Neutrosophic deep learning framework for uncertainty-aware prediction in chemical process optimization

This paper presents a novel theoretical and computational framework that integrates neutrosophic set theory with deep learning for uncertainty quantification in chemical property prediction. We introduce neutrosophic neural networks (NNN) where input features, weights, and activation functions operate on neutrosophic triples (truth, indeterminacy, falsity). The main theoretical contribution establishes the convergence of neutrosophic binomial distributions to neutrosophic Gaussian distributions with explicit Berry-Esseen-type bounds, providing the probabilistic foundation for uncertainty propagation in deep architectures. We derive novel theorems on the rate of convergence and construct a multi-layer perceptron with neutrosophic neurons for predicting molecular properties from the QM9 dataset. Experimental results demonstrate that the proposed framework achieves superior calibration of predictive uncertainty compared to classical Bayesian neural networks and Monte Carlo dropout methods, with mean absolute errors reduced by 12-18% on energy-related properties. The integration of neutrosophic logic with deep learning offers a mathematically rigorous approach to handling epistemic and aleatoric uncertainties in computational chemistry applications.