Transformers with Physics-Informed Encodings and Simulation-Based Inference for Robust Detection of Eccentric Binary Black Holes in Pulsar Timing Array Data

2026-07-04

AI Summary

Traditional Bayesian methods for inferring eccentric binary black hole parameters in pulsar timing arrays are hindered by high-dimensional parameter spaces, complex noise models, and computationally expensive likelihood evaluations. This work proposes a novel framework that integrates a physics-informed positional encoding scheme within a Transformer architecture and leverages simulation-based inference. For the first time, analytical gravitational-wave phase evolution is embedded directly into the positional encoding, enabling physics-aware, end-to-end posterior inference. By combining discrete and continuous conditional normalizing flows, the method significantly outperforms baseline approaches lacking physical priors across a range of signal-to-noise ratios, yielding sharper and more accurate posterior distributions while substantially improving computational efficiency. The modular design of the framework naturally accommodates realistic scenarios, such as the inclusion of red noise.

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.

Problem

• pulsar timing arrays
• eccentric binary black holes
• gravitational waves
• parameter inference
• noise modeling

Innovation

• Physics-Informed Transformer
• Simulation-Based Inference
• Pulsar Timing Arrays
• Eccentric Binary Black Holes
• Conditional Normalizing Flows