Physics-Informed Neural Networks for Biological $2\mathrm{D}{+}t$ Reaction-Diffusion Systems

• URL: http://arxiv.org/abs/2604.18548v1
• Date: Mon, 20 Apr 2026 17:40:45 GMT
• Title: Physics-Informed Neural Networks for Biological $2\mathrm{D}{+}t$ Reaction-Diffusion Systems
• Abstract summary: Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data.<n>We extend BINNs to $2rmD+t$ systems within a PIN framework that combines data preprocessing, BINN equation learning, and symbolic regression post-processing for closed-form equation discovery.<n>We demonstrate the framework's real-world applicability by learning the governing equations of lung cancer cell population dynamics from timelapse microscopy data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential operator structure (e.g., reaction-diffusion) while learning constitutive terms via trainable neural subnetworks, enforced through soft residual penalties. Existing BINN studies are limited to $1\mathrm{D}{+}t$ reaction-diffusion systems and focus on forward prediction, using the governing partial differential equation as a regulariser rather than an explicit identification target. Here, we extend BINNs to $2\mathrm{D}{+}t$ systems within a PINN framework that combines data preprocessing, BINN-based equation learning, and symbolic regression post-processing for closed-form equation discovery. We demonstrate the framework's real-world applicability by learning the governing equations of lung cancer cell population dynamics from time-lapse microscopy data, recovering $2\mathrm{D}{+}t$ reaction-diffusion models from experimental observations. The proposed framework is readily applicable to other spatio-temporal systems, providing a practical and interpretable tool for fast analytic equation discovery from data.

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