AI forecasting of higher-order wave modes of spinning binary black hole mergers

2024-09-05

arXiv.org

AI Summary

Accurately modeling higher-order gravitational-wave modes (up to (l leq 4), including the ((5,5)) mode) during the late inspiral–merger–ringdown phase ((-100M) to (+130M)) of binary black hole coalescences remains computationally demanding for numerical relativity and challenging for surrogate models. Method: We propose a physics-informed Transformer architecture, incorporating priors from the NRHybSur3dq8 numerical relativity waveform model, enabling end-to-end prediction of all dominant and subdominant modes across varying mass ratios, spins, and inclination angles. Contribution/Results: This work presents the first AI-driven, joint surrogate model for the full set of higher-order modes. Evaluated on 840,000 test waveforms, it achieves mean/median matches of 0.996/0.997 against NR. Training on million-scale waveforms requires only 15 hours using distributed A100/H100 accelerators. All code and trained models are publicly released.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

We present a physics-inspired transformer model that predicts the non-linear dynamics of higher-order wave modes emitted by quasi-circular, spinning, non-precessing binary black hole mergers. The model forecasts the waveform evolution from the pre-merger phase through the ringdown, starting with an input time-series spanning $ t in [-5000 extrm{M}, -100 extrm{M}) $. The merger event, defined as the peak amplitude of waveforms that include the $l = |m| = 2$ modes, occurs at $ t = 0 extrm{M} $. The transformer then generates predictions over the time range $ t in [-100 extrm{M}, 130 extrm{M}] $. We produced training, evaluation and test sets using the NRHybSur3dq8 model, considering a signal manifold defined by mass ratios $ q in [1, 8] $; spin components $ s^z_{{1,2}} in [-0.8, 0.8] $; modes up to $l leq 4$, including the $(5,5)$ mode but excluding the $(4,0)$ and $(4,1)$ modes; and inclination angles $ heta in [0, pi]$. We trained the model on 14,440,761 waveforms, completing the training in 15 hours using 16 NVIDIA A100 GPUs in the Delta supercomputer. We used 4 H100 GPUs in the DeltaAI supercomputer to compute, within 7 hours, the overlap between ground truth and predicted waveforms using a test set of 840,000 waveforms, finding that the mean and median overlaps over the test set are 0.996 and 0.997, respectively. Additionally, we conducted interpretability studies to elucidate the waveform features utilized by our transformer model to produce accurate predictions. The scientific software used for this work is released with this manuscript.

Problem

• Modeling higher-order gravitational wave modes from binary black hole mergers
• Predicting waveform evolution from late inspiral to ringdown phases
• Generalizing model accuracy beyond training data for diverse system parameters

Innovation

• Transformer models higher-order gravitational wave modes
• Surrogate model data trains on 14M samples
• Generalizes to mass ratios up to q=15