# Fourier Neural Operators for Fast Multi-Physics Sensor Response Prediction: Applications in Thermal, Acoustic, and Flow Measurement Systems

## TL;DR

This paper introduces a new AI method called Fourier Neural Operators (FNO) to predict sensor responses in thermal, acoustic, and flow systems much faster than traditional methods.

## Contribution

The paper introduces the first systematic use of FNO for multi-physics sensor prediction and a novel H-FNO architecture to address spectral bias.

## Key findings

- FNO achieves thermal sensor predictions with R2>0.98 and 8300× speedup over FEM.
- Acoustic sensor modeling with <0.5 dB error and 4000× speedup over BEM is demonstrated.
- Flow sensor velocity predictions exceed 97% accuracy with 31,000× speedup over CFD.

## Abstract

Accurate and rapid prediction of sensor responses is critical for real-time measurement systems, digital twin implementations, and sensor design optimization. Traditional numerical methods such as Finite Element Method (FEM) and Computational Fluid Dynamics (CFD) provide high-fidelity solutions but suffer from prohibitive computational costs, limiting their applicability in time-sensitive applications. This paper presents a novel framework utilizing Fourier Neural Operators (FNO) as surrogate models for fast multi-physics sensor response prediction across thermal, acoustic, and flow measurement domains. Unlike conventional neural networks that learn finite-dimensional mappings, FNO learns operators between infinite-dimensional function spaces by parameterizing the integral kernel in Fourier space, enabling resolution-invariant predictions with remarkable computational efficiency. We demonstrate the framework’s efficacy through three comprehensive case studies: (1) thermal sensor response prediction achieving R2>0.98 with 8300× speedup over FEM, (2) acoustic sensor array modeling with mean absolute error below 0.5 dB and 4000× speedup over BEM, and (3) flow sensor characterization with velocity field prediction accuracy exceeding 97% and 31,000× speedup over CFD. The proposed FNO-based surrogate models are trained on simulation datasets generated from high-fidelity numerical solvers and validated against simulation holdout data for all three case studies, with additional experimental validation conducted for the thermal sensor case. Results indicate that FNO architectures effectively capture the underlying physics governing sensor behavior while reducing inference time from minutes to milliseconds. The framework enables real-time sensor calibration, uncertainty quantification, and design optimization, opening new possibilities for intelligent measurement systems and Industry 4.0 applications. We also investigate the spectral characteristics of FNO predictions, addressing the inherent low-frequency bias through a hybrid architecture combining FNO with local convolutional layers. The primary contributions of this work include: (1) the first systematic application of FNO-based surrogate modeling specifically tailored for sensor response prediction across multiple physics domains, (2) a novel H-FNO architecture that combines spectral operators with local convolutions to mitigate spectral bias in sensor applications, and (3) comprehensive validation including both simulation and experimental data for practical deployment. This work establishes FNO as a powerful tool for accelerating sensor simulation and advancing the field of AI-enhanced instrumentation and measurement.