# APOD: reasoning-guided agentic population ordinary differential equation discovery for pharmacological digital twins

arXiv: https://arxiv.org/abs/2610.06227 · HTML: https://mlsanity.com/paper/2610.06227/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical and scientific domain agents, one of 16 directions in LLM agents and tool use.
- Builds on 3 of its 19 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Placed in

- LLM agents and tool use / [Medical and scientific domain agents](https://mlsanity.com/agents/medical-and-scientific-domain-agents/)

## Builds on (most cited first, 3 of 3)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Automatically Learning Hybrid Digital Twins of Dynamical Systems](https://mlsanity.com/paper/2410.23691/) (2024)

## Abstract (arXiv)

Establishing ordinary differential equations (ODEs) describing population data is a fundamental part of mathematical modeling in pharmacology, crucial to developing digital twins. However, doing so from sparse, noisy data is a slow, expert-driven task. Existing automated methods either search a restricted model space or ignore population inter-individual variability. Here we introduce APOD (Agentic Population ODE Discovery), a language-model agent that iteratively reasons over biological knowledge and fit diagnostics in an open-ended search space to discover a population digital twin (PDT), i.e., a shared ODE system with between-subject variability. On synthetic pharmacokinetic and tumor-dynamics benchmarks, APOD recovered ground-truth structures in 94-100% of runs, 12-fold faster in median than an established library-based search. On real cohorts it converged to valid structures, and proposed a PDT of radioligand-therapy-induced platelet dynamics that predicts thrombocytopenia from first-cycle data and simulates alternative dosing schedules that lower the predicted risk of toxicity.