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In recent years, Artificial intelligence (AI) has become ubiquitous, empowering various fields, especially integrating artificial intelligence and traditional science (AI for Science: Artificial intelligence for science), which has attracted widespread attention. In AI for Science, using artificial intelligence algorithms to solve partial differential equations (AI for PDEs: Artificial intelligence for partial differential equations) has become a focal point in computational mechanics. The core of AI for PDEs is the fusion of data and partial differential equations (PDEs), which can solve almost any PDEs. Therefore, this article provides a comprehensive review of the research on AI for PDEs, summarizing the existing algorithms and theories. The article discusses the applications of AI for PDEs in computational mechanics, including solid mechanics, fluid mechanics, and biomechanics. The existing AI for PDEs algorithms include those based on Physics-Informed Neural Networks (PINNs), Deep Energy Methods (DEM), Operator Learning, and Physics-Informed Neural Operator (PINO). AI for PDEs represents a new method of scientific simulation that provides approximate solutions to specific problems using large amounts of data, then fine-tuning according to specific physical laws, avoiding the need to compute from scratch like traditional algorithms. Thus, AI for PDEs is the prototype for future foundation models in computational mechanics, capable of significantly accelerating traditional numerical algorithms.

In recent years, artificial intelligence (AI) has become increasingly integrated into education, reshaping traditional learning environments. Despite this, there has been limited investigation into fully operational artificial human lecturers. To the best of our knowledge, our paper presents the world's first study examining their deployment in a real-world educational setting. Specifically, we investigate the use of "digital teachers," AI-powered virtual lecturers, in a postgraduate course at the Hong Kong University of Science and Technology (HKUST). Our study explores how features such as appearance, non-verbal cues, voice, and verbal expression impact students' learning experiences. Findings suggest that students highly value naturalness, authenticity, and interactivity in digital teachers, highlighting areas for improvement, such as increased responsiveness, personalized avatars, and integration with larger learning platforms. We conclude that digital teachers have significant potential to enhance education by providing a more flexible, engaging, personalized, and accessible learning experience for students., Comment: 28 pages, 6 figures (10 sub-figures), 3 tables

The study of cycloaddition mechanisms is central to the fabrication of extended sp2 carbon nanostructures. Reaction modeling in this context has focused mostly on putative, energetically preferred, exothermic products with limited consideration for symmetry allowed or forbidden mechanistic effects. Here, we introduce a scheme for classifying symmetry-forbidden reaction coordinates in Woodward-Hoffmann correlation diagrams. Topological classifiers grant access to the study of reaction pathways and correlation diagrams in the same footing, for the purpose of elucidating mechanisms and products of polycyclic aromatic azomethine ylide (PAMY) cycloadditions with pentacene-yielding polycyclic aromatic hydrocarbons with an isoindole core in the solid-state and on surfaces as characterized by mass spectrometry and scanning tunneling microscopy, respectively. By means of a tight-binding reaction model and density functional theory (DFT) we find topologically-allowed pathways if a product is endothermic, and topologically-forbidden if a product is exothermic. Our work unveils topological classification as a crucial element for reaction modeling for nanographene engineering, and highlights its fundamental role in the design of cycloadditions in on-surface and solid-state chemical reactions, while underscoring that exothermic pathways can be topologically-forbidden.

AI for partial differential equations (PDEs) has garnered significant attention, particularly with the emergence of Physics-informed neural networks (PINNs). The recent advent of Kolmogorov-Arnold Network (KAN) indicates that there is potential to revisit and enhance the previously MLP-based PINNs. Compared to MLPs, KANs offer interpretability and require fewer parameters. PDEs can be described in various forms, such as strong form, energy form, and inverse form. While mathematically equivalent, these forms are not computationally equivalent, making the exploration of different PDE formulations significant in computational physics. Thus, we propose different PDE forms based on KAN instead of MLP, termed Kolmogorov-Arnold-Informed Neural Network (KINN) for solving forward and inverse problems. We systematically compare MLP and KAN in various numerical examples of PDEs, including multi-scale, singularity, stress concentration, nonlinear hyperelasticity, heterogeneous, and complex geometry problems. Our results demonstrate that KINN significantly outperforms MLP regarding accuracy and convergence speed for numerous PDEs in computational solid mechanics, except for the complex geometry problem. This highlights KINN's potential for more efficient and accurate PDE solutions in AI for PDEs.

