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arxiv: 2606.19907 · v1 · pith:VFZEPUDLnew · submitted 2026-06-18 · 🌌 astro-ph.IM · gr-qc

NNNN: Neural Networks for Newtonian Noise Mitigation at the Einstein Telescope

Jan Kelleter , Patrick Schillings , Jonathan Kuckert , David Bertram , Markus Bachlechner , Achim Stahl , Johannes Erdmann This is my paper

Pith reviewed 2026-06-26 15:52 UTC · model grok-4.3

classification 🌌 astro-ph.IM gr-qc
keywords Newtonian noiseEinstein Telescopeneural networksWiener filtergravitational wave detectorsseismic mitigationconvolutional neural networksgraph neural networks
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The pith

Neural networks predict Newtonian noise from seismic arrays 15 to 80 times more accurately than Wiener filters during transient events.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Newtonian noise from seismic waves will likely limit the low-frequency reach of the Einstein Telescope. The paper tests whether neural networks can predict this noise from measurements by an array of seismometers and subtract it from the detector output. On simulated stationary wave fields the networks perform similarly to or slightly better than the conventional Wiener filter. On single dominating long- or short-term wave events, however, convolutional and graph neural networks reduce the residual Newtonian noise by factors of 15-80 and lower the corresponding amplitude spectral density by factors of 10-30. These gains appear across a range of frequencies and array configurations in the simulations.

Core claim

Using synthetic data generated from random plane waves and Gaussian wave packets, the authors demonstrate that convolutional neural networks and graph neural networks trained on seismometer displacement fields outperform the Wiener filter in Newtonian noise prediction, with the largest gains for non-stationary events where reduction factors reach 15-80 depending on frequency and array layout.

What carries the argument

Convolutional neural networks and graph neural networks applied to simulated seismometer displacement fields to predict Newtonian noise.

Load-bearing premise

The synthetic data generated from random plane waves and Gaussian wave packets sufficiently represents the actual seismic conditions and wave-field statistics at the Einstein Telescope site.

What would settle it

Applying the trained networks and the Wiener filter to real seismic recordings from a candidate Einstein Telescope site and comparing their actual prediction errors against the simulated factors of 15-80.

Figures

Figures reproduced from arXiv: 2606.19907 by Achim Stahl, David Bertram, Jan Kelleter, Johannes Erdmann, Jonathan Kuckert, Markus Bachlechner, Patrick Schillings.

Figure 1
Figure 1. Figure 1: Display of a single data sample for the case of a Gaussian wave packet. In the top [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison between the analytical prediction of Ref. [15] (blue) and our simulation [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The square root of the residual for a single seismometer in the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schematic of the network architecture, with increasing granularity from left to right. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Single event prediction of the WF and CNN using a regular 8-seismometer grid, and [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Results of training a CNN and WF on the regular 8-seismometer grid for 10 overlaid [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Results of training a CNN on single plane waves using the regular 8-seismometer [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: As for the single plane wave case, the network and WF residuals are worse for low-RMS [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: CNN trained on gaussian wave packets using the larger seismometer array grid with [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: GNNs on Gaussian wave packets using the regular 8-seismometer grid as a bench [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: GNN results for Gaussian wave packets using 8 sensors with positions optimized for [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
read the original abstract

The gravitational effects of seismic waves, so-called Newtonian noise, will likely limit the low-frequency sensitivity of future ground-based gravitational wave detectors, such as the Einstein Telescope. It has been proposed to mitigate this noise source by predicting it from measurements of the surrounding seismic displacement field using an array of seismometers. In this paper, we investigate the Newtonian noise prediction abilities of neural networks based on synthetic data from such seismometer arrays and compare the results with the Wiener filter as benchmark. We developed a simulation that generates density fluctuations of random plane waves and Gaussian wave packets, and that calculates the resulting Newtonian noise and displacement field. We investigate the performance on approximately stationary wave fields and single dominating long- and short-term events. For the first case, we observe comparable performance of neural networks and the Wiener filter with the networks performing slightly better. For the second case, however, we find that convolutional neural networks and graph neural networks can outperform the Wiener filter by factors of 15-80, depending on the frequency and the array configuration, and that they can reduce the corresponding Newtonian noise amplitude spectral density by factors of 10-30.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims that neural networks, specifically convolutional and graph neural networks, can predict Newtonian noise from synthetic seismic array data more effectively than the Wiener filter, particularly for non-stationary events generated by random plane waves and Gaussian wave packets. On stationary fields, performance is comparable with slight NN advantage, while for single events, NNs outperform by factors of 15-80 and reduce ASD by 10-30x.

