# AI-Assisted Tumor-Growth Law Discovery from Sparse Data: Refitting and LLM-Based Ranking

arXiv: https://arxiv.org/abs/2610.16891 · HTML: https://mlsanity.com/paper/2610.16891/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 7 of 7)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [Numerical differentiation of noisy data: A unifying multi-objective optimization framework](https://mlsanity.com/paper/2009.01911/) (2020)
- [Al-Khwarizmi: Discovering Physical Laws with Foundation Models](https://mlsanity.com/paper/2502.01702/) (2025)

## Abstract (arXiv)

Inferring tumor-growth laws from sparse, noisy observations requires more than accurate curve fitting. We study an AI-assisted workflow involving symbolic regression, mathematical admissibility checks, coefficient refitting, and large language model (LLM) ranking. Synthetic Gompertz data allow trajectory fit, forecasting, and recovery of the governing growth law to be assessed separately. A dense noiseless control recovers the generating family, but sparse noisy sampling frequently leads to alternative forms. Among retained candidates in the tested configurations, physics-informed neural network refitting often increases growth-law error, whereas classical nonlinear least squares usually reduces it. A separate exploratory analysis of archived LLM rankings shows no consistent improvement over selection by training error and identifies errors in mathematical reasoning. Plausible saturation, accurate trajectory fits, and convincing explanations can therefore coexist with incorrect growth laws. Mathematical validity and law recovery require evaluation alongside predictive performance.