The concept of the generalized entanglement wedge was recently proposed by Bousso and Penington, which states that any bulk gravitational region $a$ possesses an associated generalized entanglement wedge $E(a)\supset a$ on a static Cauchy surface $M$ in general gravitational spacetimes, where $E(a)$ may contain an entanglement island $I(a)$. It suggests that the fine-grained entropy for bulk region $a$ is given by the generalized entropy $S_{\text{gen}}(E(a))$. Motivated by this proposal, we extend the quantum bit thread description to general gravitational spacetimes, no longer limited to the AdS spacetime. By utilizing the convex optimization techniques, a dual flow description for the generalized entropy $S_{\text{gen}}(E(a))$ of a bulk gravitational region $a$ is established on the static Cauchy surface $M$, such that $S_{\text{gen}}(E(a))$ is equal to the maximum flux of any flow that starts from the boundary $\partial M$ and ends at bulk region $a$, or equivalently, the maximum number of bit threads that connect the boundary $\partial M$ to the bulk region $a$. In addition, the nesting property of flows is also proved. Thus the basic properties of the entropy for bulk regions, i.e. the monotonicity, subadditivity, Araki-Lieb inequality and strong subadditivity, can be verified from flow perspectives by using properties of flows, such as the nesting property. Moreover, in max thread configurations, we find that there exists some lower bounds on the bulk entanglement entropy of matter fields in the region $E(a)\setminus a$, particularly on an entanglement island region $I(a) \subset (E(a)\setminus a)$, as required by the existence of a nontrivial generalized entanglement wedge. Our quantum bit thread formulation may provide a way to investigate more fine-grained entanglement structures in general spacetimes., Comment: 32 pages, 4 figures; improvements to presentation; Figure 2 and Footnote 10 are added; published version in JHEP

The generation and manipulation of the valley polarization in solids are crucial for valleytronics, which is mainly limited to the analysis of inversion and time-reversal symmetries for two-dimensional (2D) hexagonal systems. Here, through group theory analysis, we propose general rules for the generation and manipulation of valley polarization in 2D hexagonal lattices. The generation of valley polarization requires breaking the specific enforced symmetry that is associated with different valleys or reverses the sign of Berry curvature. Further manipulation of valley polarization requires asymmetry operators connecting two states with opposite signs of Berry curvature. These rules for generating and manipulating valley polarization are extendable to generic points in momentum space. Combined with first-principles calculations, we realize the controllable valley polarization in three representative systems, i.e., monolayer FeCl2, bilayer TcGeSe3, and monolayer CrOBr. Our work provides symmetry rules for designing valleytronic materials that could facilitate the experimental detection and realistic applications., Comment: 16 pages, 4 figures

Reconstructing and editing 3D objects and scenes both play crucial roles in computer graphics and computer vision. Neural radiance fields (NeRFs) can achieve realistic reconstruction and editing results but suffer from inefficiency in rendering. Gaussian splatting significantly accelerates rendering by rasterizing Gaussian ellipsoids. However, Gaussian splatting utilizes a single Spherical Harmonic (SH) function to model both texture and lighting, limiting independent editing capabilities of these components. Recently, attempts have been made to decouple texture and lighting with the Gaussian splatting representation but may fail to produce plausible geometry and decomposition results on reflective scenes. Additionally, the forward shading technique they employ introduces noticeable blending artifacts during relighting, as the geometry attributes of Gaussians are optimized under the original illumination and may not be suitable for novel lighting conditions. To address these issues, we introduce DeferredGS, a method for decoupling and editing the Gaussian splatting representation using deferred shading. To achieve successful decoupling, we model the illumination with a learnable environment map and define additional attributes such as texture parameters and normal direction on Gaussians, where the normal is distilled from a jointly trained signed distance function. More importantly, we apply deferred shading, resulting in more realistic relighting effects compared to previous methods. Both qualitative and quantitative experiments demonstrate the superior performance of DeferredGS in novel view synthesis and editing tasks.

