Stochastic Port-Hamiltonian Neural Networks: Universal Approximation with Passivity Guarantees

Stochastic port-Hamiltonian systems represent open dynamical systems with dissipation, inputs, and stochastic forcing in an energy based form. We introduce stochastic port-Hamiltonian neural networks, SPH-NNs, which parameterize the Hamiltonian with a feedforward network and enforce skew symmetry of the interconnection matrix and positive semidefiniteness of the dissipation matrix. For Itô dynamics we establish a weak passivity inequality in expectation under an explicit generator condition, stated for a stopped process on a compact set. We also prove a universal approximation result showing that, on any compact set and finite horizon, SPH-NNs approximate the coefficients of a target stochastic port-Hamiltonian system with $C^2$ accuracy of the Hamiltonian and yield coupled solutions that remain close in mean square up to the exit time. Experiments on noisy mass spring, Duffing, and Van der Pol oscillators show improved long horizon rollouts and reduced energy error relative to a multilayer perceptron baseline.

Enhancing Multistep Brent Oil Price Forecasting with a Multi-Aspect Metaheuristic Optimization Approach and Ensemble Deep Learning Models

Accurate crude oil price forecasting is crucial for various economic activities, including energy trading, risk management, and investment planning. Although deep learning models have emerged as powerful tools for crude oil price forecasting, achieving accurate forecasts remains challenging. Deep learning models' performance is heavily influenced by hyperparameters tuning, and they are expected to perform differently under various circumstances. Furthermore, price volatility is also sensitive to external factors such as world events. To address these limitations, we propose a hybrid approach combining metaheuristic optimisation and an ensemble of five popular neural network architectures used in time series forecasting. Unlike existing methods that apply metaheuristics to optimise hyperparameters within the neural network architecture, we exploit the GWO metaheuristic optimiser at four levels: feature selection, data preparation, model training, and forecast blending. The proposed approach has been evaluated for forecasting three-ahead days using real-world Brent crude oil price data, and the obtained results demonstrate that the proposed approach improves the forecasting performance measured using various benchmarks, achieving 0.000127 of MSE.

Enhancing Multi-Step Brent Oil Price Forecasting with Ensemble Multi-Scenario Bi-GRU Networks

Despite numerous research efforts in applying deep learning to time series forecasting, achieving high accuracy in multi-step predictions for volatile time series like crude oil prices remains a significant challenge. Moreover, most existing approaches primarily focus on one-step forecasting, and the performance often varies depending on the dataset and specific case study. In this paper, we introduce an ensemble model to capture Brent oil price volatility and enhance the multi-step prediction. Our methodology employs a two-pronged approach. First, we assess popular deep-learning models and the impact of various external factors on forecasting accuracy. Then, we introduce an ensemble multi-step forecasting model for Brent oil prices. Our approach generates accurate forecasts by employing ensemble techniques across multiple forecasting scenarios using three BI-GRU networks.Extensive experiments were conducted on a dataset encompassing the COVID-19 pandemic period, which had a significant impact on energy markets. The proposed model's performance was evaluated using the standard evaluation metrics of MAE, MSE, and RMSE. The results demonstrate that the proposed model outperforms benchmark and established models.