DASyR-LLM: Domain-Aware Symbolic Regression with LLMs for Kinetic Model Discovery

Source: arXiv:2608.05120 · Published 2026-08-05 · By Roberto Aliaga Medina, Paulina Quintanilla, Antonio del Rio Chanona

TL;DR

This paper addresses the core challenge of kinetic model discovery in chemical engineering, where accurate rate laws are essential but difficult to infer from noisy experimental data. Traditional symbolic regression (SR) approaches can identify interpretable functional forms but typically lack embedded domain knowledge, often exploring physically implausible models and requiring numerous costly experiments. The authors introduce DASyR-LLM, a novel domain-aware framework that integrates a large language model (LLM) into an iterative SR and model-based design of experiments (MBDoE) loop. The LLM performs two key tasks each iteration: it qualitatively critiques the physicochemical plausibility of the top SR candidate rate laws and generates new candidate expressions informed by this critique and embedded chemical knowledge. This hybrid approach leverages the LLM’s reasoning ability to guide the SR search toward meaningful, interpretable kinetic models more efficiently.

The framework is evaluated on four synthetic reaction kinetics case studies of increasing complexity, representing heterogeneous catalysis and bioprocess systems. Compared to a state-of-the-art SR baseline lacking LLM input, DASyR-LLM reduces the number of iterations required to identify the true underlying models by 41.7% to 79.3%. In over half of the guided runs, the LLM directly proposes the correct model structure, effectively accelerating the discovery process. Both approaches achieve high predictive accuracy (R^2 > 0.98) on held-out validation data, demonstrating that the LLM guidance does not compromise model quality. Ablation studies also show that the LLM scale and presence meaningfully impact discovery efficiency, with smaller models retaining much of the benefit. Overall, the results indicate that LLMs can inject domain reasoning into symbolic model discovery, substantially reducing experimental effort while preserving data-driven flexibility.

Key findings

• DASyR-LLM reduces iterations to find ground-truth kinetic models by 41.7% to 79.3% compared to a state-of-the-art SR baseline without LLM guidance.
• In over 50% of guided runs, the LLM directly proposes the exact correct kinetic rate expression structure.
• Predictive performance on an independent validation set is equivalent between DASyR-LLM and the baseline, with R^2 > 0.98 across all case studies.
• Ablation studies confirm that both the SR backbone and LLM scale significantly contribute to discovery efficiency; a reduced-size LLM retains most benefits.
• The LLM serves dual roles each iteration: (1) qualitative physicochemical critique of top SR candidates, and (2) domain-informed proposal of new candidate models.
• In practical lab settings where each iteration corresponds to an experiment, DASyR-LLM’s iteration reduction translates directly to decreased experimental cost and time.
• The iterative framework combines SR, parameter estimation, LLM-guided candidate generation, AIC model selection, and MBDoE in a closed loop, maintaining flexibility for novel model discovery.
• The LLM module is robust to noise in synthetic data and operates without requiring changes to the underlying SR or MBDoE procedures.

Threat model

The adversary is n/a since the work focuses on scientific model discovery rather than security. The assumption is that data are noisy and incomplete but not maliciously manipulated. The LLM module is trusted to provide domain knowledge without adversarial attacks, and no threat from attackers is considered.

Methodology — deep read

The authors build upon the Automated Discovery of Kinetic models strong formulation (ADoK-S) framework, which integrates symbolic regression (SR), parameter estimation, model selection, and model-based experimental design (MBDoE) in an iterative loop. The threat model assumes an honest-but-limited data source: no direct adversarial attacks, but noisy measurement data and unknown kinetic model structures to be discovered.

Data are synthetic, generated by simulating known ground-truth kinetic systems representing heterogeneous catalysis and bioprocess reactions. Each case study’s initial dataset includes two experiments derived from distinct initial concentrations. Gaussian noise (σ=0.1) is added to emulate experimental uncertainty. As the iterative loop proceeds, MBDoE adds new experiments up to a total budget of 12 iterations (11 additional data points).

The core SR procedure uses PySRRegressor, an evolutionary algorithm framework. SR is applied in two stages per iteration: first, to fit symbolic expressions for species concentration trajectories directly from noisy data; second, to fit symbolic kinetic rate laws from the numerically estimated derivatives of the trajectories. The first stage uses a moderate computational budget and standard arithmetic operators (+, -, ×, ÷, exp) to ensure smooth, interpretable trajectories. The second stage uses a larger search budget to identify mechanistically meaningful rate laws mapping species concentrations to their time derivatives.

Parameter estimation refines kinetic model parameters via integration of the candidate rate laws within ordinary differential equations, minimizing the sum of squared errors versus noisy concentration trajectories. Optimization employs L-BFGS-B with 20 random multi-start initializations to avoid local minima.

The novel LLM module is embedded within the iterative discovery loop. After SR and parameter estimation of top-k (k=5) candidate rate laws per iteration, the LLM receives structured prompts containing symbolic model equations, parameter values, and statistical metrics (AIC, NLL). It performs two defined tasks: (1) qualitatively critiques physicochemical plausibility of the candidates considering reaction context, parameter values, and prior chemical knowledge; (2) proposes ngen=3 new candidate symbolic rate laws informed by its critique and scientific domain knowledge, seeking structural novelty. LLM outputs are free-form and manually parsed for parameter estimation refinement and evaluation.

These LLM-proposed candidates are combined with SR-derived models, and all are ranked by AIC. The top two models progress to guide MBDoE for next-experiment design. This iterative loop continues until the ground-truth kinetic model is identified or the experimental budget is exhausted.

This approach effectively injects domain-aware qualitative reasoning and knowledge-guided model proposal within a statistically rigorous SR-MBDoE discovery pipeline. The framework is evaluated end-to-end on four kinetic model case studies, measuring iteration count to ground-truth discovery, model predictive accuracy, and effects of ablating components such as LLM scale.

Reproducibility is ensured through open source PySRRegressor for SR and a released source code repository for the entire DASyR-LLM framework along with detailed prompt templates. Datasets are synthetic and publicly described. The LLM configuration details and tuning parameters are documented, but the exact LLM model version used is unspecified in the source. No mention of frozen weights is given.

Technical innovations

• Integration of an LLM as an iterative domain-aware module performing both qualitative physicochemical critique and knowledge-guided candidate generation within a symbolic regression workflow.
• Embedding LLM reasoning within a closed iterative MBDoE loop jointly combining SR, parameter estimation, model selection, and experimental design to accelerate kinetic model discovery.
• Two-stage SR approach: separate symbolic approximation of concentration trajectories followed by SR on numerically differentiated rates to stabilize model discovery and improve interpretability.
• Use of structured LLM prompts containing symbolic expressions, parameters, and AIC metrics, enabling explicit qualitative assessment rather than purely scalar scoring.
• Manual parsing of free-form LLM-generated expressions into kinetic candidate rate laws compatible with parameter estimation and statistical evaluation.

Datasets

• Synthetic kinetic datasets for four case studies of increasing complexity generated via simulation of known ground-truth reaction networks with added Gaussian noise (σ=0.1) on concentration data.

Baselines vs proposed

• Baseline SR-only framework: average iteration count to ground-truth model = 12; DASyR-LLM: 41.7%–79.3% fewer iterations required.
• Baseline SR-only framework: validation R^2 > 0.98; DASyR-LLM: validation R^2 > 0.98 (equivalent predictive accuracy).
• Ablation with smaller LLM: iteration count reduction maintained majority of DASyR-LLM benefit, confirming LLM scale contribution.
• In more than 50% of LLM-guided runs, the LLM directly proposes the exact ground-truth kinetic model structure, not achieved by the baseline alone.

Limitations

• Evaluations are limited to synthetic in silico kinetics datasets; no physical experimental validation presented.
• Adversarial robustness or attacks against the LLM-guided process are not addressed.
• Manual parsing of LLM-generated expressions limits scalability and introduces human-in-the-loop dependency.
• The choice of a particular LLM model and its training details are not fully disclosed, limiting reproducibility of the exact results.
• The approach may be sensitive to LLM prompt engineering; robustness to prompt variations is unclear.
• Noise model assumes Gaussian i.i.d. noise; real experimental noise distributions and measurement errors may be more complex.

Open questions / follow-ons

• How will the framework perform on real experimental data with complex noise and measurement errors?
• Can the LLM module be trained or fine-tuned specifically on chemical kinetics corpora to improve knowledge injection?
• Is it possible to automate parsing of LLM-generated candidate expressions to scale the workflow to larger systems?
• How robust is the framework to variations in LLM prompting strategies or different LLM architectures?

Why it matters for bot defense

For bot-defense and CAPTCHA practitioners, this paper illustrates how LLMs can be embedded as domain-aware reasoning agents within iterative model discovery pipelines to improve search efficiency and align candidate generation with domain constraints. The approach shows that LLMs can effectively reduce combinatorially expensive search spaces by incorporating expert knowledge qualitatively, reducing the number of costly iterations required to find correct models. This insight could be analogously applied in bot detection pipelines where complex model hypotheses or behavioral patterns are explored, helping intelligently narrow or guide the search. However, unlike static CAPTCHA challenges, this method relies on iterative experimental or data collection cycles, which may limit direct translation to real-time bot detection. Nevertheless, the core idea of LLMs serving dual critique-and-proposal roles to guide symbolic or explainable model generation is broadly applicable and worth further exploration in security-relevant settings.

Cite

@article{arxiv2608_05120,
  title={ DASyR-LLM: Domain-Aware Symbolic Regression with LLMs for Kinetic Model Discovery },
  author={ Roberto Aliaga Medina and Paulina Quintanilla and Antonio del Rio Chanona },
  journal={arXiv preprint arXiv:2608.05120},
  year={ 2026 },
  url={https://arxiv.org/abs/2608.05120}
}

Read the full paper

• arXiv:2608.05120 (abstract)
• arXiv:2608.05120 (PDF)