened snapshots from simulations that vary in initial conditions or physical parameters. These datasets are offered in uniform grid formats and use HDF5 files, ensuring high data integrity and easy access for computational analysis. The data is available with a PyTorch interface, allowing for seamless integration into existing ML pipelines. The provided baselines include models such as the Fourier Neural Operator (FNO), Tucker-Factorized FNO (TFNO), and different variants of U-net architectures. These baselines illustrate the challenges involved in modeling complex spatiotemporal systems, offering benchmarks against which new surrogate models can be tested.
The diversity and extensibility of the datasets in “The Well” are among its key benefits. Researchers can explore a wide range of physical phenomena using a unified dataset collection. Each dataset includes metadata and training/testing splits, enabling easy benchmarking of different machine-learning models. The variety and granularity of the datasets encourage the development of generalizable models capable of solving a broad spectrum of problems in physics, chemistry, and engineering. With its standardized data format and accessibility, “The Well” lowers the barrier to entry for using ML in physical sciences, thereby enabling a wider range of researchers to participate.
The significance of “The Well” goes beyond its size and scope. It provides a benchmark for the emerging class of physics surrogate models and establishes a standard for evaluating models on complex physical tasks. The diversity of the included datasets allows researchers to assess the robustness of their ML models against realistic physical systems with varying degrees of complexity. By providing a unified platform for these datasets, PolymathicAI has bridged the gap between domain experts and machine learning researchers, facilitating collaboration on challenging physical problems. Initial benchmarks show that models such as CNextU-net perform well in some datasets, while others favor more specialized architectures like the Fourier Neural Operator. This underscores the nuanced nature of surrogate modeling and the need for tailored approaches depending on the type of physical phenomena.
Conclusion
PolymathicAI’s “The Well” is a valuable asset for the ML community, particularly for researchers working on surrogate modeling for physical sciences. By making these diverse datasets publicly accessible, PolymathicAI facilitates the development of new models and helps improve existing ones through rigorous benchmarking and testing. “The Well” represents an important step forward in the availability of standardized, diverse, and high-quality datasets for physical simulations, making it a key resource for future advancements in both ML and physics.
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