Quantum transport calculations are essential for understanding and designing nanoelectronic devices, yet the trade-off between accuracy and computational efficiency has long limited their practical applications. We present a general framework that combines the deep learning tight-binding Hamiltonian (DeePTB) approach with the non-equilibrium Green's Function (NEGF) method, enabling efficient quantum transport calculations while maintaining first-principles accuracy. We demonstrate the capabilities of the DeePTB-NEGF framework through two representative applications: comprehensive simulation of break junction systems, where conductance histograms show good agreement with experimental measurements in both metallic contact and single-molecule junction cases; and simulation of carbon nanotube field effect transistors through self-consistent NEGF-Poisson calculations, capturing essential physics including the electrostatic potential and transfer characteristic curves under finite bias conditions. This framework bridges the gap between first-principles accuracy and computational efficiency, providing a powerful tool for high-throughput quantum transport simulations across different scales in nanoelectronics.

Predicting quantum operator matrices such as Hamiltonian, overlap, and density matrices in the density functional theory (DFT) framework is crucial for understanding material properties. Current methods often focus on individual operators and struggle with efficiency and scalability for large systems. Here we introduce a novel deep learning model, SLEM (strictly localized equivariant message-passing) for predicting multiple quantum operators, that achieves state-of-the-art accuracy while dramatically improving computational efficiency. SLEM's key innovation is its strict locality-based design, constructing local, equivariant representations for quantum tensors while preserving physical symmetries. This enables complex many-body dependence without expanding the effective receptive field, leading to superior data efficiency and transferability. Using an innovative SO(2) convolution technique, SLEM reduces the computational complexity of high-order tensor products and is therefore capable of handling systems requiring the $f$ and $g$ orbitals in their basis sets. We demonstrate SLEM's capabilities across diverse 2D and 3D materials, achieving high accuracy even with limited training data. SLEM's design facilitates efficient parallelization, potentially extending DFT simulations to systems with device-level sizes, opening new possibilities for large-scale quantum simulations and high-throughput materials discovery.

Understanding the informative behaviour of deep neural networks is challenged by misused estimators and the complexity of network structure, which leads to inconsistent observations and diversified interpretation. Here we propose the LogDet estimator -- a reliable matrix-based entropy estimator that approximates Shannon differential entropy. We construct informative measurements based on LogDet estimator, verify our method with comparable experiments and utilize it to analyse neural network behaviour. Our results demonstrate the LogDet estimator overcomes the drawbacks that emerge from highly diverse and degenerated distribution thus is reliable to estimate entropy in neural networks. The Network analysis results also find a functional distinction between shallow and deeper layers, which can help understand the compression phenomenon in the Information bottleneck theory of neural networks.