Impurities exist inevitably in two-dimensional materials as they spontaneously adsorb onto the surface during fabrication, usually exerting detrimental effects on electronic transport. Here, we focus on a special type of impurities that preferentially adsorb onto the hollow regions of graphene nanoribbons (GNRs), and study how they affect the quantum transport in GNRs. Contrary to previous knowledge that random adatoms should localize electrons, the so-called Anderson localization, noteworthy quantized conductance peaks (QCPs) are observed at specific electron energies. These QCPs are remarkably robust against variations in system size, GNR edge, and adatom properties, and they can reappear at identical energies following an arithmetic sequence of device width. Further investigation of wavefunction reveals a unique transport mode at each QCP energy which transmits through disordered GNRs reflectionlessly, while all the others become fully Anderson localized, indicating the survival of quantum ballistic transport in the localized regime. Our findings highlight the potential utility of hollow adatoms as a powerful tool to manipulate the conductivity of GNRs, and deepen the understanding of the interplay between impurities and graphene., Comment: 8 pages, 4 figures, and 1 table; comments are welcome

Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a scene. Nevertheless, it is challenging for users to directly deform or manipulate these implicit representations with large deformations in the real-time fashion. Gaussian Splatting(GS) has recently become a promising method with explicit geometry for representing static scenes and facilitating high-quality and real-time synthesis of novel views. However,it cannot be easily deformed due to the use of discrete Gaussians and lack of explicit topology. To address this, we develop a novel GS-based method that enables interactive deformation. Our key idea is to design an innovative mesh-based GS representation, which is integrated into Gaussian learning and manipulation. 3D Gaussians are defined over an explicit mesh, and they are bound with each other: the rendering of 3D Gaussians guides the mesh face split for adaptive refinement, and the mesh face split directs the splitting of 3D Gaussians. Moreover, the explicit mesh constraints help regularize the Gaussian distribution, suppressing poor-quality Gaussians(e.g. misaligned Gaussians,long-narrow shaped Gaussians), thus enhancing visual quality and avoiding artifacts during deformation. Based on this representation, we further introduce a large-scale Gaussian deformation technique to enable deformable GS, which alters the parameters of 3D Gaussians according to the manipulation of the associated mesh. Our method benefits from existing mesh deformation datasets for more realistic data-driven Gaussian deformation. Extensive experiments show that our approach achieves high-quality reconstruction and effective deformation, while maintaining the promising rendering results at a high frame rate(65 FPS on average)., Comment: 11 pages, 7 figures

We explore the generalized holographic complexity of odd-dimensional Myers-Perry asymptotically Anti-de Sitter (MP-AdS) black holes with equal angular momenta within the ``complexity equals anything'' proposal. We begin by determining the codimension-one generalized volume complexity by finding the extremum of the generally covariant volume functional. Locally, we show that its late-time growth rate aligns with the critical momenta associated with the extremal hypersurfaces. Globally, we discover diverse phase transitions for the complexity at early times, including first-order, second-order, and multi-critical transitions. An area law and a phase diagram are proposed to adapt to these phase behaviours, highlighting the effects of the black hole's angular momentum. At zero time, we define the generalized holographic complexity of formation and examine its scaling relations for both large near-extremal MP-AdS black holes and static charged black holes. We find that the scaling behaviours of the generalized volume complexity of formation maintain uniformity with those of the original holographic complexity formulations, except in cases where the scalar functional defining the generalized holographic complexity is infinite in the vacuum limit or at spatial infinity. Additionally, we show that these findings can be applied to codimension-zero observables., Comment: 38 pages, 15 figures

