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Automatically Learning Hybrid Digital Twins of Dynamical Systems
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Proposes HDTwinGen, an LLM-driven evolutionary framework where a modeling agent writes hybrid mechanistic+neural digital twin code, offline optimizers fit parameters, and an evaluation agent gives natural-language feedback to evolve better models.
Problem
Automatically specifying and parameterizing hybrid digital twins (mechanistic plus neural components) of dynamical systems that generalize out-of-distribution, learn from little data, and can be evolved, where the combinatorial model space makes manual or search-based design intractable.
Approach
Use LLM agents in an evolutionary loop: a modeling agent proposes code-represented hybrid model specifications, offline gradient-based optimization fits their parameters, and an evaluation agent turns per-component validation errors and requirements into natural-language feedback that guides the next generation.
Key results
- HDTwinGen achieves the lowest test MSE on all six benchmark datasets averaged over ten seeds, e.g. 0.0889 vs 7.48 for the best neural baseline (Transformer) on Lung Cancer (with Chemo.) and 2.51e-06 vs 3.69e-05 (Transformer) on Plankton Microcosm.
- On out-of-distribution shifts, DyNODE's error increases by about two orders of magnitude from IID to OOD, while SINDy increases by about one order of magnitude, supporting hybrid robustness claims.
- HDTwinGen can adapt a single parameter of its generated model to represent an unobserved COVID-19 lockdown intervention, which the authors say no other evaluated data-driven method can do without new trajectories.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HDTwinGen instead of the strongest conventional baseline, Transformer | dynamical-system modeling · Lung Cancer | test MSE: 7.48$\pm$1.06 -> 4.41$\pm$8.07 | Helped |
| Use HDTwinGen instead of the strongest conventional baseline, Transformer | dynamical-system modeling · Lung Cancer (with Chemo.) | test MSE: 0.348$\pm$0.0618 -> 0.0889$\pm$0.0453 | Helped |
| Use HDTwinGen instead of the strongest conventional baseline, Transformer | dynamical-system modeling · Lung Cancer (with Chemo. & Radio.) | test MSE: 0.216$\pm$0.0345 -> 0.131$\pm$0.198 | Helped |
| Use HDTwinGen instead of the strongest conventional baseline, APHYNITY | dynamical-system modeling · Hare-Lynx | test MSE: 321$\pm$12.6 -> 291$\pm$30.3 | Helped |
| Use HDTwinGen instead of the strongest conventional baseline, Transformer | dynamical-system modeling · Plankton Microcosm | test MSE: 3.69e-05$\pm$1.83e-05 -> 2.51e-06$\pm$2.2e-06 | Helped |
| Use HDTwinGen instead of the strongest conventional baseline, Transformer | dynamical-system modeling · COVID-19 | test MSE: \bf 0.309$\pm$0.222 -> 1.72$\pm$2.28 | Hurt |
| Add iterative model evolution and evaluation feedback to a one-shot generated, parameter-optimized HDTwin (ablation) | HDTwinGen · Lung Cancer | test MSE: 216$\pm$172 -> 4.41$\pm$8.07 | Helped |
| Add parameter optimization to a one-shot generated HDTwin (ablation) | HDTwinGen · Lung Cancer (with Chemo.) | test MSE: 292$\pm$80.2 -> 31.2$\pm$45 | Helped |
| Add iterative model evolution and evaluation feedback to a one-shot generated, parameter-optimized HDTwin (ablation) | HDTwinGen · Lung Cancer (with Chemo. & Radio.) | test MSE: 6.08$\pm$7.9 -> 0.131$\pm$0.198 | Helped |
| Add parameter optimization to a one-shot generated HDTwin (ablation) | HDTwinGen · Plankton Microcosm | test MSE: 0.325$\pm$0.242 -> 0.0132$\pm$0.00116 | Helped |
| Add iterative model evolution and evaluation feedback to a one-shot generated, parameter-optimized HDTwin (ablation) | HDTwinGen · COVID-19 | test MSE: 7.88$\pm$0.0414 -> 1.72$\pm$2.28 | Helped |
| Add iterative model evolution and evaluation feedback to a one-shot generated, parameter-optimized HDTwin (ablation) | HDTwinGen · Hare-Lynx | test MSE: 353$\pm$0 -> 291$\pm$30.3 | Helped |
Surprising findings
- The zero-shot LLM-generated model without parameter optimization (ZeroShot) performs very poorly on most datasets, showing that offline parameter fitting is essential.
Limitations
- Efficacy depends on human-provided system specifications and the LLM's domain knowledge and code generation ability.
- Only continuous-time systems are considered.
- Potential bias transmission from black-box LLMs into evolved models.
Experimental setup
Datasets: Cancer PKPD simulated lung cancer data COVASIM COVID-19 agent-based simulation Plankton Microcosm Hare-Lynx
Benchmarks: Lung Cancer Lung Cancer (with Chemo.) Lung Cancer (with Chemo. & Radio.) Hare-Lynx Plankton Microcosm COVID-19
Metrics: test MSE
Baselines: SINDy Genetic Programming DyNODE RNN Transformer APHYNITY ZeroShot ZeroOptim
Builds on: neural ODE SINDy APHYNITY DyNODE
Closest papers by meaning
- Continuously Updating Digital Twins using Large Language Models (ICML 2025 · similarity 0.91)
- Learning Hybrid Dynamics Models with Simulator-Informed Latent States (AAAI 2024 · similarity 0.87)
- Amortized Equation Discovery in Hybrid Dynamical Systems (ICML 2024 · similarity 0.86)
- A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems (NeurIPS 2026 · similarity 0.85)
- DISCO: learning to DISCover an evolution Operator for multi-physics-agnostic prediction (ICML 2025 · similarity 0.85)
- EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutions (ICML 2025 · similarity 0.85)
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