mlsanityData to 14 Oct 2026

APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs

arXiv 2411.00180 ↗First posted 31 Oct 2024cs.LGcited by 60

Not on the map. Why?

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.

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

Builds on

0 of 0 references.

No references here yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 12; 2026: 47.

60 papers.

Sort:

By area:

  1. 2025Walrus: A Cross-Domain Foundation Model for Continuum Dynamicscited by 36
  2. 2025PDE-Transformer: Efficient and Versatile Transformers for Physics Simulationscited by 32
  3. 2026RealPDEBench: A Benchmark for Complex Physical Systems with Real-World Datacited by 16
  4. 2026Test-time Generalization for Physics through Neural Operator Splittingcited by 10
  5. 2024Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogatescited by 8
  6. 2025Neural Emulator Superiority: When Machine Learning for PDEs Surpasses its Training Datacited by 6
  7. 2026Diagnosing Failure Modes of Neural Operators Across Diverse PDE Familiescited by 6
  8. 2026DiffusionRollout: Uncertainty-Aware Rollout Planning in Long-Horizon PDE Solvingcited by 5
  9. 2026Semigroup Consistency as a Diagnostic for Learned Physics Simulatorscited by 4
  10. 2026Out-of-distribution generalization of deep-learning surrogates for 2D PDE-generated dynamics in the small-data regimecited by 3
  11. 2026Discovering Physical Directions in Weight Space: Composing Neural PDE Expertscited by 3
  12. 2026JEPA-Anything: Learning Predictive Models across Different Worldscited by 3
38 more
  1. 2025Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solverscited by 2
  2. 2025AneumoBench: A Source-Linked Benchmark for Synthetic-Geometry Transfer in Aneurysm CFDcited by 2
  3. 2025DRIFT-Net: A Spectral--Coupled Neural Operator for PDEs Learningcited by 2
  4. 2025Reframing Generative Models for Physical Systems using Stochastic Interpolantscited by 2
  5. 2025Generalizing PDE Emulation with Equation-Aware Neural Operatorscited by 2
  6. 2025Convolutional-neural-operator-based transfer learning for solving PDEscited by 2
  7. 2026Learning Physical Operators using Neural Operatorscited by 2
  8. 2026Flowers: A Warp Drive for Neural PDE Solverscited by 2
  9. 2026BRICKS: Compositional Neural Markov Kernels for Zero-Shot Radiation-Matter Simulationcited by 2
  10. 2026Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Trainingcited by 2
  11. 2025Pre-Generating Multi-Difficulty PDE Data for Few-Shot Neural PDE Solverscited by 1
  12. 2026System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecastingcited by 1
  13. 2026Do Physics Foundation Models Learn Generalizable Physics? A Bias-Aware Benchmark Across Physical Regimes and Distribution Shiftscited by 1
  14. 2026Operator Boosting Produces Pareto-Efficient PDE Surrogatescited by 1
  15. 2026HERO: History-Enriched Rollout Training for Long-Horizon Autoregressive Neural Operatorscited by 1
  16. 2026TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learningcited by 1
  17. 2026Unsupervised Adaptation of PDE Foundation Modelscited by 1
  18. 2026ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiabilitycited by 1
  19. 2025ChannelFlow-Tools: A Configuration-Driven Pipeline for Generating Machine-Learning-Ready Datasets of 3D Obstructed Channel Flowscited by 0
  20. 2025PHASE: Physics-Integrated, Heterogeneity-Aware Surrogates for Scientific Simulationscited by 0
  21. 2026Generative Neural Operators through Diffusion Last Layercited by 0
  22. 2026Direct Learning of Calibration-Aware Uncertainty for Neural PDE Surrogatescited by 0
  23. 2026SGNO: Spectral Generator Neural Operators for Stable Long Horizon PDE Rolloutscited by 0
  24. 2026Deep Invertible Autoencoders for Dimensionality Reduction of Dynamical Systemscited by 0
  25. 2026A neural operator framework for data-driven discovery of stability and receptivity in physical systemscited by 0
  26. 2026A Robust In-Context Model for Conservation Laws: Injecting Context into Flux Neural Operators via Recurrent Vision Transformerscited by 0
  27. 2026CarCrashNet: A Large-Scale Dataset and Hierarchical Neural Solver for Data-Driven Structural Crash Simulationcited by 0
  28. 2026Exactness Matters for Physical Rule Enforcementcited by 0
  29. 2026Breakeven complexity: A new perspective on neural partial differential equation solverscited by 0
  30. 2026DiffUNet^2: Bidirectional Conditional Diffusion for Probabilistic Scientific Spatiotemporal Modelingcited by 0
  31. 2026Mosaic: A Benchmark Suite for Differentiable Physics Solverscited by 0
  32. 2026Label-Free Finite-Volume-Residual Training of Attention Graph Neural Networks for Coupled Thermo-Fluid Fieldscited by 0
  33. 2026From Fixed Grids to Moving Particles:A Transferable Latent Operator for Fluid Dynamicscited by 0
  34. 2026One-Step Evolution for Long-Time Extrapolation: An Error-Bound-Informed and Prior-Guided Neural Residual Framework for Autonomous PDEscited by 0
  35. 2026Physics-Integrated Operator Learning via Gaussian Splatting Representationscited by 0
  36. 2026TWIG: A Time-Causal Wavelet Operator for Autoregressive Forecasting on Irregular Graphscited by 0
  37. 2026NEMSim: Learning Control-Conditioned Multi-Event Physical Dynamics via Executable Event-Mechanism Priorscited by 0
  38. 2026Staying on the Attractor: Supervising Neural Surrogates of 3D Turbulence Where They Leave Itcited by 0

50 most cited of 60 All 60 (JSON)