Cuckoo Search-Deep Neural Network Hybrid Model for Uncertainty Quantification and Optimization of Dielectric Energy Storage in Na<sub><b>1/2</b></sub>Bi<sub><b>1/2</b></sub>TiO<sub><b>3</

This study introduces a hybrid Cuckoo Search-Deep Neural Network (CS-DNN) model for uncertainty quantification and composition optimization of Na1/2Bi1/2TiO3 (NBT)-based dielectric energy storage ceramics. Addressing the limitations of traditional ferroelectric materials—such as hysteresis loss and low breakdown strength under high electric fields—we fabricate (1 − x)NBBT8-xBMT solid solutions via chemical modification and systematically investigate their temperature stability and composition-dependent energy storage performance through XRD, SEM, and electrical characterization. The key innovation lies in integrating the CS metaheuristic algorithm with a DNN, overcoming local minima in training and establishing a robust composition-property prediction framework. Our model accurately predicts room-temperature dielectric constant (εr), maximum dielectric constant (εmax), dielectric loss (tan δ), discharge energy density (Wrec), and charge-discharge efficiency (η) from compositional inputs. A Monte Carlo-based uncertainty quantification framework, combined with the 3σ statistical criterion, demonstrates that CS-DNN outperforms conventional DNN models in three critical aspects: Higher prediction accuracy (R2 = 0.9717 vs. 0.9382 for εmax); Tighter error distribution, satisfying the 99.7% confidence interval under the 3σ principle; Enhanced robustness, maintaining stable predictions across a 25% composition span in generalization tests. While the model’s generalization is constrained by both the limited experimental dataset (n = 45) and the underlying assumptions of MC-based data augmentation, the CS-DNN framework establishes a machine learning-guided paradigm for accelerated discovery of high-temperature dielectric capacitors through its unique capability in quantifying composition-level energy storage uncertainties.