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In this paper, we calculate the semileptonic decay $D\to K_0^\ast(1430)\ell\nu_{\ell}$ with $\ell=(e,\mu)$ induced by $c\to s\ell\nu_{\ell}$ transition. For the key component, $D\to K_0^\ast(1430)$ transition form factors (TFFs) $f_{\pm}(q^2)$ are calculated within the framework of QCD light-cone sum rule. Then, we consider two scenarios for $K_0^\ast(1430)$-meson twist-2 distribution amplitude. For the scenario 1 (S1), we take the truncated form based on Gegenbauer polynomial series. Meanwhile, we also consider the scenario 2 (S2) constructed by light-cone harmonic oscillator model, where the model parameters are fixed by the $K_0^\ast(1430)$-meson twist-2 distribution amplitude $10$th-order $\xi$-moments calculated by using the background field theory. For the TFFs at large recoil point, we have $f_+^{\rm (S1)}(0)=0.597^{+0.122}_{-0.121}$ and $f_-^{\rm (S1)}(0)=-0.136^{+0.023}_{-0.035}$, $f_+^{\rm (S2)}(0)= 0.663^{+0.135}_{-0.134}$ and $f_-^{\rm (S2)}(0)=-0.202^{+0.026}_{-0.046}$. After extrapolating TFFs to the whole physical $q^2$-region, we calculate the branching fractions of $D^0\to K_0^{\ast +}(1430)\ell^-\bar\nu_\ell$ and $D^+\to K_0^{\ast 0}(1430)\ell^+\nu_\ell$ which at $10^{-4}$-order level for the S1 and S2 cases. Meanwhile, we predict the CKM matrix $|V_{cs}|^{\rm (S1)}=0.997^{+0.258}_{-0.172}, |V_{cs}|^{\rm (S2)}=0.903^{+0.233}_{-0.155}$, and leptonic flavour universality $\mathcal{R}^{\rm (S1)}_{K_0^*}=0.768^{+0.560}_{-0.368}, \mathcal{R}_{K_0^*}^{\rm (S2)}=0.764^{+0.555}_{-0.365}$. Finally, we discuss the angular observables of forward-backward asymmetries, lepton polarization asymmetries and $q^2$-differential flat terms for this decay., Comment: 10 pages, 5 figures, comments welcome

Given a group size m and a sensitive dataset D, group privacy (GP) releases information about D with the guarantee that the adversary cannot infer with high confidence whether the underlying data is D or a neighboring dataset D' that differs from D by m records. GP generalizes the well-established notion of differential privacy (DP) for protecting individuals' privacy; in particular, when m=1, GP reduces to DP. Compared to DP, GP is capable of protecting the sensitive aggregate information of a group of up to m individuals, e.g., the average annual income among members of a yacht club. Despite its longstanding presence in the research literature and its promising applications, GP is often treated as an afterthought, with most approaches first developing a DP mechanism and then using a generic conversion to adapt it for GP, treating the DP solution as a black box. As we point out in the paper, this methodology is suboptimal when the underlying DP solution involves subsampling, e.g., in the classic DP-SGD method for training deep learning models. In this case, the DP-to-GP conversion is overly pessimistic in its analysis, leading to low utility in the published results under GP. Motivated by this, we propose a novel analysis framework that provides tight privacy accounting for subsampled GP mechanisms. Instead of converting a black-box DP mechanism to GP, our solution carefully analyzes and utilizes the inherent randomness in subsampled mechanisms, leading to a substantially improved bound on the privacy loss with respect to GP. The proposed solution applies to a wide variety of foundational mechanisms with subsampling. Extensive experiments with real datasets demonstrate that compared to the baseline convert-from-blackbox-DP approach, our GP mechanisms achieve noise reductions of over an order of magnitude in several practical settings, including deep neural network training., Comment: accepted for publication in Proceedings of VLDB Endowment (PVLDB) 2025

Ref.[BCOW17] introduced a pioneering quantum approach (coined BCOW algorithm) for solving linear differential equations with optimal error tolerance. Originally designed for a specific class of diagonalizable linear differential equations, the algorithm was extended by Krovi in [Kro23] to encompass broader classes, including non-diagonalizable and even singular matrices. Despite the common misconception, the original algorithm is indeed applicable to non-diagonalizable matrices, with diagonalisation primarily serving for theoretical analyses to establish bounds on condition number and solution error. By leveraging basic estimates from [Kro23], we derive bounds comparable to those outlined in the Krovi algorithm, thereby reinstating the advantages of the BCOW approach. Furthermore, we extend the BCOW algorithm to address time-dependent linear differential equations by transforming non-autonomous systems into higher-dimensional autonomous ones, a technique also applicable for the Krovi algorithm., Comment: quantum algorithm for ODEs

