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，但科学机器学习领域仍缺乏易于使用、同时具有挑战性且能代表广泛问题的基准测试集。我们提出PDEBench，一个基于偏微分方程（PDEs）的时变模拟任务基准测试套件。PDEBench包含代码和数据集，用于评估新型机器学习模型相对于经典数值模拟和机器学习基线模型的性能。我们提出的基准测试问题具有以下独特特征：（1）与现有基准相比，覆盖更广泛的PDE范围，从相对常见的示例到更现实且困难的问题；（2）与先前工作相比，提供更大的即用数据集，包含多种初始条件、边界条件和PDE参数下的多次模拟运行；（3）提供更具扩展性的源代码，配备用户友好的API用于数据生成，并包含主流机器学习模型（FNO、U-Net、PINN、基于梯度的逆方法）的基线结果。PDEBench允许研究人员通过标准化API自由扩展基准测试以满足自身需求，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，旨在更全面地理解科学机器学习背景下的学习方法。借助这些指标，我们识别出对当前机器学习方法具有挑战性的任务，并将其作为社区未来的研究方向。代码可从https://github.com/pdebench/PDEBench获取。