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Data-Driven Discovery of Dynamical Systems in Pharmacology using Large Language Models
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Proposes D3, a three-agent GPT-4-driven loop that iteratively generates, evaluates, and extends ODE models (white-box or hybrid) with acquired features, and applies it to pharmacokinetic and other dynamical system datasets including Warfarin.
Problem
Discovering accurate and interpretable closed-form ODE models of dynamical systems (e.g., drug pharmacokinetics) is manual, costly, and limited by expert knowledge and by the difficulty of choosing which features to acquire.
Approach
An LLM-driven loop with a Modeling Agent (generates PyTorch ODE code conditioned on context, feedback and top-k memory), a Feature Acquisition Agent (zero/few-shot value-of-information estimate for new features), and an Evaluation Agent (validation MSE plus verbal feedback) that jointly searches white-box and hybrid ODE model spaces.
Key results
- On Warfarin, D3-hybrid achieves test MSE 0.271 and D3-white-box 0.39 versus 0.646 for the existing standard warfarin PK model.
- D3-hybrid reports the lowest test MSE on all six benchmarks in Table 2 (e.g., 4.72 on Lung Cancer vs 7.07 for Transformer and 326 for DyNODE).
- In feature acquisition experiments on Lung Cancer (Chemo & Radio), LLM-guided acquisition converges fastest and reaches the lowest error versus random and no-acquisition policies.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use D3-hybrid instead of the strongest non-D3 baseline | Lung Cancer · Lung Cancer | test MSE: 7.07±0.558 -> 4.72±9.16 | Helped |
| use D3-hybrid instead of the strongest non-D3 baseline | Lung Cancer (with Chemo.) · Lung Cancer (with Chemo.) | test MSE: 0.346±0.0701 -> 0.0978±0.0463 | Helped |
| use D3-hybrid instead of the strongest non-D3 baseline | Lung Cancer (with Chemo. & Radio.) · Lung Cancer (with Chemo. & Radio.) | test MSE: 0.207±0.0318 -> 0.135±0.225 | Helped |
| use D3-hybrid instead of the strongest non-D3 baseline | Plankton Microcosm · Plankton Microcosm | test MSE: 3.42e-05±1.97e-05 -> 1.86e-06±1.87e-06 | Helped |
| use D3-hybrid instead of the strongest non-D3 baseline | COVID-19 · COVID-19 | test MSE: 0.261±0.0915 -> 1.88±2.57 | Hurt |
| use D3-hybrid instead of the strongest non-D3 baseline | Warfarin PK · Warfarin PK | test MSE: 0.0495±0.0406 -> 0.647±0.167 | Hurt |
| use the discovered white-box model instead of the existing Warfarin PK model | Warfarin · Warfarin | test MSE: 0.646 -> 0.39 | Helped |
| use the discovered hybrid model instead of the existing Warfarin PK model | Warfarin · Warfarin | test MSE: 0.646 -> 0.271 | Helped |
| optimize the ZeroShot model's parameters on training data (ablation) | D3 on Lung Cancer · Lung Cancer | test MSE: 5.78e+03±7.6e+03 -> 225±204 | Helped |
| optimize the ZeroShot model's parameters on training data (ablation) | D3 on Lung Cancer (with Chemo.) · Lung Cancer (with Chemo.) | test MSE: 304±86.1 -> 33.8±50.8 | Helped |
| optimize the ZeroShot model's parameters on training data (ablation) | D3 on Lung Cancer (with Chemo. & Radio.) · Lung Cancer (with Chemo. & Radio.) | test MSE: 6.44e+03±4.27e+03 -> 6.38±8.97 | Helped |
| optimize the ZeroShot model's parameters on training data (ablation) | D3 on Plankton Microcosm · Plankton Microcosm | test MSE: 0.333±0.274 -> 0.0133±0.0013 | Helped |
Surprising findings
- On the Warfarin dataset, the ZeroOptim ablation gave a very high MSE (398 with large variance), and D3-white-box had high variance (19.6 ± 40.3), indicating unstable outcomes across seeds.
Limitations
- Relies on a capable tool-using LLM (GPT-4); results depend on that model.
- Assumes an acquired feature is available for all individuals in the dataset.
- Requires a user-provided system description; the Warfarin case study uses a single small dataset of 33 patients.
Experimental setup
Datasets: Cancer PKPD lung cancer simulator (Geng et al. 2017) COVASIM COVID-19 simulator Plankton Microcosm (Bonnaffe and Coulson 2023) Warfarin PK NOMEN dataset (Janssen et al. 2022)
Benchmarks: Lung Cancer PKPD variants COVID-19 (COVASIM) Plankton Microcosm Warfarin PK
Metrics: test MSE validation MSE
Baselines: DyNODE SINDy RNN Causal Transformer ZeroShot ZeroOptim Existing Warfarin PK model
Builds on: Neural ODE SINDy Eureka/Eureqa Active Feature Acquisition Reflexion
Closest papers by meaning
- No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs (ICLR 2025 · similarity 0.89)
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- Skip the Equations: Learning Behavior of Personalized Dynamical Systems Directly From Data (ICML 2025 · similarity 0.85)
- PharmacoMatch: Efficient 3D Pharmacophore Screening via Neural Subgraph Matching (ICLR 2025 · similarity 0.85)
- A Dataset for Distilling Knowledge Priors from Literature for Therapeutic Design (NeurIPS 2025 · similarity 0.85)
- Generating Novel Leads for Drug Discovery Using LLMs with Logical Feedback (AAAI 2024 · similarity 0.84)
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