Creating relightable and animatable avatars from multi-view or monocular videos is a challenging task for digital human creation and virtual reality applications. Previous methods rely on neural radiance fields or ray tracing, resulting in slow training and rendering processes. By utilizing Gaussian Splatting, we propose a simple and efficient method to decouple body materials and lighting from sparse-view or monocular avatar videos, so that the avatar can be rendered simultaneously under novel viewpoints, poses, and lightings at interactive frame rates (6.9 fps). Specifically, we first obtain the canonical body mesh using a signed distance function and assign attributes to each mesh vertex. The Gaussians in the canonical space then interpolate from nearby body mesh vertices to obtain the attributes. We subsequently deform the Gaussians to the posed space using forward skinning, and combine the learnable environment light with the Gaussian attributes for shading computation. To achieve fast shadow modeling, we rasterize the posed body mesh from dense viewpoints to obtain the visibility. Our approach is not only simple but also fast enough to allow interactive rendering of avatar animation under environmental light changes. Experiments demonstrate that, compared to previous works, our method can render higher quality results at a faster speed on both synthetic and real datasets.

Graph Convolutional Networks (GCNs) are a popular machine learning model with a wide range of applications in graph analytics, including healthcare, transportation, and finance. Similar to other neural networks, a GCN may memorize parts of the training data through its model weights. Thus, when the underlying graph data contains sensitive information such as interpersonal relationships, a GCN trained without privacy-protection measures could be exploited to extract private data, leading to potential violations of privacy regulations such as GDPR. To defend against such attacks, a promising approach is to train the GCN with differential privacy (DP), which is a rigorous framework that provides strong privacy protection by injecting random noise into the trained model weights. However, training a large graph neural network under DP is a highly challenging task. Existing solutions either introduce random perturbations in the graph topology, which leads to severe distortions of the network's message passing, or inject randomness into each neighborhood aggregation operation, which leads to a high noise scale when the GCN performs multiple levels of aggregations. Motivated by this, we propose GCON, a novel and effective solution for training GCNs with edge differential privacy. The main idea is to (i) convert the GCN training process into a convex optimization problem, and then (ii) apply the classic idea of perturbing the objective function to satisfy DP. Extensive experiments using multiple benchmark datasets demonstrate GCON's consistent and superior performance over existing solutions in a wide variety of settings.

We propose a GPU-based iterative method for accelerated elastodynamic simulation with the log-barrier-based contact model. While Newton's method is a conventional choice for solving the interior-point system, the presence of ill-conditioned log barriers often necessitates a direct solution at each linearized substep and costs substantial storage and computational overhead. Moreover, constraint sets that vary in each iteration present additional challenges in algorithm convergence. Our method employs a novel barrier-augmented Lagrangian method to improve system conditioning and solver efficiency by adaptively updating an augmentation constraint sets. This enables the utilization of a scalable, inexact Newton-PCG solver with sparse GPU storage, eliminating the need for direct factorization. We further enhance PCG convergence speed with a domain-decomposed warm start strategy based on an eigenvalue spectrum approximated through our in-time assembly. Demonstrating significant scalability improvements, our method makes simulations previously impractical on 128 GB of CPU memory feasible with only 8 GB of GPU memory and orders-of-magnitude faster. Additionally, our method adeptly handles stiff problems, surpassing the capabilities of existing GPU-based interior-point methods. Our results, validated across various complex collision scenarios involving intricate geometries and large deformations, highlight the exceptional performance of our approach., Comment: 17 pages, 30 figures

