Fighting Newtonian Noise with Gradient-Based Optimization at the Einstein Telescope

TL;DR

This paper introduces a gradient-based optimization method to determine optimal seismometer placements around the Einstein Telescope to mitigate Newtonian noise, outperforming traditional metaheuristics in efficiency and effectiveness.

Contribution

It reformulates the seismometer placement problem as a differentiable optimization, enabling efficient gradient-based solutions for Newtonian noise reduction in gravitational wave detectors.

Findings

Gradient-based optimization matches metaheuristics for small seismometer arrays.

It outperforms metaheuristics in larger arrays by a factor of 2.25 in noise reduction.

Gradient methods are more computationally efficient than metaheuristics.

Abstract

Newtonian noise in gravitational wave detectors originates from density fluctuations in the adjacency of the interferometer mirrors. At the Einstein Telescope, this noise source is expected to be dominant for low frequencies. Its impact is proposed to be reduced with the help of an array of seismometers that will be placed around the interferometer endpoints. We reformulate and implement the problem of finding the optimal seismometer positions in a differentiable way. We then explore the use of first-order gradient-based optimization for the design of the seismometer array for 1 Hz and 10 Hz and compare its performance and computational cost to two metaheuristic algorithms. For 1 Hz, we introduce a constraint term to prevent unphysical optimization results in the gradient-based method. In general, we find that it is an efficient strategy to initialize the gradient-based optimizer with a fast metaheuristic algorithm. For a small number of seismometers, this strategy results in approximately the same noise reduction as with the metaheuristics. For larger numbers of seismometers, gradient-based optimization outperforms the two metaheuristics by a factor of 2.25 for the faster of the two and a factor of 1.4 for the other one, which is significantly outperformed by gradient-based optimization in terms of computational efficiency.