# Prior or Feedback? What an LLM Uses When Adapting Neural Operators

arXiv: https://arxiv.org/abs/2610.12325 · HTML: https://mlsanity.com/paper/2610.12325/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 21 of 21)

- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [Multiple Physics Pretraining for Physical Surrogate Models](https://mlsanity.com/paper/2310.02994/) (2023)
- [Using Large Language Models for Hyperparameter Optimization](https://mlsanity.com/paper/2312.04528/) (2023)
- [CodePDE: An Inference Framework for LLM-driven PDE Solver Generation](https://mlsanity.com/paper/2505.08783/) (2025)
- [Walrus: A Cross-Domain Foundation Model for Continuum Dynamics](https://mlsanity.com/paper/2511.15684/) (2025)
- [Sequential Large Language Model-Based Hyper-parameter Optimization](https://mlsanity.com/paper/2410.20302/) (2024)
- [Can LLMs Beat Classical Hyperparameter Optimization Algorithms? A Study on autoresearch](https://mlsanity.com/paper/2603.24647/) (2026)
- [Auditing Provenance Sensitivity in LLM Agent Action Selection](https://mlsanity.com/paper/2607.20827/) (2026)
- [Lang-PINN: From Language to Physics-Informed Neural Networks via a Multi-Agent Framework](https://mlsanity.com/paper/2510.05158/) (2025)
- [Agentic Bayesian Optimization through Surrogate-Augmented Autoresearch](https://mlsanity.com/paper/2608.00316/) (2026)
- [OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inference](https://mlsanity.com/paper/2602.01493/) (2026)
- [How Consistent Are LLM Agents? Measuring Behavioral Reproducibility in Multi-Step Tool-Calling Pipelines](https://mlsanity.com/paper/2605.28840/) (2026)
- [When Is an LLM Worth It for Hyperparameter Optimization? A Budget-Matched Study on Tabular Data Finds the Warm-Start Is a Default Configuration, Not the Model](https://mlsanity.com/paper/2606.21641/) (2026)
- [Physics-informed fine-tuning of foundation models for partial differential equations](https://mlsanity.com/paper/2603.15431/) (2026)
- [AgentHPOBench: A Benchmark For Evaluating LLM Agents as Sequential Hyperparameter Optimizers](https://mlsanity.com/paper/2607.29626/) (2026)
- [Can AI Scientist Agents Learn from Lab-in-the-Loop Feedback? Evidence from Iterative Perturbation Discovery](https://mlsanity.com/paper/2603.26177/) (2026)
- [Human-in-the-Loop Meta Bayesian Optimization for Fusion Energy and Scientific Applications](https://mlsanity.com/paper/2605.00068/) (2026)
- [Prior Knowledge or Search? A Study of LLM Agents in Hardware-Aware Code Optimization](https://mlsanity.com/paper/2605.19782/) (2026)
- [Unsupervised Adaptation of PDE Foundation Models](https://mlsanity.com/paper/2608.07053/) (2026)

## Abstract (arXiv)

Do LLM scientific agents rely only on their initial task context, or do they adapt their decisions in response to experimental feedback? We study this question in neural operator adaptation, where a large language model (LLM) selects fine-tuning configurations under a limited trial budget. Across transfers within and between partial differential equation (PDE) families, the LLM achieves lower held-out test nRMSE than random search and Bayesian optimisation in nearly every matched comparison. Endpoint performance alone cannot distinguish what happens, so we verify each attribution with controlled interventions. Before observing any validation score, the LLM's first configuration already ranks near the top of the corresponding random-search pool, indicating a useful initial bias. A complementary cold-start intervention shows that the selected base learning rate shifts with the PDE description. Once feedback becomes available, reassigning validation scores among evaluated configurations changes the next proposal in every case tested, whereas a value-preserving rewrite produces no comparable aggregate effect. These interventions establish that the LLM's decision-level actions respond to the given task and observed outcomes, showing that it combines a task-dependent prior with sensitivity to experimental feedback.