Generative AI models, such as GPT-4 and Stable Diffusion, have demonstrated powerful and disruptive capabilities in natural language and image tasks. However, deploying these models in decentralized environments remains challenging. Unlike traditional centralized deployment, systematically guaranteeing the integrity of AI model services in fully decentralized environments, particularly on trustless blockchains, is both crucial and difficult. In this paper, we present a new inference paradigm called \emph{proof of quality} (PoQ) to enable the deployment of arbitrarily large generative models on blockchain architecture. Unlike traditional approaches based on validating inference procedures, such as ZKML or OPML, our PoQ paradigm focuses on the outcome quality of model inference. Using lightweight BERT-based cross-encoders as our underlying quality evaluation model, we design and implement PQML, the first practical protocol for real-world NLP generative model inference on blockchains, tailored for popular open-source models such as Llama 3 and Mixtral. Our analysis demonstrates that our protocol is robust against adversarial but rational participants in ecosystems, where lazy or dishonest behavior results in fewer benefits compared to well-behaving participants. The computational overhead of validating the quality evaluation is minimal, allowing quality validators to complete the quality check within a second, even using only a CPU. Preliminary simulation results show that PoQ consensus is generated in milliseconds, 1,000 times faster than any existing scheme., Comment: 12 pages, 5 figures

Existing diffusion-based text-to-3D generation methods primarily focus on producing visually realistic shapes and appearances, often neglecting the physical constraints necessary for downstream tasks. Generated models frequently fail to maintain balance when placed in physics-based simulations or 3D printed. This balance is crucial for satisfying user design intentions in interactive gaming, embodied AI, and robotics, where stable models are needed for reliable interaction. Additionally, stable models ensure that 3D-printed objects, such as figurines for home decoration, can stand on their own without requiring additional supports. To fill this gap, we introduce Atlas3D, an automatic and easy-to-implement method that enhances existing Score Distillation Sampling (SDS)-based text-to-3D tools. Atlas3D ensures the generation of self-supporting 3D models that adhere to physical laws of stability under gravity, contact, and friction. Our approach combines a novel differentiable simulation-based loss function with physically inspired regularization, serving as either a refinement or a post-processing module for existing frameworks. We verify Atlas3D's efficacy through extensive generation tasks and validate the resulting 3D models in both simulated and real-world environments.

X-ray Computed Tomography (CT) is one of the most important diagnostic imaging techniques in clinical applications. Sparse-view CT imaging reduces the number of projection views to a lower radiation dose and alleviates the potential risk of radiation exposure. Most existing deep learning (DL) and deep unfolding sparse-view CT reconstruction methods: 1) do not fully use the projection data; 2) do not always link their architecture designs to a mathematical theory; 3) do not flexibly deal with multi-sparse-view reconstruction assignments. This paper aims to use mathematical ideas and design optimal DL imaging algorithms for sparse-view tomography reconstructions. We propose a novel dual-domain deep unfolding unified framework that offers a great deal of flexibility for multi-sparse-view CT reconstruction with different sampling views through a single model. This framework combines the theoretical advantages of model-based methods with the superior reconstruction performance of DL-based methods, resulting in the expected generalizability of DL. We propose a refinement module that utilizes unfolding projection domain to refine full-sparse-view projection errors, as well as an image domain correction module that distills multi-scale geometric error corrections to reconstruct sparse-view CT. This provides us with a new way to explore the potential of projection information and a new perspective on designing network architectures. All parameters of our proposed framework are learnable end to end, and our method possesses the potential to be applied to plug-and-play reconstruction. Extensive experiments demonstrate that our framework is superior to other existing state-of-the-art methods. Our source codes are available at https://github.com/fanxiaohong/MVMS-RCN., Comment: 12 pages, submitted

We present ElastoGen, a knowledge-driven model that generates physically accurate and coherent 4D elastodynamics. Instead of relying on petabyte-scale data-driven learning, ElastoGen leverages the principles of physics-in-the-loop and learns from established physical knowledge, such as partial differential equations and their numerical solutions. The core idea of ElastoGen is converting the global differential operator, corresponding to the nonlinear elastodynamic equations, into iterative local convolution-like operations, which naturally fit modern neural networks. Each network module is specifically designed to support this goal rather than functioning as a black box. As a result, ElastoGen is exceptionally lightweight in terms of both training requirements and network scale. Additionally, due to its alignment with physical procedures, ElastoGen efficiently generates accurate dynamics for a wide range of hyperelastic materials and can be easily integrated with upstream and downstream deep modules to enable end-to-end 4D generation.

