Physics-Informed Neural Operators for Signal Modeling in Particle-based Communications

Data-driven channel models often require extensive simulation data and capture only limited statistics of the underlying physical process. To address these limitations in diffusion-based particle signaling, we build upon physics-informed machine learning to develop a framework that fuses sparse channel measurements with governing diffusion-reaction laws. This work explores physics-informed operator learning for particle-based communication channels, aiming to bridge mechanistic PDE modeling and data-driven surrogates in this domain. Our method employs a Physics-Informed Neural Operator (PINO) to predict the spatiotemporal particle concentration field and generalizes across channel configurations with reduced dependence on explicit geometric parameterization. We further extend the framework to model quorum sensing between bacterial colonies and capture autoinducer dynamics. Compared with Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets), PINO achieves high accuracy and significant computational efficiency: on the nanomachine channel, PINO reduces the relative ℓ₂ error from 99.3% to 9.2%; on the quorum sensing model, PINO improves R² from 0.808 (DeepONet) to 0.999, while multi-resolution inference yields 4-5× speed-ups on coarse grids. These results highlight physics-informed operator learning as a promising method for particle-based communication networks.