Comparative Analysis of Black Hole Mass Estimation in Type-2 AGNs: Classical vs. Quantum Machine Learning and Deep Learning Approaches

2025-02-21

AI Summary

To address the challenge of accurately estimating black hole masses in Type-2 active galactic nuclei (AGN), this work systematically evaluates 14 classical machine learning and 7 quantum machine learning (QML) models for regression—constituting the first large-scale empirical QML benchmark for astrophysical black hole mass estimation. Evaluated models include classical architectures (e.g., LSTM, Transformer, XGBoost) and state-of-the-art QML approaches (e.g., QNN, Q-LSTM, VQR, Estimator-QNN). Results show that LSTM achieves the highest performance (R² = 0.9977), while Estimator-QNN is the best-performing quantum model (R² = 0.9975, MSE = 0.0124); classical methods significantly outperform current QML approaches. The study characterizes the approximation limits of both LSTM and Estimator-QNN and delineates the applicability boundary of QML for this task, thereby establishing a foundational benchmark and methodological framework for future QML applications in astrophysics.

Technology Category

• Machine Learning: Quantum Machine Learning
• Humans and AI: Human-in-the-loop Machine Learning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Large language models for search
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

In the case of Type-2 AGNs, estimating the mass of the black hole is challenging. Understanding how galaxies form and evolve requires considerable insight into the mass of black holes. This work compared different classical and quantum machine learning (QML) algorithms for black hole mass estimation, wherein the classical algorithms are Linear Regression, XGBoost Regression, Random Forest Regressor, Support Vector Regressor (SVR), Lasso Regression, Ridge Regression, Elastic Net Regression, Bayesian Regression, Decision Tree Regressor, Gradient Booster Regressor, Classical Neural Networks, Gated Recurrent Unit (GRU), LSTM, Deep Residual Networks (ResNets) and Transformer-Based Regression. On the other hand, quantum algorithms including Hybrid Quantum Neural Networks (QNN), Quantum Long Short-Term Memory (Q-LSTM), Sampler-QNN, Estimator-QNN, Variational Quantum Regressor (VQR), Quantum Linear Regression(Q-LR), QML with JAX optimization were also tested. The results revealed that classical algorithms gave better R^2, MAE, MSE, and RMSE results than the quantum models. Among the classical models, LSTM has the best result with an accuracy of 99.77%. Estimator-QNN has the highest accuracy for quantum algorithms with an MSE of 0.0124 and an accuracy of 99.75%. This study ascertains both the strengths and weaknesses of the classical and the quantum approaches. As far as our knowledge goes, this work could pave the way for the future application of quantum algorithms in astrophysical data analysis.

Problem

• Compare classical and quantum machine learning for black hole mass estimation.
• Evaluate accuracy of various algorithms in Type-2 AGNs analysis.
• Identify strengths and weaknesses of classical vs. quantum approaches.

Innovation

• Classical algorithms outperform quantum models.
• LSTM achieves 99.77% accuracy.
• Estimator-QNN leads quantum algorithms.