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

Area of Science:

• Computational science
• Biophysics
• Machine learning

Background:

• Data-driven models for particle-based communication channels often need extensive data and capture limited physical process statistics.
• Bridging mechanistic partial differential equation (PDE) modeling with data-driven surrogates is crucial for improving channel model accuracy and efficiency.

Purpose of the Study:

• To develop a physics-informed machine learning framework for diffusion-based particle signaling channels.
• To fuse sparse channel measurements with governing diffusion-reaction laws for enhanced modeling.
• To explore physics-informed operator learning for particle-based communication channels.

Main Methods:

• Developed a Physics-Informed Neural Operator (PINO) framework to predict spatiotemporal particle concentration fields.
• Applied PINO to diffusion-based particle signaling and bacterial quorum sensing models.
• Compared PINO with Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets).

Main Results:

• PINO significantly reduced relative L2 error from 99.3% to 9.2% on a nanomachine channel model.
• PINO improved R-squared from 0.808 (DeepONet) to 0.999 for a quorum sensing model.
• Multi-resolution inference with PINO achieved 4-5x speed-ups on coarse grids, demonstrating computational efficiency.

Conclusions:

• Physics-informed operator learning offers a promising approach for modeling particle-based communication networks.
• PINO provides high accuracy and computational efficiency compared to existing methods.
• The framework generalizes across channel configurations with reduced dependence on geometric parameterization.