Transformer-based neural-network quantum states (NNQS) have shown great promise in representing quantum many-body ground states, offering high flexibility and accuracy. However, the interpretability of such models remains limited, especially in terms of connecting network components to physically meaningful quantities. We propose that the attention mechanism - a central module in transformer architectures - explicitly models the conditional information flow between orbitals. Intuitively, as the transformer learns to predict orbital configurations by optimizing an energy functional, it approximates the conditional probability distribution $p(x_n|x_1,\ldots,x_{n-1})$, implicitly encoding conditional mutual information (CMI) among orbitals. This suggests a natural correspondence between attention maps and CMI structures in quantum systems. To probe this idea, we compare weighted attention scores from trained transformer wavefunction ansatze with CMI matrices across several representative small molecules. In most cases, we observe a positive rank-level correlation (Kendall's tau) between attention and CMI, suggesting that the learned attention can reflect physically relevant orbital dependencies. This study provides a quantitative link between transformer attention and conditional mutual information in the NNQS setting. Our results provide a step toward explainable deep learning in quantum chemistry, pointing to opportunities in interpreting attention as a proxy for physical correlations.

The rapid advancement of machine learning based tight-binding Hamiltonian (MLTB) methods has opened new avenues for efficient and accurate electronic structure simulations, particularly in large-scale systems and long-time scenarios. This review begins with a concise overview of traditional tight-binding (TB) models, including both (semi-)empirical and first-principles approaches, establishing the foundation for understanding MLTB developments. We then present a systematic classification of existing MLTB methodologies, grouped into two major categories: direct prediction of TB Hamiltonian elements and inference of empirical parameters. A comparative analysis with other ML-based electronic structure models is also provided, highlighting the advancement of MLTB approaches. Finally, we explore the emerging MLTB application ecosystem, highlighting how the integration of MLTB models with a diverse suite of post-processing tools from linear-scaling solvers to quantum transport frameworks and molecular dynamics interfaces is essential for tackling complex scientific problems across different domains. The continued advancement of this integrated paradigm promises to accelerate materials discovery and open new frontiers in the predictive simulation of complex quantum phenomena.

Accurately predicting the synthesizability of inorganic crystal materials serves as a pivotal tool for the efficient screening of viable candidates, substantially reducing the costs associated with extensive experimental trial-and-error processes. However, existing methods, limited by static structural descriptors such as chemical composition and lattice parameters, fail to account for atomic vibrations, which may introduce spurious correlations and undermine predictive reliability. Here, we propose a deep learning model termed integrating graph and dynamical stability (IGDS) for predicting the synthesizability of inorganic crystals. IGDS employs graph representation learning to construct crystal graphs that precisely capture the static structures of crystals and integrates phonon spectral features extracted from pre-trained machine learning interatomic potentials to represent their dynamic properties. Our model exhibits outstanding performance in predicting the synthesizability of low-energy unsynthesizable crystals across 41 material systems, achieving precision and recall values of 0.916/0.863 for ternary compounds. By capturing both static structural descriptors and dynamic features, IGDS provides a physics-informed method for predicting the synthesizability of inorganic crystals. This approach bridges the gap between theoretical design concepts and their practical implementation, thereby streamlining the development cycle of new materials and enhancing overall research efficiency.

Understanding the complex deformation mechanisms of non-equimolar multi-principal element alloys (MPEAs) requires high-fidelity atomic-scale simulations. This study develops a deep potential (DP) model to enable molecular dynamics simulations of the Ta$_{0.4}$Ti$_{2}$Zr (Ta$_{0.4}$) alloy. Monte Carlo simulations using this potential reveal Ta atom precipitation in the Ta$_{0.4}$ alloy. Under uniaxial tensile loading along the [100] direction in the NPT ensemble, the alloy undergoes a remarkable sequence of phase transformations: an initial body-centered cubic (BCC$_{1}$) to face-centered cubic (FCC) transformation, followed by a reverse transformation from FCC to a distinct BCC phase (BCC$_{2}$), and finally a BCC$_{2}$ to hexagonal close-packed (HCP) transformation. Critically, the reverse FCC to BCC$_{2}$ transformation induces significant volume contraction. We demonstrate that the inversely transformed BCC$_{2}$ phase primarily accommodates compressive stress. Concurrently, the reorientation of BCC$_{2}$ crystals contributes substantially to the observed high strain hardening. These simulations provide atomic-scale insights into the dynamic structural evolution, sequential phase transformations, and stress partitioning during deformation of the Ta$_{0.4}$ alloy. The developed DP model and the revealed mechanisms offer fundamental theoretical guidance for accelerating the design of high-performance MPEAs.

Current experimental techniques still face challenges in clarifying the structural and dynamic properties of helium (He) in liquid lithium (Li). A critical example of this technical hurdle is the formation of He bubbles, which significantly affects the transport of He within liquid Li - a vital aspect when considering liquid Li as a plasma-facing material in nuclear fusion reactors. We develop a machine-learning-based deep potential (DP) with ab initio accuracy for the Li-He system and perform molecular dynamics simulations at temperatures ranging from 470 K to 1270 K with a wide range of He concentrations. We observe that He atoms exhibit a tendency to aggregate and form clusters and bubbles in liquid Li. Notably, He clusters exhibit a significant increase in size at elevated temperatures and high concentrations of He, accompanied by the phase separation of Li and He atoms. We also observe an anomalous non-linear relationship between the diffusion coefficient of He and temperature, which is attributed to the larger cluster size at higher temperatures. Our study provides a deeper understanding of the behavior of He in liquid Li and further supports the potential application of liquid Li under extreme conditions.

Lead (Pb) is a typical low-melting-point ductile metal and serves as an important model material in the study of dynamic responses. Under shock-wave loading, its dynamic mechanical behavior comprises two key phenomena: plastic deformation and shock-induced phase transitions. The underlying mechanisms of these processes are still poorly understood. Revealing these mechanisms remains challenging for experimental approaches. Non-equilibrium molecular dynamics (NEMD) simulations are an alternative theoretical tool for studying dynamic responses, as they capture atomic-scale mechanisms such as defect evolution and deformation pathways. However, due to the limited accuracy of empirical interatomic potentials, the reliability of previous NEMD studies has been questioned. Using our newly developed machine learning potential for Pb-Sn alloys, we revisited the microstructural evolution in response to shock loading under various shock orientations. The results reveal that shock loading along the [001] orientation of Pb exhibits a fast, reversible, and massive phase transition and stacking-fault evolution. The behavior of Pb differs from previous studies by the absence of twinning during plastic deformation. Loading along the [011] orientation leads to slow, irreversible plastic deformation, and a localized FCC-BCC phase transition in the Pitsch orientation relationship. This study provides crucial theoretical insights into the dynamic mechanical response of Pb, offering a theoretical input for understanding the microstructure-performance relationship under extreme conditions.