We present a framework of elastic locomotion, which allows users to enliven an elastic body to produce interesting locomotion by prescribing its high-level kinematics. We formulate this problem as an inverse simulation problem and seek the optimal muscle activations to drive the body to complete the desired actions. We employ the interior-point method to model wide-area contacts between the body and the environment with logarithmic barrier penalties. The core of our framework is a mixed second-order differentiation algorithm. By combining both analytic differentiation and numerical differentiation modalities, a general-purpose second-order differentiation scheme is made possible. Specifically, we augment complex-step finite difference (CSFD) with reverse automatic differentiation (AD). We treat AD as a generic function, mapping a computing procedure to its derivative w.r.t. output loss, and promote CSFD along the AD computation. To this end, we carefully implement all the arithmetics used in elastic locomotion, from elementary functions to linear algebra and matrix operation for CSFD promotion. With this novel differentiation tool, elastic locomotion can directly exploit Newton's method and use its strong second-order convergence to find the needed activations at muscle fibers. This is not possible with existing first-order inverse or differentiable simulation techniques. We showcase a wide range of interesting locomotions of soft bodies and creatures to validate our method., Comment: 13 pages, 14 figures

This paper presents meta-homogenization, a spatially varying homogenization scheme for knitwear simulation. We are motivated by the observation that macro-scale fabric dynamics is strongly correlated with its underlying knitting patterns. Therefore, homogenization towards a single material is less effective when the knitting is complex and non-repetitive. Our method tackles this challenge by homogenizing the yarn-level material locally at volumetric elements. Assigning a virtual volume of a knitting structure enables us to model bending and twisting effects via a simple volume-preserving penalty and thus effectively alleviates the material nonlinearity. We employ an adjoint Gauss-Newton formulation to battle the dimensionality challenge of such per-element material optimization. This intuitive material model makes the forward simulation GPU-friendly. To this end, our pipeline also equips a novel domain-decomposed subspace solver crafted for GPU projective dynamics, which makes our simulator hundreds of times faster than the yarn-level simulator. Experiments validate the capability and effectiveness of meta-homogenization. Our method produces realistic animations of knitwear matching the quality of full-scale yarn-level simulations. It is also orders of magnitude faster than existing homogenization techniques in both the training and simulation stages.

Traditional 3D garment creation is labor-intensive, involving sketching, modeling, UV mapping, and texturing, which are time-consuming and costly. Recent advances in diffusion-based generative models have enabled new possibilities for 3D garment generation from text prompts, images, and videos. However, existing methods either suffer from inconsistencies among multi-view images or require additional processes to separate cloth from the underlying human model. In this paper, we propose GarmentDreamer, a novel method that leverages 3D Gaussian Splatting (GS) as guidance to generate wearable, simulation-ready 3D garment meshes from text prompts. In contrast to using multi-view images directly predicted by generative models as guidance, our 3DGS guidance ensures consistent optimization in both garment deformation and texture synthesis. Our method introduces a novel garment augmentation module, guided by normal and RGBA information, and employs implicit Neural Texture Fields (NeTF) combined with Score Distillation Sampling (SDS) to generate diverse geometric and texture details. We validate the effectiveness of our approach through comprehensive qualitative and quantitative experiments, showcasing the superior performance of GarmentDreamer over state-of-the-art alternatives. Our project page is available at: https://xuan-li.github.io/GarmentDreamerDemo/.

PBD and its extension, XPBD, have been predominantly applied to compliant constrained elastodynamics, with their potential in finite strain (visco-) elastoplasticity remaining underexplored. XPBD is often perceived to stand in contrast to other meshless methods, such as the MPM. MPM is based on discretizing the weak form of governing partial differential equations within a continuum domain, coupled with a hybrid Lagrangian-Eulerian method for tracking deformation gradients. In contrast, XPBD formulates specific constraints, whether hard or compliant, to positional degrees of freedom. We revisit this perception by investigating the potential of XPBD in handling inelastic materials that are described with classical continuum mechanics-based yield surfaces and elastoplastic flow rules. Our inspiration is that a robust estimation of the velocity gradient is a sufficiently useful key to effectively tracking deformation gradients in XPBD simulations. By further incorporating implicit inelastic constitutive relationships, we introduce a plasticity in-the-loop updated Lagrangian augmentation to XPBD. This enhancement enables the simulation of elastoplastic, viscoplastic, and granular substances following their standard constitutive laws. We demonstrate the effectiveness of our method through high-resolution and real-time simulations of diverse materials such as snow, sand, and plasticine, and its integration with standard XPBD simulations of cloth and water.

