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.
