By name: physicsinformed-neural-networks-biological-2mathrmdt-reactio description: "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 Activation: neural, network, dynamics, population"
Physics-Informed Neural Networks for Biological $2\mathrm{D}{+}t$ Reaction-Diffusion Systems
OverviePhysics-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.
Source Paper
- Title: Physics-Informed Neural Networks for Biological $2\mathrm{D}{+}t$ Reaction-Diffusion Systems
- Authors: William Lavery, Jodie A. Cochrane, Christian Olesen et al.
- arXiv: 2604.18548v1
- Published: 2026-04-20
- Categories: cs.LG, q-bio.QM
- PDF: Download
Key Contributions
Based on the abstract, this paper makes the following contributions:
- Novel approach to neural, network, dynamics, population
- Methodology bridging computational neuroscience with practical applications
- Evaluation demonstrating effectiveness in relevant tasks
Core Concepts
Methodology
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
Technical Details
- The paper introduces a framework/method for neuroscience-related computation
- Key innovation in handling neural, network, dynamics data/tasks
- Provides theoretical grounding and experimental validation
Practical Applications
Application Area
This research has implications for:
- Brain-computer interfaces
- Neural decoding and encoding
- Computational modeling of brain function
- AI systems inspired by neuroscience
Implementation Considerations
Key implementation aspects:
- Data preprocessing for neuroimaging/neural signals
- Model architecture choices
- Training and evaluation protocols
Related Work
This work builds on existing research in:
- Computational neuroscience methods
- neural, network, dynamics analysis
- Brain-inspired AI architectures
References
- William Lavery, Jodie A. Cochrane, Christian Olesen et al. (2026). "Physics-Informed Neural Networks for Biological $2\mathrm{D}{+}t$ Reaction-Diffusion Systems." arXiv:2604.18548v1.
Activation Keywords
neural, network, dynamics, population