In this paper, we carry out an investigation into the semileptonic decays $D_s^+ \to K^0\ell^+\nu_\ell$ with $\ell=(e,\mu)$ by employing the QCD light-cone sum rules approach. The vector transition form factor (TFF) $f_+^{D_s^+ K^0}(q^2)$ for $D_s^+\to K^0$ decay is calculated while considering its next-to-leading order contribution. Subsequently, we briefly introduce the twist-2, 3 kaon distribution amplitudes, which are calculated by using QCD sum rules within the framework of the background field theory. At the large recoil point, the TFF has $f_+^{D_s^+ K^0}(0)=0.692_{-0.026}^{+0.027}$. Then, we extrapolate $f_+^{D_s^+ K^0}(q^2)$ to the whole physical $q^2$-region via the simplified $z(q^2,t)$-series expansion, and the behavior of TFF $f_+^{D_s^+ K^0}(q^2)$ is exhibited in the numerical results part, including the theoretical and experimental predictions for comparison. In addition, we compute the differential branching fraction $\mathcal{B}(D_s^+ \to K^0\ell^+\nu_\ell)$ with the electron and muon channels, which are expected to be $\mathcal{B}(D_s^+ \to K^0e^+\nu_e)=3.379_{-0.275}^{+0.301}\times 10^{-3}$ and $\mathcal{B}(D_s^+ \to K^0\mu^+\nu_\mu)=3.351_{-0.273}^{+0.299}\times 10^{-3}$ as well as contained other results for comparison. Our results show good agreement with the BESIII measurements and theoretical predictions. Furthermore, we present our prediction with respect to the CKM matrix element $|V_{cd}|$ by using the $\mathcal{B}(D_s^+ \to K^0e^+\nu_e)$ result from BESIII Collaboration, yielding $|V_{cd}|=0.221_{-0.010}^{+0.008}$. Finally, we provide the ratio between $D_s^+ \to K^0e^+\nu_e$ and $D_s^+ \to \eta e^+\nu_e$ channels, i.e. $\mathcal{R}_{K^0/\eta}^e=0.144_{-0.020}^{+0.028}$., Comment: 5 pages, 3 figures, comments welcome

We present X-SLAM, a real-time dense differentiable SLAM system that leverages the complex-step finite difference (CSFD) method for efficient calculation of numerical derivatives, bypassing the need for a large-scale computational graph. The key to our approach is treating the SLAM process as a differentiable function, enabling the calculation of the derivatives of important SLAM parameters through Taylor series expansion within the complex domain. Our system allows for the real-time calculation of not just the gradient, but also higher-order differentiation. This facilitates the use of high-order optimizers to achieve better accuracy and faster convergence. Building on X-SLAM, we implemented end-to-end optimization frameworks for two important tasks: camera relocalization in wide outdoor scenes and active robotic scanning in complex indoor environments. Comprehensive evaluations on public benchmarks and intricate real scenes underscore the improvements in the accuracy of camera relocalization and the efficiency of robotic navigation achieved through our task-aware optimization. The code and data are available at https://gapszju.github.io/X-SLAM., Comment: To be published in ACM SIGGRAPH 2024

We present Real-time Gaussian SLAM (RTG-SLAM), a real-time 3D reconstruction system with an RGBD camera for large-scale environments using Gaussian splatting. The system features a compact Gaussian representation and a highly efficient on-the-fly Gaussian optimization scheme. We force each Gaussian to be either opaque or nearly transparent, with the opaque ones fitting the surface and dominant colors, and transparent ones fitting residual colors. By rendering depth in a different way from color rendering, we let a single opaque Gaussian well fit a local surface region without the need of multiple overlapping Gaussians, hence largely reducing the memory and computation cost. For on-the-fly Gaussian optimization, we explicitly add Gaussians for three types of pixels per frame: newly observed, with large color errors, and with large depth errors. We also categorize all Gaussians into stable and unstable ones, where the stable Gaussians are expected to well fit previously observed RGBD images and otherwise unstable. We only optimize the unstable Gaussians and only render the pixels occupied by unstable Gaussians. In this way, both the number of Gaussians to be optimized and pixels to be rendered are largely reduced, and the optimization can be done in real time. We show real-time reconstructions of a variety of large scenes. Compared with the state-of-the-art NeRF-based RGBD SLAM, our system achieves comparable high-quality reconstruction but with around twice the speed and half the memory cost, and shows superior performance in the realism of novel view synthesis and camera tracking accuracy., Comment: To be published in ACM SIGGRAPH 2024

