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Nonlinear optical (NLO) effects in materials with band crossings have attracted significant research interests due to the divergent band geometric quantities around these crossings. Most current research has focused on band crossings between the valence and conduction bands. However, such crossings are absent in insulators, which are more relevant for NLO applications. In this work, we demonstrate that NLO effects can be significantly enhanced by band crossings within the valence or conduction bands, which we designate as "deep band crossings" (DBCs). As an example, in two dimensions, we show that shift conductivity can be substantially enhanced or even divergent due to a mirror-protected "deep Dirac nodal point". In three dimensions, we propose GeTe as an ideal material where shift conductivity is enhanced by "deep Dirac nodal lines". The ubiquity of this enhancement is further confirmed by high-throughput calculations. Other types of DBCs and NLO effects are also discussed. By manipulating band crossings between arbitrary bands, our work offers a simple, practical, and universal way to greatly enhance NLO effects.

Deep learning electronic structures from ab initio calculations holds great potential to revolutionize computational materials studies. While existing methods proved success in deep-learning density functional theory (DFT) Hamiltonian matrices, they are limited to DFT programs using localized atomic-like bases and heavily depend on the form of the bases. Here, we propose the DeepH-r method for deep-learning DFT Hamiltonians in real space, facilitating the prediction of DFT Hamiltonian in a basis-independent manner. An equivariant neural network architecture for modeling the real-space DFT potential is developed, targeting a more fundamental quantity in DFT. The real-space potential exhibits simplified principles of equivariance and enhanced nearsightedness, further boosting the performance of deep learning. When applied to evaluate the Hamiltonian matrix, this method significantly improved in accuracy, as exemplified in multiple case studies. Given the abundance of data in the real-space potential, this work may pave a novel pathway for establishing a ``large materials model" with increased accuracy.

The combination of deep learning and ab initio materials calculations is emerging as a trending frontier of materials science research, with deep-learning density functional theory (DFT) electronic structure being particularly promising. In this work, we introduce a neural-network method for modeling the DFT density matrix, a fundamental yet previously unexplored quantity in deep-learning electronic structure. Utilizing an advanced neural network framework that leverages the nearsightedness and equivariance properties of the density matrix, the method demonstrates high accuracy and excellent generalizability in multiple example studies, as well as capability to precisely predict charge density and reproduce other electronic structure properties. Given the pivotal role of the density matrix in DFT as well as other computational methods, the current research introduces a novel approach to the deep-learning study of electronic structure properties, opening up new opportunities for deep-learning enhanced computational materials study.

Deep-learning density functional theory (DFT) shows great promise to significantly accelerate material discovery and potentially revolutionize materials research. However, current research in this field primarily relies on data-driven supervised learning, making the developments of neural networks and DFT isolated from each other. In this work, we present a theoretical framework of neural-network DFT, which unifies the optimization of neural networks with the variational computation of DFT, enabling physics-informed unsupervised learning. Moreover, we develop a differential DFT code incorporated with deep-learning DFT Hamiltonian, and introduce algorithms of automatic differentiation and backpropagation into DFT, demonstrating the capability of neural-network DFT. The physics-informed neural-network architecture not only surpasses conventional approaches in accuracy and efficiency, but also offers a new paradigm for developing deep-learning DFT methods., Comment: 6 pages, 4 figures

Point clouds obtained from capture devices or 3D reconstruction techniques are often noisy and interfere with downstream tasks. The paper aims to recover the underlying surface of noisy point clouds. We design a novel model, NoiseTrans, which uses transformer encoder architecture for point cloud denoising. Specifically, we obtain structural similarity of point-based point clouds with the assistance of the transformer's core self-attention mechanism. By expressing the noisy point cloud as a set of unordered vectors, we convert point clouds into point embeddings and employ Transformer to generate clean point clouds. To make the Transformer preserve details when sensing the point cloud, we design the Local Point Attention to prevent the point cloud from being over-smooth. In addition, we also propose sparse encoding, which enables the Transformer to better perceive the structural relationships of the point cloud and improve the denoising performance. Experiments show that our model outperforms state-of-the-art methods in various datasets and noise environments.

The design of complex systems is typically uncertain and ambiguous at early stages. Set-Based Design is a promising approach to complex systems design as it supports alternative exploration and gradual uncertainty reduction. When designing a complex system, functional requirements decomposition is a common and effective approach to progress the design incrementally. However, the current literature on Set-Based Design lacks formal guidance in functional requirements decomposition. To bridge the gap, we propose a formal process to hierarchically decompose the functional requirements for Set-Based Design. A four-step formal process is proposed to systematically define, reason, and narrow the sets, and eventually decompose the functional requirement into the sub-requirements. Such a process can be used by the individual suppliers working in parallel at multiple levels of abstraction and guarantee that the resulting system will eventually satisfy the top-level functional requirements. An example of designing a cruise control system is applied to demonstrate the feasibility of the proposed process.

With the rapid advancement of Formal Methods, Model-based Safety Analysis (MBSA) has been gaining tremendous attention for its ability to rigorously verify whether the safety-critical scenarios are adequately addressed by the design solution of a cyber-physical human system. However, there is a gap. If specific safety-critical scenarios are not included in the given design solution (i.e., the model) in the first place, the results of MBSA cannot be trusted for safety assurance. To tackle this problem, we propose a new safety-guided design methodology (called STPA+) to complement MBSA. Inspired by STPA, STPA+ treats a system as a control structure, which is particularly fit for systems with complex interactions between human, machine, and automation. Three methods are developed in STPA+ to tackle the possible omissions of safety-critical scenarios caused by incorrectly defined safety constraints, improperly constrained process model, and inadequately designed controller. In this way, STPA+ directly derives an adequately defined design solution as the input to an MBSA verification program and bridges the gap between current MBSA approaches and safety assurance.