Graph Neural Networks for Interferometer Simulations

TL;DR

The paper develops graph neural networks to accelerate interferometer simulations, focusing on steady-state optical fields in LIGO-like cavities. It constructs a graph-based representation of optical components, trains GNNs to predict both powers and spatial intensity distributions, and introduces a DeepKAN-based pipeline to exploit radial symmetry in the intensity maps. The approach yields substantial speedups over FINESSE and SIS while achieving accurate predictions for multiple topologies, though challenges remain in generalization to unseen configurations. The work provides a benchmarking dataset and outlines concrete directions to incorporate more physics and scale toward full interferometer design.

Abstract

In recent years, graph neural networks (GNNs) have shown tremendous promise in solving problems in high energy physics, materials science, and fluid dynamics. In this work, we introduce a new application for GNNs in the physical sciences: instrumentation design. As a case study, we apply GNNs to simulate models of the Laser Interferometer Gravitational-Wave Observatory (LIGO) and show that they are capable of accurately capturing the complex optical physics at play, while achieving runtimes 815 times faster than state of the art simulation packages. We discuss the unique challenges this problem provides for machine learning models. In addition, we provide a dataset of high-fidelity optical physics simulations for three interferometer topologies, which can be used as a benchmarking suite for future work in this direction.

Figures (4)

• Figure 1: Interferometer simulation pipeline. The FINESSE interferometer model is converted into an optical graph, where each optic is broken down into a node for each incoming or outgoing field. This graph is fed to the model, which produces a radial intensity distribution, which is then rotated to produce the final intensity distribution.
• Figure 2: Correlations between dataset and mixed model predictions for the Fabry-Perot cavity. Units are in watts. Best fit lines are plotted in blue. A slope close to 1 indicates strong agreement between model predictions and ground truth data. In order, the slopes of the lines of best fit are $m=1.00, 1.16, 0.95, 0.82$.
• Figure 3: An example of intensity prediction results on coupled-cavity dataset. We note the following: The intensity prediction model accurately captures the differences in power at different points in the interferometer. Despite the similar, Gaussian profiles in the laser field and the cavity field, the intensity is almost an order of magnitude larger in the cavity, which the model captures. Equally importantly, the model captures the higher order modes present in fields at other points in the interferometer, namely in the reflected field, which contains a higher order modes, producing the second ring seen in the intensity profile. Errors in the first three rows are visible as a small bright patch in the center of the image; they are orders of magnitude smaller than the true intensity.
• Figure 4: The interferometer topologies that we consider in this paper, in order of increasing complexity. a) A Fabry-Perot resonator is the simplest optical cavity. It consists of two curved mirrors, which reflect the light back and forth, building up power inside the cavity. b) A coupled cavity system. Two more mirrors are placed after the Fabry-Perot cavity, creating a second cavity, which must be mode matched to the first. c) a Arm-SRC coupled cavity (CC). This topology contains an a Fabry-Perot resonator, labelled the "arm cavity", and a signal recycling cavity (SRC), which is used to amplify the power in the signal light. d) A dual recycled Fabry-Perot Michelson interferometer. This is the style of interferometer that LIGO is. In addition to the Arm-SRC coupled cavity case, we add the second interferometer arm, and the power recycling cavity (PRC), whose design closely mimics the SRC.