Transformers with Physics-Informed Encodings and Simulation-Based Inference for Robust Detection of Eccentric Binary Black Holes in Pulsar Timing Array Data
Abstract
Pulsar timing arrays (PTAs) provide a unique window into nanohertz gravitational waves (GWs), but extracting astrophysical parameters from noisy, long-baseline timing residuals remains computationally challenging with traditional Bayesian techniques due to the high dimensionality of the parameter space, complex and correlated noise models, and the cost of repeated likelihood evaluations. We introduce a Transformer with a physics-informed positional-encoding framework for the efficient inference of eccentric binary black holes in relativistic orbits from PTA data. Our approach embeds analytical GW phase evolution directly into the model through structured positional encodings, enabling the network to learn physically meaningful representations from raw PTA timing residuals. We then use generative models, including discrete and continuous conditional normalizing flows, to infer posterior distributions within a simulation-based inference framework. Across a range of signal-to-noise ratios, the proposed method achieves improved accuracy, sharper posteriors, and faster inference compared to physics-agnostic baselines. While presented for deterministic white-noise signals, the modular framework readily generalizes to realistic PTA analyses incorporating red noise and additional components. This work highlights the potential of physics-aware deep learning models as scalable alternatives to conventional inference pipelines for next-generation PTA datasets.
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BibTeX
@misc{dandapat2026transformers,
title = {{Transformers with Physics-Informed Encodings and Simulation-Based Inference for Robust Detection of Eccentric Binary Black Holes in Pulsar Timing Array Data}},
author = {Subhajit Dandapat and Alvin J. K. Chua},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.03904},
eprint = {2607.03904},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.03904},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Transformers with Physics-Informed Encodings and Simulation-Based Inference for Robust Detection of Eccentric Binary Black Holes in Pulsar Timing Array Data
AU - Subhajit Dandapat
AU - Alvin J. K. Chua
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2607.03904
UR - https://arxiv.org/abs/2607.03904
AB - Pulsar timing arrays (PTAs) provide a unique window into nanohertz gravitational waves (GWs), but extracting astrophysical parameters from noisy, long-baseline timing residuals remains computationally challenging with traditional Bayesian techniques due to the high dimensionality of the parameter space, complex and correlated noise models, and the cost of repeated likelihood evaluations. We introduce a Transformer with a physics-informed positional-encoding framework for the efficient inference of eccentric binary black holes in relativistic orbits from PTA data. Our approach embeds analytical GW phase evolution directly into the model through structured positional encodings, enabling the network to learn physically meaningful representations from raw PTA timing residuals. We then use generative models, including discrete and continuous conditional normalizing flows, to infer posterior distributions within a simulation-based inference framework. Across a range of signal-to-noise ratios, the proposed method achieves improved accuracy, sharper posteriors, and faster inference compared to physics-agnostic baselines. While presented for deterministic white-noise signals, the modular framework readily generalizes to realistic PTA analyses incorporating red noise and additional components. This work highlights the potential of physics-aware deep learning models as scalable alternatives to conventional inference pipelines for next-generation PTA datasets.
ER -