Combining Machine Learning with Recurrence Analysis for resonance detection (2412.19683v1)

Abstract: The width of a resonance in a nearly integrable system, i.e. in a non-integrable system where chaotic motion is still not prominent, can tell us how a perturbation parameter is driving the system away from integrability. Although the tool that we are presenting here can be used is quite generic and can be used in a variety of systems, our particular interest lies in binary compact object systems known as extreme mass ratio inspirals (EMRIs). In an EMRI a lighter compact object, like a black hole or a neutron star, inspirals into a supermassive black hole due to gravitational radiation reaction. During this inspiral the lighter object crosses resonances, which are still not very well modeled. Measuring the width of resonances in EMRI models allows us to estimate the importance of each perturbation parameter able to drive the system away from resonances and decide whether its impact should be included in EMRI waveform modeling or not. To tackle this issue in our study we show first that recurrence quantifiers of orbits carry imprints of resonant behavior, regardless of the system's dimensionality. As a next step, we apply a long short-term memory machine learning architecture to automate the resonance detection procedure. Our analysis is developed on a simple standard map and gradually we extend it to more complicated systems until finally we employ it in a generic deformed Kerr spacetime known in the literature as the Johannsen-Psaltis spacetime.

• The paper’s main contribution is integrating RQA with LSTM networks to accurately detect resonances in complex EMRI dynamics.
• Methodology employs recurrence quantifiers such as recurrence rate and determinism to capture resonant behavior in diverse system models.
• The framework enhances gravitational waveform predictions, offering valuable insights for astrophysical research and observatories like LISA.

Combining Machine Learning with Recurrence Analysis for Resonance Detection

The paper focuses on blending machine learning techniques with recurrence analysis to detect resonances in dynamical systems, with a pronounced interest in extreme mass-ratio inspirals (EMRIs). The analysis is rooted in understanding how the resonance width in nearly integrable systems can inform the deviation driven by perturbation parameters. Given the intricate dynamics of EMRIs, which involve a lighter compact object inspiraling into a supermassive black hole and traversing resonance zones, accurately modeling these phenomena is paramount for the generation of EMRI waveform models.

Key Insights and Methodology

The outlined paper demonstrates that recurrence quantifiers of orbits reliably capture resonant behaviors. The authors initially employ recurrence quantification analysis (RQA) to evaluate trajectories in phase space. This analysis is leveraged irrespective of the system's dimensionality, thus allowing broad application. They explore different quantitative measures, including recurrence rate, determinism, and laminarity, providing a numerical insight into the system's dynamics.

Subsequently, a long short-term memory (LSTM) neural network architecture is deployed to automate resonance detection. The LSTM network processes time-series data and identifies resonances by analyzing patterns in the recurrence quantifiers obtained from RQA. The method is validated on various systems, progressing from a simple standard map to the more complex Johannsen-Psaltis spacetime—a deformed Kerr spacetime that simulates an astrophysical environment for detecting EMRI resonances.

Numerical Results and Findings

The resonance detection framework is powered by a blend of RQA measures and machine learning. The results, especially when applied to systems like the de Vogeleare map and Johannsen-Psaltis spacetime, reveal the ability to detect resonances effectively. For instance, when tested on the Johannsen-Psaltis spacetime, the LSTM network identified orbital resonances with significant precision. This demonstrates the robustness and utility of combining RQA and LSTM in tackling high-dimensional, weakly non-integrable problems.

Implications and Future Prospects

The fusion of RQA with machine learning marks a significant step towards refining the detection and analysis of resonances in complex dynamical systems such as EMRIs. Practically, the method enhances our capability to predict gravitational waveforms emitted by EMRIs, which holds importance for observatories like LISA. Theoretically, it provides a viable path to handling high-dimensional dynamical systems where traditional Poincaré-based methods fall short.

Looking forward, there is potential to improve the network's architecture and the diversity and generality of training datasets to enhance performance further. Future research could focus on applying the developed technique to other multi-degree-of-freedom systems, potentially improving the paper of resonant orbital dynamics and expanding applications across complex physical systems.