Physics-Informed Neural Networks Simulate Dopamine Diffusion: Innovative Applications of PINN in Neuroscience

Key Takeaways: This project implements a Physics-Informed Neural Network (PINN) using JAX to simulate the 2D reaction-diffusion process of dopamine in synaptic clefts, addressing the limitations of traditional numerical methods in handling complex boundaries and inverse problems. The project supports solving both forward problems (concentration field prediction) and inverse problems (parameter inversion), and integrates uncertainty quantification, providing an open-source computational tool for research on dopamine-related neurological diseases such as Parkinson's disease. The project code is open-sourced on GitHub, and the associated paper is under review at PLOS Computational Biology.

Dopamine is a key neurotransmitter that regulates functions such as movement and emotion. Its release, diffusion, and reuptake processes in synaptic clefts are crucial for neural signal transmission, and abnormal dynamics are associated with Parkinson's disease. Traditional modeling relies on finite difference methods, but has limitations in solving complex geometric boundaries and inverse problems. As an integration of deep learning and scientific computing, PINN provides a new approach for neurobiophysics modeling.

Tech Stack: Pure JAX implementation using libraries like Flax NNX, Optax, and jaxopt, leveraging JIT and automatic differentiation features. Core Mathematical Model: 2D reaction-diffusion equation ∂C/∂t = D·∇²C -k·C, where parameters D=0.32µm²/ms (diffusion coefficient) and k=0.05 1/ms (reuptake rate) are based on experimental data from classic literature. Neural Network Architecture: A 4-layer fully connected network (64 neurons per layer, tanh activation, Glorot initialization) that takes spatiotemporal coordinates (x,y,t) as input to predict concentration, trained by minimizing PDE residuals and violations of initial/boundary conditions.

Forward Problem: Verify PINN's ability to predict the spatiotemporal evolution of dopamine concentration using three validation methods: comparison with the approximate analytical solution for infinite domains, cross-validation with finite difference methods, and comparison with the DeepXDE reference implementation. Inverse Problem: Infer D and k from noisy observation data by exposing the parameters as learnable ones, using logarithmic parameterization to ensure positive values, recovering parameters from 400 observation points with 2% noise, and testing convergence with offset initial guesses.

Implementation of Uncertainty Quantification:

• Laplace Approximation: Estimate parameter uncertainty using posterior Gaussian approximation;
• Hamiltonian Monte Carlo (HMC): Exact Bayesian posterior sampling;
• Noise Sensitivity Analysis: Test recovery performance under 5 noise levels;
• Observation Density Scaling: Analyze the relationship between the number of observation points and parameter recovery accuracy. These analyses enhance the model's reliability on real experimental data.

Experimental Results: Generate visual outputs such as spatiotemporal snapshot comparisons (PINN vs analytical solution vs finite difference), concentration heatmaps, parameter convergence trajectories, and posterior distribution plots; results are saved in metrics.json. Performance: Completes in 5-10 minutes on GPU, 10-15 minutes on CPU, memory ≤4GB, fixed random seed ensures reproducibility. Academic Value: Provides a new tool for neurotransmitter diffusion research, supports studies on Parkinson's disease mechanisms, demonstrates the potential of interdisciplinary integration, and is open-source and reproducible. Application prospects include drug design, disease modeling, brain-computer interfaces, and other fields.