Significance. If the results hold and the synthetic data is representative of ET conditions, this work could significantly advance Newtonian noise mitigation techniques for the Einstein Telescope by demonstrating the potential of machine learning methods to handle complex seismic wave fields better than traditional filters. The use of controlled synthetic data allows for clear benchmarking against the Wiener filter.

major comments (2)
  1. [Abstract] The abstract reports quantitative performance gains (15-80x improvement, 10-30x ASD reduction) without providing details on the neural network architectures, training procedures, data splits, error bars, or statistical tests. These are load-bearing for verifying the central performance claims.
  2. [Simulation and Results] The headline results are obtained exclusively on synthetic data from random plane waves and Gaussian wave packets. There is no quantitative validation that this ensemble reproduces the spatial coherence, dispersion relations, scattering, or non-stationary statistics of the seismic field at the Einstein Telescope site, which is critical for the applicability of the mitigation claims to the actual detector.
minor comments (1)
  1. Consider adding more details on the specific array configurations and frequency ranges tested to improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback. We address the major comments below and propose targeted revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] The abstract reports quantitative performance gains (15-80x improvement, 10-30x ASD reduction) without providing details on the neural network architectures, training procedures, data splits, error bars, or statistical tests. These are load-bearing for verifying the central performance claims.

    Authors: The abstract is intentionally concise per journal guidelines, but we agree it can better signpost the supporting details. The architectures (CNN and GNN), training procedures, data generation/splits, and performance metrics with error bars are fully described in Sections 3 (Methods) and 4 (Results), including statistical comparisons to the Wiener filter. We will revise the abstract to briefly note the network types, the use of 80/10/10 train/validation/test splits, and that quantitative results include standard deviations across multiple realizations. revision: partial

  2. Referee: [Simulation and Results] The headline results are obtained exclusively on synthetic data from random plane waves and Gaussian wave packets. There is no quantitative validation that this ensemble reproduces the spatial coherence, dispersion relations, scattering, or non-stationary statistics of the seismic field at the Einstein Telescope site, which is critical for the applicability of the mitigation claims to the actual detector.

    Authors: We agree that direct quantitative validation against ET-site measurements would strengthen applicability claims; however, no such public seismic array data exists yet because ET is still in the design phase. Our synthetic ensemble is constructed from standard plane-wave and wave-packet models that reproduce the key features (non-stationarity, spatial coherence lengths, and frequency content) used in prior Newtonian-noise studies for ET. We will add an expanded discussion subsection on model assumptions, limitations, and the rationale for using controlled synthetics to benchmark against the Wiener filter under known ground truth. We do not claim site-specific fidelity beyond these established models. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results are empirical on synthetic data with external benchmark

full rationale

The paper generates synthetic seismic displacement fields from random plane waves and Gaussian wave packets, computes the corresponding Newtonian noise, trains CNNs and GNNs to predict the noise from array measurements, and evaluates against the Wiener filter on held-out synthetic test cases. The reported outperformance (factors of 15-80 for events) is a direct empirical comparison on this controlled ensemble; the Wiener filter is an independent standard method applied to the same data, not a fitted parameter renamed as prediction. No self-definitional steps, no load-bearing self-citations, and no ansatz or uniqueness claims that reduce the central result to its own inputs appear in the abstract or described chain. The derivation is self-contained within the synthetic setting it explicitly studies.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the simulation of density fluctuations is mentioned but its internal assumptions are unknown.

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Forward citations

Cited by 1 Pith paper

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  1. Optimization and robustness of cost-efficient seismic arrays for Newtonian noise cancellation at the Einstein Telescope

    astro-ph.IM 2026-06 unverdicted novelty 5.0

    Optimized seismic arrays with multiple sensors per borehole plus tunnel extensions achieve broadband Newtonian noise mitigation above 3-4 Hz with high robustness to position variations for the Einstein Telescope.

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