PDEBench: An Extensive Benchmark for Scientific Machine Learning

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 repre- sentative 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 con- tribute the following unique features: (1) A much wider range of PDEs compared to existing benchmarks, ranging from relatively common examples to more real- istic and difficult problems; (2) much larger ready-to-use datasets compared to prior work, comprising multiple simulation runs across a larger number of ini- tial 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).