Text-Trained LLMs Can Zero-Shot Extrapolate PDE Dynamics, Revealing a Three-Stage In-Context Learning Mechanism

arXiv:2509.06322 · cs.LG · Submitted 2025-09-08 · Read on arXiv

cs.LG

Submitted: 2025-09-08

Updated: 2026-03-11

Journal ref: Mach. Learn.: Sci. Technol. 7 (2026) 055001

DOI: 10.1088/2632-2153/ae9c8a

Code: https://github.com/Jiajun-Bao/LLM-PDE-Dynamics

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

Terminology

• Accuracy — 33× in this paper · explained in 1 episode
• Quantization — 11× in this paper · explained in 12 episodes
• Benchmark — 9× in this paper · explained in 2 episodes
• Fine-Tuning — 8× in this paper · explained in 5 episodes
• In-Context Learning — 8× in this paper · explained in 4 episodes
• Foundation Model — 6× in this paper · explained in 3 episodes
• Foundation Models — 6× in this paper · explained in 7 episodes
• Scaling Laws — 6× in this paper · explained in 4 episodes
• Generalization — 5× in this paper · explained in 13 episodes
• Tokenization — 5× in this paper · explained in 2 episodes
• Alignment — 4× in this paper · explained in 1 episode
• Embeddings — 4× in this paper · explained in 2 episodes
• Large Language Models (LLMs) — 3× in this paper · explained in 6 episodes
• Robustness — 3× in this paper · explained in 5 episodes
• Transformer — 3× in this paper · explained in 2 episodes
• Diffusion Model — 2× in this paper · explained in 8 episodes
• In-Context Learning (ICL) — 2× in this paper · explained in 5 episodes
• Root Mean Square Error — 2× in this paper
• Uncertainty Quantification — 2× in this paper · explained in 8 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Adaptation — 1× in this paper · explained in 1 episode
• Chain-of-Thought Prompting — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Diffusion Models — 1× in this paper · explained in 6 episodes
• Dynamical regimes — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Initial Data — 1× in this paper · explained in 2 episodes
• Instruction Tuning — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Latent Diffusion Model — 1× in this paper · explained in 2 episodes
• Latent Diffusion Models — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Time Series Forecasting — 1× in this paper · explained in 3 episodes
• Universal Physics Solver — 1× in this paper

Sources

• Phi-4 Technical Report
• GPT-4 Technical Report
• Pre-trained Large Language Models Learn Hidden Markov Models In-context
• A Survey on In-context Learning
• The Llama 3 Herd of Models
• CodePDE: An Inference Framework for LLM-driven PDE Solver Generation
• Explain Like I'm Five: Using LLMs to Improve PDE Surrogate Models with Text
• PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs
• Gemma 3 Technical Report
• Llama 2: Open Foundation and Fine-Tuned Chat Models
• Large Language Models as Markov Chains
• A Survey of Large Language Models
• Text2PDE: Latent Diffusion Models for Accessible Physics Simulation

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