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：近年来，基于机器学习的物理系统建模受到越来越多的关注。尽管取得了一些令人瞩目的进展，但在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套件。PDEBench包含代码和数据，用于评估新型机器学习模型在经典数值仿真和机器学习基线方法上的性能。我们提出的基准问题集具有以下独特特征：（1）比现有基准涵盖更广泛的PDE类型，从相对常见的例子到更现实且困难的问题；（2）相比先前工作，提供更大的现成数据集，涵盖更多初始条件、边界条件和PDE参数下的多次仿真运行；（3）具有用户友好的API用于数据生成和常见机器学习模型（FNO、U-Net、PINN、基于梯度的逆方法）的基线结果，且源代码可扩展性强。PDEBench允许研究人员通过标准化API自由扩展基准用于自身目的，并比较新模型与现有基线方法的性能。我们还提出了新的评估指标，旨在提供对科学机器学习背景下学习方法更全面的理解。利用这些指标，我们识别出当前机器学习方法难以处理的任务，并将其作为未来社区面临的挑战。代码开源在https://github.com/pdebench/PDEBench。