Capacitive Touch Sensor Modeling With a Physics-informed Neural Network and Maxwell's Equations

TL;DR

This work addresses the need for rapid, physics-consistent modeling of capacitive touch sensors by developing a 3D physics-informed neural network that solves electrostatic Maxwell equations under an electroquasistatic approximation. By jointly optimizing data-driven and physics-driven losses over a non-uniform 3D grid, the approach predicts $\mathbf{E}$, $V$, and $\rho$ for varying finger distances with good generalization to unseen configurations. The results show substantial inference-time speedups (≈10x) over traditional FEM-like solvers and demonstrate the network’s capability to handle multiple finger positions, while highlighting boundary-region challenges near the finger where errors are larger. The method offers a promising surrogate for fast design optimization and can be extended to sensor arrays and more complex geometries in automotive and consumer electronics contexts.

Abstract

Maxwell's equations are the fundamental equations for understanding electric and magnetic field interactions and play a crucial role in designing and optimizing sensor systems like capacitive touch sensors, which are widely prevalent in automotive switches and smartphones. Ensuring robust functionality and stability of the sensors in dynamic environments necessitates profound domain expertise and computationally intensive multi-physics simulations. This paper introduces a novel approach using a Physics-Informed Neural Network (PINN) based surrogate model to accelerate the design process. The PINN model solves the governing electrostatic equations describing the interaction between a finger and a capacitive sensor. Inputs include spatial coordinates from a 3D domain encompassing the finger, sensor, and PCB, along with finger distances. By incorporating the electrostatic equations directly into the neural network's loss function, the model captures the underlying physics. The learned model thus serves as a surrogate sensor model on which inference can be carried out in seconds for different experimental setups without the need to run simulations. Efficacy results evaluated on unseen test cases demonstrate the significant potential of PINNs in accelerating the development and design optimization of capacitive touch sensors.

Figures (2)

• Figure 1: System Architecture of the PINN Process
• Figure 2: Comparison of PINN Output and Simulation Target as Heatmaps at the Cross-section Plane $x=0$