In this paper, we develop a general framework for multicontinuum homogenization in perforated domains. The simulations of problems in perforated domains are expensive and, in many applications, coarse-grid macroscopic models are developed. Many previous approaches include homogenization, multiscale finite element methods, and so on. In our paper, we design multicontinuum homogenization based on our recently proposed framework. In this setting, we distinguish different spatial regions in perforations based on their sizes. For example, very thin perforations are considered as one continua, while larger perforations are considered as another continua. By differentiating perforations in this way, we are able to predict flows in each of them more accurately. We present a framework by formulating cell problems for each continuum using appropriate constraints for the solution averages and their gradients. These cell problem solutions are used in a multiscale expansion and in deriving novel macroscopic systems for multicontinuum homogenization. Our proposed approaches are designed for problems without scale separation. We present numerical results for two continuum problems and demonstrate the accuracy of the proposed methods.

In this paper, we propose a novel multiscale model reduction strategy tailored to address the Poisson equation within heterogeneous perforated domains. The numerical simulation of this intricate problem is impeded by its multiscale characteristics, necessitating an exceptionally fine mesh to adequately capture all relevant details. To overcome the challenges inherent in the multiscale nature of the perforations, we introduce a coarse space constructed using the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM). This involves constructing basis functions through a sequence of local energy minimization problems over eigenspaces containing localized information pertaining to the heterogeneities. Through our analysis, we demonstrate that the oversampling layers depend on the local eigenvalues, thereby implicating the local geometry as well. Additionally, we provide numerical examples to illustrate the efficacy of the proposed scheme.

Local differential privacy (LDP) is a strong privacy standard that has been adopted by popular software systems. The main idea is that each individual perturbs their own data locally, and only submits the resulting noisy version to a data aggregator. Although much effort has been devoted to computing various types of aggregates and building machine learning applications under LDP, research on fundamental perturbation mechanisms has not achieved significant improvement in recent years. Towards a more refined result utility, existing works mainly focus on improving the worst-case guarantee. However, this approach does not necessarily promise a better average performance given the fact that the data in practice obey a certain distribution, which is not known beforehand. In this paper, we propose the advanced adaptive additive (AAA) mechanism, which is a distribution-aware approach that addresses the average utility and tackles the classical mean estimation problem. AAA is carried out in a two-step approach: first, as the global data distribution is not available beforehand, the data aggregator selects a random subset of individuals to compute a (noisy) quantized data descriptor; then, the data aggregator collects data from the remaining individuals, which are perturbed in a distribution-aware fashion. The perturbation involved in the latter step is obtained by solving an optimization problem, which is formulated with the data descriptor obtained in the former step and the desired properties of task-determined utilities. We provide rigorous privacy proofs, utility analyses, and extensive experiments comparing AAA with state-of-the-art mechanisms. The evaluation results demonstrate that the AAA mechanism consistently outperforms existing solutions with a clear margin in terms of result utility, on a wide range of privacy constraints and real-world and synthetic datasets.

Mil2 pushes the performance of high-resolution cloth simulation, making the simulation interactive (in milliseconds) for models with one million degrees of freedom (DOFs) while keeping every triangle untangled. The guarantee of being penetration-free is inspired by the interior-point method, which converts the inequality constraints to barrier potentials. Nevertheless, we propose a major overhaul of this modality by defining a novel and simple barrier formulation which does not depend on the distance between mesh primitives. Such a non-distance barrier model allows a new way to integrate collision detection into the simulation pipeline. Another contributor to the performance boost comes from the so-called subspace reuse strategy. This is based on the observation that low-frequency strain vibrations are near orthogonal to the deformation induced by collisions or self-collisions, often of high frequency. Subspace reuse then takes care of low-frequency residuals, while high-frequency residuals can also be effectively smoothed by GPU-based iterative solvers. We show that our method outperforms existing fast cloth simulators by nearly one order while keeping the entire simulation penetration-free and producing high-equality animations of high-resolution models.

We introduce vertex block descent, a block coordinate descent solution for the variational form of implicit Euler through vertex-level Gauss-Seidel iterations. It operates with local vertex position updates that achieve reductions in global variational energy with maximized parallelism. This forms a physics solver that can achieve numerical convergence with unconditional stability and exceptional computation performance. It can also fit in a given computation budget by simply limiting the iteration count while maintaining its stability and superior convergence rate. We present and evaluate our method in the context of elastic body dynamics, providing details of all essential components and showing that it outperforms alternative techniques. In addition, we discuss and show examples of how our method can be used for other simulation systems, including particle-based simulations and rigid bodies.

