PDEBENCH: An Extensive Benchmark for Scientific Machine Learning
PDEBENCH: An Extensive Benchmark for Scientific Machine Learning
复制标题
PDEBENCH：科学机器学习的广泛基准
DOI：
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Mathias Niepert
中科院分区：
文献类型：
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作者：
M. Takamoto;T. Praditia;Raphael Leiteritz;Dan MacKinlay;F. Alesiani;D. Pflüger;Mathias Niepert
近年来，基于机器学习的物理系统建模受到了越来越多的关注。尽管取得了一些令人印象深刻的进展，但科学机器学习仍然缺乏易于使用但仍然具有挑战性并代表广泛问题的基准。我们介绍PDEBench，一个基准套件的时间依赖性的模拟任务的偏微分方程（PDE）的基础上。PDEBench包含代码和数据，用于针对经典数值模拟和机器学习基线对新型机器学习模型的性能进行基准测试。我们提出的一组基准问题贡献了以下独特的功能：（1）与现有基准相比，范围更广的PDE，从相对常见的例子到更现实和困难的问题;（2）与以前的工作相比，更大的现成的数据集，包括在大量的初始和边界条件和PDE参数的多个模拟运行;（3）更可扩展的源代码，具有用户友好的API，用于数据生成和流行机器学习模型（FNO，U-Net，PINN，基于一致性的逆方法）的基线结果。PDEBench允许研究人员使用标准化的API自由扩展基准，并将新模型的性能与现有的基准方法进行比较。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的更全面的理解。通过这些指标，我们确定了最近ML方法具有挑战性的任务，并将这些任务作为社区未来的挑战。该代码可在https://github.com/pdebench/PDEBench上获得。
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.
可解释的多项式神经常微分方程。
DOI：
10.1063/5.0130803
发表时间：
2023
期刊：
Chaos (Woodbury, N.Y.)
影响因子：
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作者：
Fronk,Colby;Petzold,Linda
通讯作者：
Petzold,Linda
由偏微分方程驱动的深度神经网络
影响因子：
2
作者：
Ruthotto, Lars;Haber, Eldad
通讯作者：
Haber, Eldad