I’m excited to share our APEBench paper and the corresponding source code, to be presented at NeurIPS. Congratulations Felix and Simon 😀 👍 At its core, APEBench features a lightning-fast ⚡️ fully differentiable spectral solver with a huge range of differen PDEs.
- Paper http://arxiv.org/abs/2411.00180
- Source code https://github.com/tum-pbs/apebench
It also comes with an integrated GPU-based volume renderer “VAPE” (https://keksboter.github.io/vape4d/), that works in your browser (and in Jupyter). If you’re patient, try it here (note – this link downloads 100MB, so it can take a moment): https://vape.niedermayr.dev/?file=https://huggingface.co/datasets/vollautomat/vape4d/resolve/main/gray_scott_3d.npy&colormap=https://huggingface.co/datasets/vollautomat/vape4d/resolve/main/colormap.json
Paper abstract: We introduce the Autoregressive PDE Emulator Benchmark (APEBench), a comprehensive benchmark suite to evaluate autoregressive neural emulators for solving partial differential equations. APEBench is based on JAX and provides a seamlessly integrated differentiable simulation framework employing efficient pseudo-spectral methods, enabling 46 distinct PDEs across 1D, 2D, and 3D. Facilitating systematic analysis and comparison of learned emulators, we propose a novel taxonomy for unrolled training and introduce a unique identifier for PDE dynamics that directly relates to the stability criteria of classical numerical methods. APEBench enables the evaluation of diverse neural architectures, and unlike existing benchmarks, its tight integration of the solver enables support for differentiable physics training and neural-hybrid emulators. Moreover, APEBench emphasizes rollout metrics to understand temporal generalization, providing insights into the long-term behavior of emulating PDE dynamics. In several experiments, we highlight the similarities between neural emulators and numerical simulators.
