Bayesian-EOS-Inference: Probabilistic Modeling of Neutron Star Parameters

📌 Project Overview

Bayesian-EOS-Inference is a deep learning framework designed to solve a multi-target regression problem in astrophysics: predicting the macroscopic properties of Neutron Stars (Mass, Radius, Tidal Deformability) based on nuclear equation of state (EOS) parameters.

Traditional methods for deriving these parameters involve computationally expensive numerical integration of the Tolman-Oppenheimer-Volkoff (TOV) equations. This project replaces that bottleneck with a Bayesian Neural Network (BNN) capable of:

1. High-Dimensional Mapping: Modeling non-linear relationships between 7-parameter Relativistic Mean Field (RMF) inputs and physical observables.
2. Uncertainty Quantification: Using Monte Carlo Dropout and Probabilistic Layers to output confidence intervals, distinguishing between aleatoric (data) and epistemic (model) uncertainty.
3. Robust Inference: Outperforming baseline XGBoost and deterministic ANN models in noisy data environments.

Data Sources: The dataset consists of simulated Equation of State (EOS) families derived from Relativistic Mean Field (RMF) theory.

• Input Features (7-Dimensional): Nuclear saturation parameters $(\rho_0, \epsilon_0, K, J, L, \ldots)$ representing the micro-physics of nuclear matter.
• Target Variables (3-Dimensional):
• $M_{max}$: Maximum Mass of the star.
• $R_{1.4}$: Radius of a 1.4 solar mass star.
• $\Lambda_{1.4}$: Tidal Deformability.

Data Provenance: The data was generated based on the theoretical frameworks established in:

• EOS by RMF: Understanding Neutron Star Equation of State using Relativistic Mean Field Models.
• GW_EOS: Preliminary constraints on EOS from Gravitational Wave observations.

Preprocessing: Data was normalized using Min-Max scaling to ensure stability during Gradient Descent. The dataset includes three variations with differing correlation structures to test model robustness.

Results and Evaluation:

We evaluated models based on RMSE (Root Mean Square Error) for accuracy and NLL (Negative Log Likelihood) for probabilistic calibration.

Key Findings:

1. Deterministic vs. Probabilistic: While deterministic ANNs achieved high accuracy on the training set, they failed to generalize well on edge cases. BNNs provided slightly higher RMSE but offered critical uncertainty bounds (confidence intervals) necessary for physical interpretation.
2. Architecture Search: We compared custom-built BNNs (variational inference from scratch) against TensorFlow Probability layers. The TF-Probability implementation using Monte Carlo Dropout yielded the most stable convergence.
3. Feature Importance: Exploratory analysis confirmed that the "Slope of Symmetry Energy" (L) is the dominant predictor for Stellar Radius ($R_{1.4}$), aligning with theoretical nuclear physics constraints.

ANN Prediction | BNN Prediction :-------------------------:|:-------------------------: |

Future Work

• Architecture Upgrade: Implement Transformer-based architectures to capture inter-feature dependencies more effectively.
• Deployment: Containerize the best model using Docker and serve it via a FastAPI endpoint for real-time inference.
• Active Learning: Use the model's uncertainty output to identify which regions of the parameter space require more simulation data.

Acknowledgments & References

• Project Mentors: Dr. Kinjal Banerjee and Dr. Tuhin Malik (BITS Pilani).
• Reference Papers:
• Malik et al., "Unveiling the correlations of tidal deformability with the nuclear symmetry energy parameters."
• Blundell et al., "Weight Uncertainty in Neural Networks."