The use of physics-informed neural networks (PINNs) to map the Zn2+ nanoparticles diffusion in Swiss chard: an AI simplified modelling approach

Abstract

Electrochemical processes are central to energy storage, catalysis, corrosion and sensing, yet understanding and optimising these systems remains challenging. Physics-informed neural networks (PINNs) offer a promising approach by integrating physical laws into machine learning models for improved interpretability and accuracy. In this work, we develop a PINN to simulate the diffusion and electric-field-driven transport of Zn²⁺ ions released from ZnO nanoparticles in the beetroot – Swiss chard – leaf tissue. The model embeds the Poisson’s equation for electric potential and the Nernst–Planck equation for ion flux into the network’s loss function, enabling it to learn physically consistent potential and concentration fields with minimal data. The PINN predictions reveal that Zn²⁺ ions accumulate near leaf edges, a phenomenon also observed experimentally. Using the trained model, we evaluate microelectrode sensor array designs and find that a hexagonal electrode layout would capture the edge-concentrated Zn²⁺ distribution more effectively than a uniform grid. This case study demonstrates how AI modelling informed by physics can accurately replicate experimental trends and guide the design of better electrochemical sensors. The results highlight the broader potential of PINNs to advance electrochemical research by combining data-driven learning with established physical electrochemical principles.