APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs
This addresses the need for standardized evaluation of neural emulators in computational physics, though it is incremental as it builds on existing benchmarking efforts.
The authors introduced APEBench, a benchmark suite for evaluating autoregressive neural emulators in solving partial differential equations, providing 46 distinct PDEs across 1D, 2D, and 3D with integrated differentiable simulation and rollout metrics for temporal generalization.
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.