Machine learning-based modeling of physical systems has experienced increased interest in recent years. Despite some impressive progress, there is still a lack of benchmarks for Scientific ML that are easy to use but still challenging and representative of a wide range of problems. We introduce PDEBench, a benchmark suite of time-dependent simulation tasks based on Partial Differential Equations (PDEs). PDEBench comprises both code and data to benchmark the performance of novel machine learning models against both classical numerical simulations and machine learning baselines. Our proposed set of benchmark problems contribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more realistic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of initial and boundary conditions and PDE parameters; (3) more extensible source codes with user-friendly APIs for data generation and baseline results with popular machine learning models (FNO, U-Net, PINN, Gradient-Based Inverse Method). PDEBench allows researchers to extend the benchmark freely for their own purposes using a standardized API and to compare the performance of new models to existing baseline methods. We also propose new evaluation metrics with the aim to provide a more holistic understanding of learning methods in the context of Scientific ML. With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community. The code is available at https://github.com/pdebench/PDEBench.

翻译：基于机器学习对物理系统进行建模近年来受到越来越多的关注。尽管取得了一些令人瞩目的进展，但科学机器学习领域仍缺乏易于使用、具有挑战性且能代表广泛问题的基准测试。我们提出PDEBench，一个基于偏微分方程（PDE）的时变仿真任务基准测试套件。PDEBench包含代码与数据，用于评估新型机器学习模型相较于经典数值仿真和机器学习基线方法的性能。我们提出的基准测试问题集具有以下独特特点：（1）相比现有基准测试涵盖更广泛的PDE类型，从相对常见的示例到更现实且困难的问题；（2）相比先前工作提供规模更大的可直接使用的数据集，包含跨越多组初始条件、边界条件及PDE参数的多次仿真运行；（3）具备更具扩展性的源代码和用户友好的API，用于数据生成和基于主流机器学习模型（FNO、U-Net、PINN、基于梯度的逆方法）的基线结果。PDEBench允许研究者通过标准化API自由扩展基准测试，并将新模型性能与现有基线方法进行比较。我们还提出了新的评估指标，旨在更全面地理解科学机器学习中的学习方法。基于这些指标，我们识别出当前机器学习方法难以处理的任务，并建议将其作为未来社区面临的挑战。代码开源在https://github.com/pdebench/PDEBench。