Decoding Cell Signaling Dynamics: Biophysics-Informed Operator Learning to Accelerate Reaction-Diffusion PDE Simulations

Overview

Cell signaling is the process by which cells sense external cues, convert them into biochemical signals, and trigger physiological responses such as gene expression or protein activation. Mathematically, these processes are modeled by reaction-diffusion partial differential equations (PDEs) describing how biomolecules distribute and interact within cells. Accurate simulation of reaction-diffusion systems is essential for drug discovery, cancer biology, and neuroscience. However, solving reaction-diffusion PDEs within realistic cellular geometries is computationally expensive, with numerical methods such as the Finite Element Method (FEM) exhibiting prohibitively long computation times for high-resolution geometries, limiting parameter sweeps and uncertainty analyses. Machine learning offers promising alternatives, but Physics-Informed Neural Networks (PINNs) require retraining for new parameters, while Fourier Neural Operators (FNOs) lack mechanisms for enforcing biophysical constraints. This research develops a biophysics-informed operator learning framework integrating the parametric efficiency of FNOs with the physical consistency of PINNs, enabling fast, accurate simulations across geometries and parameter spaces. The framework was trained on ground-truth FEM simulations, combining data loss with physics-informed loss computed via finite differences (rectangular geometries) or FEM mass/stiffness matrices (irregular geometries). The framework was validated on multiple systems: the diffusion–decay PDE, the Schnakenberg model, and various mixed-dimensional cell signaling models in both 2D and 3D geometries. Results show high accuracy, generalization across unseen parameters, successful handling of rectangular and irregular geometries, and orders-of-magnitude inference speedups. The framework maintains computational efficiency while adhering to biophysical laws, serving as a tool for accelerated cell signaling simulations and discovery in drug development, systems biology, and related fields.

Competition history

• CSEF 2026 Physics & Astronomy (Senior Division) · Entry S-17-18

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