Neural Emulator Superiority: When Machine Learning for PDEs Surpasses its Training Data

arXiv:2510.23111 · cs.LG · Submitted 2025-10-27 · Read on arXiv

cs.LG

Submitted: 2025-10-27

Updated: 2026-01-14

Comments: Accepted at NeurIPS 2025: https://neurips.cc/virtual/2025/poster/116770 ; V2: Updated references, fix typos

DOI: 10.52202/085713-5521

Code: https://github.com/oogle/jax

Project page: https://tum-pbs.github.io/emulator-superiority

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Fidelity — 57× in this paper · explained in 2 episodes
• Generalization — 22× in this paper · explained in 13 episodes
• Transformer — 14× in this paper · explained in 2 episodes
• Accuracy — 13× in this paper · explained in 1 episode
• Loss Function — 7× in this paper · explained in 2 episodes
• Ablation — 5× in this paper · explained in 1 episode
• Benchmarking — 5× in this paper · explained in 4 episodes
• Direct Finite Difference — 5× in this paper
• Adam — 4× in this paper · explained in 2 episodes
• Core — 4× in this paper · explained in 2 episodes
• Fourier Neural Operator — 4× in this paper
• Ablation study — 3× in this paper · explained in 1 episode
• Discrete Fourier Transform — 3× in this paper
• Benchmark — 2× in this paper · explained in 2 episodes
• Foundation Model — 2× in this paper · explained in 3 episodes
• Foundation Models — 2× in this paper · explained in 7 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Abstraction — 1× in this paper · explained in 1 episode
• Adversarial Examples — 1× in this paper · explained in 2 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Forward Time Centered Space — 1× in this paper
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Model Predictive Control (MPC) — 1× in this paper · explained in 5 episodes
• Munich Center for Machine Learning — 1× in this paper
• Over-smoothing — 1× in this paper · explained in 4 episodes
• PDE residual — 1× in this paper · explained in 2 episodes
• Physical Constraints — 1× in this paper · explained in 7 episodes
• Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 6 episodes
• Regularization — 1× in this paper · explained in 3 episodes

Sources

• Explaining and Harnessing Adversarial Examples
• Adam: A Method for Stochastic Optimization
• Physics-Informed Neural Operator for Learning Partial Differential Equations
• What You See is Not What You Get: Neural Partial Differential Equations and The Illusion of Learning
• Learned Coarse Models for Efficient Turbulence Simulation
• Multi-Scale Context Aggregation by Dilated Convolutions

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks