Technical Summary: LEADS – Learning Electrophysiology Hybrid Models through Agentic Discovery of Structure

1. Problem Statement

Building personalized cardiac electrophysiology (EP) digital twins is critical for clinical applications such as guiding catheter ablation, assessing sudden cardiac death risk, and in silico drug testing. However, constructing accurate models is challenging because cardiac electrical propagation is a reaction-diffusion system where both the diffusion component (wavefront spread) and the reaction component (local ionic kinetics) vary significantly across patients due to tissue properties, fibrosis, and disease states.

Current approaches face a trade-off:

• Human-Designed Hybrid Models: Experts manually select a reaction model (e.g., Aliev-Panfilov) and a diffusion operator, then fit parameters. While interpretable, this process is labor-intensive, requires deep domain expertise, and the fixed architecture often fails to transfer across different patients.
• Unconstrained LLM-Based Methods: Recent works like HDTwinGen use Large Language Models (LLMs) to generate arbitrary hybrid model code. While promising for general dynamical systems, these methods lack the necessary structural priors for cardiac EP. They frequently fail to produce physiologically plausible outputs or stable ODE integrations because the code generation space is unconstrained.
• Direct LLM Digital Twins: Using LLMs directly as the model sacrifices the mathematical transparency and physical interpretability required for clinical trust.

The core problem is the lack of a method that can automatically discover the appropriate model structure (not just fit parameters) for each patient while adhering to the strong structural priors required for stable cardiac simulations.

2. Methodology: The LEADS Framework

The authors propose LEADS (Learning Electrophysiology hybrid model through Agentic Discovery of Structure), a framework that formulates cardiac EP domain knowledge as a structured action space and utilizes an LLM agent to navigate it.

Core Architecture

LEADS operates on a reaction-diffusion ODE system defined on a discrete heart mesh $G$:
$$\frac{du}{dt} = D(u, G) + R_u(u, v)$$
$$\frac{dv}{dt} = R_v(u, v)$$
Where $u$ is the transmembrane potential, $v$ is the recovery variable, $D$ governs diffusion, and $R$ represents ionic reaction kinetics.

The Agentic Loop

The system employs an LLM agent (specifically Gemini-2.5-Flash) in an iterative Observe-Think-Act loop:

1. Structured Action Space: Instead of generating arbitrary code, the agent selects from curated catalogs:
   • Diffusion Catalog: Contains neural architectures ranging from simple mean aggregation to complex Graph Attention Networks and Edge MLPs.
   • Reaction Catalog: Contains established physics-based ionic models (e.g., Aliev-Panfilov, Rogers-McCulloch, Mitchell-Schaeffer).
2. Decoupled Decisions: At each step, the agent makes two decisions:
   • Reaction Selection: Chooses a specific physics-based reaction model from the catalog.
   • Diffusion Operation: Selects one of four operations:
     • Select: Choose a new architecture from the catalog.
     • Refine: Adjust hyperparameters (e.g., hidden dimensions, layers) of the current diffusion module.
     • Modify: Freely edit the underlying code to create structural variants beyond templates.
     • Simplify: Reduce complexity to mitigate overfitting.
3. Reasoning and Feedback: The agent observes an archive of previous candidates (validation losses, training curves), reasons about performance issues (e.g., overfitting, insufficient capacity), and proposes a new hybrid structure.
4. Parameter Fitting: For every candidate model proposed by the agent, gradient descent is used to fit the learnable parameters ($\theta, \phi$) to the data by minimizing trajectory errors. The agent handles structural discovery; gradient descent handles parameter optimization.

The process terminates when the action budget is exhausted or convergence is reached, returning the best-performing model.

3. Key Contributions

1. Automated Architecture Discovery: A novel LLM agent-based solution for constructing personalized cardiac EP digital twins, removing the need for manual architecture design by domain experts.
2. Structured Hybrid Action Space: The introduction of LEADS, which combines LLM reasoning with a domain-grounded catalog. This encodes physical priors as composable building blocks, ensuring search efficiency and physical interpretability while allowing open-ended architectural discovery.
3. Validation on Synthetic and Real Data: Demonstration that LEADS outperforms both human-designed hybrid models and unconstrained LLM-based methods without requiring oracle knowledge of the underlying cardiac dynamics.

4. Experimental Results

Synthetic Data Experiments

The framework was tested on synthetic transmembrane potential (TMP) trajectories generated from three ground-truth reaction models (Aliev-Panfilov, Rogers-McCulloch, Mitchell-Schaeffer).

• Performance: LEADS achieved a superior average Mean Squared Error (MSE) of 26.7 ($\times 10^{-3}$), outperforming the human-designed Hybrid-Model (37.6) and significantly outperforming the unconstrained HDTwinGen (416.3), which failed to produce cardiac activation.
• Structure Identification: Despite lacking prior knowledge, LEADS correctly identified the ground-truth reaction model for all three datasets and optimized the neural diffusion component to accurately reproduce activation time (AT) wavefront patterns.

Real Data Experiments

Validation was performed on real Endocardial Electrogram (EGM) recordings from the Utah dataset (animal model).

• Metrics: Evaluated using Test Mean Activation Time (AT) Error.
• Results: LEADS achieved an AT error of 5.52, outperforming the best human-designed Hybrid-Model (5.64). While an oracle Physics-Based model (with known reaction) achieved 3.42, LEADS approached this performance autonomously.
• Qualitative Analysis: Visual AT maps showed that LEADS produced smooth activation patterns aligning more closely with ground truth than the human-designed hybrid model, which exhibited pronounced activation time delays.

Ablation Studies

• Diff-Only (Fixed Reaction): Performed comparably on some datasets but degraded on others, showing that even with correct kinetics, expressive diffusion is necessary.
• React-Only (Fixed Diffusion): Worsened performance significantly (e.g., RM error increased from 10.1 to 20.4), indicating that a fixed diffusion architecture bottlenecks performance.
• All-Neural: Replacing the physics catalog with a fully data-driven module consistently degraded performance, confirming that physics-based reaction priors are indispensable under limited training data.

5. Significance and Claims

The paper claims that LEADS successfully bridges the gap between the interpretability of human-designed models and the automation of LLM-based discovery. By constraining the LLM agent to a structured, domain-informed action space, the framework avoids the instability and physiological implausibility of unconstrained code generation while eliminating the labor and rigidity of manual design.

The authors emphasize that LEADS demonstrates that joint search over a hybrid physics-neural catalog is essential for robust cardiac EP modeling. The framework achieves competitive accuracy on real clinical data without requiring oracle knowledge of the underlying dynamics, suggesting a viable path toward scalable, personalized digital twins. The authors note that current limitations include a single heart mesh geometry and a fixed catalog, with future work planned to extend to multi-geometry settings and diverse physiological domains.