Fourier Feature Networks for High-Fidelity Prediction of Perturbed Optical Fields

2025-08-27

AI Summary

Standard multilayer perceptrons (MLPs) suffer from spectral bias, hindering accurate modeling of high-frequency complex-valued optical field perturbations. To address this, we propose Fourier Feature Networks (FFNs), which map inputs into a perturbation-dependent Fourier basis space, transforming nonlinear learning into linear combination of precomputed basis functions. FFNs enable end-to-end learning of the complex-valued transmission matrix under multimode fiber compression. This approach significantly reduces model complexity while enhancing generalization. Experiments demonstrate that FFN achieves one-order-of-magnitude lower prediction error than standard MLPs, attains an average complex correlation coefficient of 0.995 for both amplitude and phase, and reduces parameter count by 85%. By explicitly encoding high-frequency priors via Fourier features, FFN effectively overcomes the representational bottleneck of conventional neural networks in optical high-frequency modeling.

Technology Category

• Machine Learning: Multimodal Learning
• Computer Vision: Learning & Optimization for CV
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Modelling the effects of perturbations on optical fields often requires learning highly oscillatory complex-valued functions. Standard multi-layer perceptrons (MLPs) struggle with this task due to an inherent spectral bias, preventing them from fitting high-frequency sinusoids. To overcome this, we incorporate Fourier features - a set of predefined sinusoids dependent on the perturbation - as an additional network input. This reframes the learning problem from approximating a complex function to finding a linear combination of basis functions. We demonstrate this method by training a Fourier Feature Network to predict the transmission matrix of a multimode fibre under mechanical compression. Compared to a standard MLP, our network reduces prediction error in the output field's amplitude and phase by an order of magnitude, achieving a mean complex correlation of 0.995 with the ground truth, despite using 85% fewer parameters. This approach offers a general and robust method for accurately modelling a wide class of oscillatory physical systems.

Problem

• Predicting perturbed optical fields with high accuracy
• Overcoming MLP limitations in learning oscillatory functions
• Modeling transmission matrix of compressed multimode fibers

Innovation

• Uses Fourier features as network input
• Transforms problem to linear combination
• Achieves high accuracy with fewer parameters