构建首个用于评估神经微分方程求解器的综合性基准测试平台。
APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs
- 基于JAX的可微分仿真框架，支持46种不同维度的偏微分方程求解。
- 提出新分类法与动态标识符，关联经典数值方法的稳定性条件。
- 支持可微物理训练和神经-混合模型，关注长期时序泛化能力。
我们提出了自回归偏微分方程（PDE）神经模拟器基准测试（APEBench），一个全面的评估框架，用于评估自回归神经模拟器在求解偏微分方程方面的表现。APEBench基于JAX，提供无缝集成的可微分仿真框架，采用高效的伪谱方法，支持1维、2维和3维场景下的46种不同偏微分方程。为促进对学习型模拟器的系统分析与比较，我们提出一种新的展开训练分类法，并引入一种独特的偏微分方程动力学标识符，直接关联经典数值方法的稳定性准则。APEBench支持多种神经架构的评估，且由于其与求解器的紧密集成，可实现可微物理训练和神经-混合模拟器。此外，该基准强调滚动预测指标，以理解模型在时间上的泛化能力，揭示了神经模拟器与数值模拟器之间的相似性。通过多项实验，进一步验证了其有效性。
原文摘要 · Abstract (English)
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.
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