# APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs

arXiv: https://arxiv.org/abs/2411.00180 · HTML: https://mlsanity.com/paper/2411.00180/

## Key facts

- Cited by 60 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2024.

## Built on by (most cited first, 30 of 60)

- [Walrus: A Cross-Domain Foundation Model for Continuum Dynamics](https://mlsanity.com/paper/2511.15684/) (2025)
- [PDE-Transformer: Efficient and Versatile Transformers for Physics Simulations](https://mlsanity.com/paper/2505.24717/) (2025)
- [RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Data](https://mlsanity.com/paper/2601.01829/) (2026)
- [Test-time Generalization for Physics through Neural Operator Splitting](https://mlsanity.com/paper/2602.00884/) (2026)
- [Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogates](https://mlsanity.com/paper/2412.13074/) (2024)
- [Neural Emulator Superiority: When Machine Learning for PDEs Surpasses its Training Data](https://mlsanity.com/paper/2510.23111/) (2025)
- [Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families](https://mlsanity.com/paper/2601.11428/) (2026)
- [DiffusionRollout: Uncertainty-Aware Rollout Planning in Long-Horizon PDE Solving](https://mlsanity.com/paper/2602.13616/) (2026)
- [Semigroup Consistency as a Diagnostic for Learned Physics Simulators](https://mlsanity.com/paper/2605.26324/) (2026)
- [Out-of-distribution generalization of deep-learning surrogates for 2D PDE-generated dynamics in the small-data regime](https://mlsanity.com/paper/2601.08404/) (2026)
- [Discovering Physical Directions in Weight Space: Composing Neural PDE Experts](https://mlsanity.com/paper/2605.14546/) (2026)
- [JEPA-Anything: Learning Predictive Models across Different Worlds](https://mlsanity.com/paper/2609.20800/) (2026)
- [Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solvers](https://mlsanity.com/paper/2505.14595/) (2025)
- [AneumoBench: A Source-Linked Benchmark for Synthetic-Geometry Transfer in Aneurysm CFD](https://mlsanity.com/paper/2505.14717/) (2025)
- [DRIFT-Net: A Spectral--Coupled Neural Operator for PDEs Learning](https://mlsanity.com/paper/2509.24868/) (2025)
- [Reframing Generative Models for Physical Systems using Stochastic Interpolants](https://mlsanity.com/paper/2509.26282/) (2025)
- [Generalizing PDE Emulation with Equation-Aware Neural Operators](https://mlsanity.com/paper/2511.09729/) (2025)
- [Convolutional-neural-operator-based transfer learning for solving PDEs](https://mlsanity.com/paper/2512.17969/) (2025)
- [Learning Physical Operators using Neural Operators](https://mlsanity.com/paper/2602.23113/) (2026)
- [Flowers: A Warp Drive for Neural PDE Solvers](https://mlsanity.com/paper/2603.04430/) (2026)
- [BRICKS: Compositional Neural Markov Kernels for Zero-Shot Radiation-Matter Simulation](https://mlsanity.com/paper/2605.06591/) (2026)
- [Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training](https://mlsanity.com/paper/2606.09949/) (2026)
- [Pre-Generating Multi-Difficulty PDE Data for Few-Shot Neural PDE Solvers](https://mlsanity.com/paper/2512.00564/) (2025)
- [System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting](https://mlsanity.com/paper/2603.25025/) (2026)
- [Do Physics Foundation Models Learn Generalizable Physics? A Bias-Aware Benchmark Across Physical Regimes and Distribution Shifts](https://mlsanity.com/paper/2605.29283/) (2026)
- [Operator Boosting Produces Pareto-Efficient PDE Surrogates](https://mlsanity.com/paper/2606.17460/) (2026)
- [HERO: History-Enriched Rollout Training for Long-Horizon Autoregressive Neural Operators](https://mlsanity.com/paper/2607.29135/) (2026)
- [TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning](https://mlsanity.com/paper/2608.04222/) (2026)
- [Unsupervised Adaptation of PDE Foundation Models](https://mlsanity.com/paper/2608.07053/) (2026)
- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)

## Abstract (arXiv)

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.