Quantum entanglement, crucial for understanding quantum many-body systems and quantum gravity, is commonly assessed through various measures such as von Neumann entropy, mutual information, and entanglement contour, each with its inherent limitations. In this work, we introduce the \textit{hyperfine structure of entanglement}, which dissects entanglement contours known as the fine structure into particle-number cumulants. This measure exhibits a set of universal properties with its significance in quantum information science. We apply it across diverse contexts: in Fermi gases, establishing connections to mutual information and interacting conformal field theory; in AdS$_3$/CFT$_2$ holographic duality, unveiling finer subregion-subregion duality and extending bulk reconstruction; and in Chern insulators, distinguishing between different quantum phases. Our findings suggest experimental accessibility, offering fresh insights into quantum entanglement across physical systems., Comment: title changed

In this paper, we investigate the topological numbers of the four-dimensional Schwarzschild black hole, $d$-dimensional Reissner-Nordstr\"om (RN) black hole, $d$-dimensional singly rotating Kerr black hole and five-dimensional Gauss-Bonnet black hole via the R\'enyi statistics. We find that the topological number calculated via the R\'enyi statistics is different from that obtained from the Gibbs-Boltzmann (GB) statistics. However, what is interesting is that the topological classifications of different black holes are consistent in both the R\'enyi and GB statistics: the four-dimensional RN black hole, four-dimensional and five-dimensional singly rotating Kerr black holes, five-dimensional charged and uncharged Gauss-Bonnet black holes belong to the same kind of topological class, and the four-dimensional Schwarzschild black hole and $d(>5)$-dimensional singly rotating Kerr black holes belong to another kind of topological class. In addition, our results suggest that the topological numbers calculated via the R\'enyi statistics in asymptotically flat spacetime background are equal to those calculated from the standard GB statistics in asymptotically AdS spacetime background, which provides more evidence for the connection between the nonextensivity of the R\'enyi parameter $\lambda$ and the cosmological constant $\Lambda$., Comment: 24 pages,19 figures

Building scalable vision-language models to learn from diverse, multimodal data remains an open challenge. In this paper, we introduce an Efficient Vision-languagE foundation model, namely EVE, which is one unified multimodal Transformer pre-trained solely by one unified pre-training task. Specifically, EVE encodes both vision and language within a shared Transformer network integrated with modality-aware sparse Mixture-of-Experts (MoE) modules, which capture modality-specific information by selectively switching to different experts. To unify pre-training tasks of vision and language, EVE performs masked signal modeling on image-text pairs to reconstruct masked signals, i.e., image pixels and text tokens, given visible signals. This simple yet effective pre-training objective accelerates training by 3.5x compared to the model pre-trained with Image-Text Contrastive and Image-Text Matching losses. Owing to the combination of the unified architecture and pre-training task, EVE is easy to scale up, enabling better downstream performance with fewer resources and faster training speed. Despite its simplicity, EVE achieves state-of-the-art performance on various vision-language downstream tasks, including visual question answering, visual reasoning, and image-text retrieval., Comment: Accepted by AAAI 2024

We study the information paradox of Reissner-Nordstr${\ddot{o}}$m anti-de Sitter (RN-AdS$_{d+1}$) black holes in the large dimension limit by using the island formula. The entanglement entropy of Hawking radiation is calculated both for the non-extremal and the extremal cases, in which the boundary of the radiation region is close to the outer horizon. For the non-extremal case, the entanglement entropy of Hawking radiation obeys the Page curve, i.e. the entanglement entropy of Hawking radiation increases with time and reaches saturation about twice Bekenstein-Hawking entropy at the Page time. For the extremal case, the entanglement entropy of Hawking radiation becomes ill-defined in the absence of the island due to the appearance of the singularity at the origin of the radial coordinate, while when the island exists, the entanglement entropy is found to be equal to the Bekenstein-Hawking entropy. In addition, for the case where the boundary of the radiation region is close to the horizon, there are some obvious constraints required by the existence of island solution for both non-extremal and extremal cases, which can be utilized to put constraints on the size of the black hole. These results reveal new features of the semi-classical large $d$ black holes from the island perspective., Comment: 25 pages, 7 figures