Deep Neural Networks and Bayesian Approaches for Energy Dissipation Modeling in Non-Linear System

Energy dissipation in non-linear systems plays a crucial role in diverse fields, including quantum thermodynamics, fluid dynamics, and climate modeling. Traditional mathematical models often struggle to capture the stochastic and high-dimensional nature of entropy production and energy loss in these systems. This research presents a hybrid machine learning framework that integrates Deep Neural Networks (DNNs) for learning complex dissipation patterns and Bayesian inference methods for probabilistic reasoning and uncertainty quantification. The proposed approach is validated across multiple domains: (1) Quantum systems, where the model predicts decoherence and entropy generation in non-equilibrium quantum states; (2) Fluid dynamics, where energy dissipation in turbulent flows is analyzed using deep learning-based turbulence modeling; and (3) Climate systems, where entropy production due to radiative and convective processes is estimated to improve predictive climate models. Experimental evaluations demonstrate that the hybrid DNN-Bayesian framework outperforms traditional numerical solvers by improving predictive accuracy while maintaining interpretability through probabilistic uncertainty estimates.