G-PINNs: A Bayesian-Optimized GRU-Enhanced Physics-Informed Neural Network for Advancing Short Rate Model Predictions

Interest rate modeling plays a crucial role in financial risk management, derivative pricing, and economic forecasting. To address the challenges of capturing complex stochastic dynamics, this study proposes a novel Bayesian-Optimized GRU-Enhanced Physics-Informed Neural Network (G-PINNs) architecture, integrated with the Hull–White (HW) short-rate model, to improve the prediction accuracy of yield forecasting, zero-coupon bond (ZCB) pricing, and option pricing. The proposed framework effectively models time dependent variations and stochastic behavior in interest rate dynamics by leveraging Gated Recurrent Units (GRU) for sequential pattern recognition and Physics Informed Neural Networks (PINNs) to enforce financial constraints through partial differential equations (PDEs) of the HW model. For empirical validation, US treasury yield data from April 2020 to March 2025 is utilized. To achieve the best optimal hyperparameters to enhance both predictive accuracy and training efficiency, Bayesian Optimization (BO) is employed for hyperparameter tuning. The proposed model outperforms Vanilla PINNs as evidenced by higher $R^2$ values and reduced error metrics (MAE, MSE, RMSE, Max & Min error, MSLE, Huber loss, MedAE) in yield prediction, ZCB pricing, and option pricing, as indicated by the numerical results. Furthermore, the results are statistically validated through the paired t-test, which confirms that the G-PINNs model’s performance improvement is significant and not a consequence of random variation. Also, 5-fold cross-validation is performed to ensure robust and unbiased model evaluation across different data splits.