Neural surrogates for designing gravitational wave detectors

TL;DR

This work tackles the computational bottleneck in designing gravitational wave detectors by replacing CPU-only physics simulators with neural surrogates. It introduces the quasi-Universal InterFerOmeter (UIFO) as an expressive design template and trains transformer-based surrogates to predict both sensitivity curves and component powers, enabling fast, differentiable optimization. Through an online active-learning loop (SPROUT), the method iteratively expands the training data with surrogate-generated designs that are verified by the slow simulator, achieving high-quality designs with substantially reduced compute time, especially for larger designs like the 3×3 UIFO. The approach demonstrates significant speedups and design improvements, suggesting broad applicability to other domains with expensive, non-differentiable simulators. Overall, SPROUT combines patch-based input representations, Fourier features, and GPU-accelerated optimization to advance inverse design in complex physical systems.

Abstract

Physics simulators are essential in science and engineering, enabling the analysis, control, and design of complex systems. In experimental sciences, they are increasingly used to automate experimental design, often via combinatorial search and optimization. However, as the setups grow more complex, the computational cost of traditional, CPU-based simulators becomes a major limitation. Here, we show how neural surrogate models can significantly reduce reliance on such slow simulators while preserving accuracy. Taking the design of interferometric gravitational wave detectors as a representative example, we train a neural network to surrogate the gravitational wave physics simulator Finesse, which was developed by the LIGO community. Despite that small changes in physical parameters can change the output by orders of magnitudes, the model rapidly predicts the quality and feasibility of candidate designs, allowing an efficient exploration of large design spaces. Our algorithm loops between training the surrogate, inverse designing new experiments, and verifying their properties with the slow simulator for further training. Assisted by auto-differentiation and GPU parallelism, our method proposes high-quality experiments much faster than direct optimization. Solutions that our algorithm finds within hours outperform designs that take five days for the optimizer to reach. Though shown in the context of gravitational wave detectors, our framework is broadly applicable to other domains where simulator bottlenecks hinder optimization and discovery.

Figures (7)

• Figure 1: A highly expressive ansatz: quasi-Universal InterFerOmeter (UIFO). A large variety of gravitational wave detectors can be built by aligning optical elements in an irregular rectangular grid. This expressive parametrized template is referred to as quasi-Universal InterFerOmeter, or UIFO. i) The 3x3 UIFO, with 169 parameters, has 9 beamsplitter cells surrounded by light source cells and a single photodetector. By tuning the parameters of the grid's components, using only a small subset of components, we can recreate a simplified version of the GWD used by the LIGO collaboration. ii) In the depicted design and throughout this paper, we use beamsplitters, mirrors, photodetectors, and lasers. iii) The quality of a GWD is given by the smallest spatial deformation that it can detect for each gravitational wave frequency, represented by a sensitivity curve. As shown in the top plot, these curves can fluctuate in several orders of magnitude in response to a single parameter, like the reflectivity of the top mirror in cell B2. The change is even more drastic when tinkering with the left mirror in cell C2.
• Figure 2: Iterative inverse design with surrogate models.
• Figure 3: Overview of the surrogate model's architecture. After extracting the patches from the grid-based GWD, we transform them into (larger) token representations, which are then processed by a standard transformer encoder. To turn the tokens into the final output, we compress them with a learned projection and concatenate them. The resulting array, larger than the output by design, goes through a final MLP and, after a sigmoid, is turned into the output: the values of the sensitivity curve concatenated with the light powers at each optical element.
• Figure 4: Evolution of the inverse designs' quality after (re)training the surrogate model and comparison with direct optimization. After training the surrogate model with random data we use it to produce hundreds of thousands of novel solutions via gradient-based optimization. Once the designs are verified, they are added to the previous training dataset, to finetune the model. At every generation of finetuned models the training data adds 1 million of new samples. The plotted sensitivities, which improve after every generation, come from the last step of the optimization process of the 200K inverse-designed samples. The optimizations with Finesse, detailed in Figure \ref{['fig:direct_optimization']}, were limited to 256 samples per grid size and ran for 5 days. The benefits of the surrogate models are specially prominent in the larger systems.
• Figure 5: Positioning of the optical elements. To keep the grid structure, we locate the mirrors of the optical path based on fractions of larger distances, vertical $\{V_i\}$ and horizontal $\{H_j\}$, which are also fractions of a maximum vertical and horizontal size, up to 4km. For the sake of readability, we keep the mirrors within the cells, so the mirrors between beam splitters can be localized as a fraction of half the gap between beam splitters. The distance between light sources and their nearest mirrors is fixed, since that does not affect the design performance. Same applies for the detector and its nearest mirror.