Physics-informed neural network surrogate model for capacitive touch sensors by solving maxwell's equations

Capacitive sensors based human-machine interfaces (HMI) have revolutionised in-cabin user interaction in automobiles. However, robust functionality and stability of the sensors in dynamic environmental conditions necessitate profound domain expertise coupled together with computationally intensive multi-physics simulations. As a promising alternative, this paper investigates the application of Physics-informed neural networks (PINNs) as a surrogate sensor model to capture the electrostatic behaviour of a capacitive sensor interacting with a conductor such as a human finger. Maxwell's equations are the fundamental governing laws for understanding the interplay of electric field interactions in a capacitive sensor. The PINN model solves these electrostatic equations for different positions of a finger interacting with the sensor. Given a finger position and a spatial coordinate in a 3D domain encompassing the finger, sensor, and PCB, the trained surrogate model is capable of predicting key electrostatic properties such as electric potential, electric field distribution, and charge density. The governing equations are incorporated into the neural network's loss function to capture the underlying physics. The performance of the model is evaluated on a wide range of unseen test scenarios, encompassing a diverse set of finger positions. Additionally, the capacity of the learnt PINN model to emulate a real-world sensor array setup is presented. Results demonstrate the significant potential of PINNs as surrogate models in electrostatics, thereby paving the way for a promising future in sensor design optimisation and degradation analysis.