As consumer Virtual Reality (VR) and Mixed Reality (MR) technologies gain momentum, there's a growing focus on the development of engagements with 3D virtual content. Unfortunately, traditional techniques for content creation, editing, and interaction within these virtual spaces are fraught with difficulties. They tend to be not only engineering-intensive but also require extensive expertise, which adds to the frustration and inefficiency in virtual object manipulation. Our proposed VR-GS system represents a leap forward in human-centered 3D content interaction, offering a seamless and intuitive user experience. By developing a physical dynamics-aware interactive Gaussian Splatting in a Virtual Reality setting, and constructing a highly efficient two-level embedding strategy alongside deformable body simulations, VR-GS ensures real-time execution with highly realistic dynamic responses. The components of our Virtual Reality system are designed for high efficiency and effectiveness, starting from detailed scene reconstruction and object segmentation, advancing through multi-view image in-painting, and extending to interactive physics-based editing. The system also incorporates real-time deformation embedding and dynamic shadow casting, ensuring a comprehensive and engaging virtual experience.Our project page is available at: https://yingjiang96.github.io/VR-GS/.

We demonstrate the feasibility of integrating physics-based animations of solids and fluids with 3D Gaussian Splatting (3DGS) to create novel effects in virtual scenes reconstructed using 3DGS. Leveraging the coherence of the Gaussian Splatting and Position-Based Dynamics (PBD) in the underlying representation, we manage rendering, view synthesis, and the dynamics of solids and fluids in a cohesive manner. Similar to GaussianShader, we enhance each Gaussian kernel with an added normal, aligning the kernel's orientation with the surface normal to refine the PBD simulation. This approach effectively eliminates spiky noises that arise from rotational deformation in solids. It also allows us to integrate physically based rendering to augment the dynamic surface reflections on fluids. Consequently, our framework is capable of realistically reproducing surface highlights on dynamic fluids and facilitating interactions between scene objects and fluids from new views. For more information, please visit our project page at \url{https://gaussiansplashing.github.io/}.

The Material Point Method (MPM) is a hybrid Eulerian Lagrangian simulation technique for solid mechanics with significant deformation. Structured background grids are commonly employed in the standard MPM, but they may give rise to several accuracy problems in handling complex geometries. When using (2D) unstructured triangular or (3D) tetrahedral background elements, however, significant challenges arise (\eg, cell-crossing error). Substantial numerical errors develop due to the inherent $\mathcal{C}^0$ continuity property of the interpolation function, which causes discontinuous gradients across element boundaries. Prior efforts in constructing $\mathcal{C}^1$ continuous interpolation functions have either not been adapted for unstructured grids or have only been applied to 2D triangular meshes. In this study, an Unstructured Moving Least Squares MPM (UMLS-MPM) is introduced to accommodate 2D and 3D simplex tessellation. The central idea is to incorporate a diminishing function into the sample weights of the MLS kernel, ensuring an analytically continuous velocity gradient estimation. Numerical analyses confirm the method's capability in mitigating cell crossing inaccuracies and realizing expected convergence.

We show that physics-based simulations can be seamlessly integrated with NeRF to generate high-quality elastodynamics of real-world objects. Unlike existing methods, we discretize nonlinear hyperelasticity in a meshless way, obviating the necessity for intermediate auxiliary shape proxies like a tetrahedral mesh or voxel grid. A quadratic generalized moving least square (Q-GMLS) is employed to capture nonlinear dynamics and large deformation on the implicit model. Such meshless integration enables versatile simulations of complex and codimensional shapes. We adaptively place the least-square kernels according to the NeRF density field to significantly reduce the complexity of the nonlinear simulation. As a result, physically realistic animations can be conveniently synthesized using our method for a wide range of hyperelastic materials at an interactive rate. For more information, please visit our project page at https://fytalon.github.io/pienerf/.

We introduce PhysGaussian, a new method that seamlessly integrates physically grounded Newtonian dynamics within 3D Gaussians to achieve high-quality novel motion synthesis. Employing a custom Material Point Method (MPM), our approach enriches 3D Gaussian kernels with physically meaningful kinematic deformation and mechanical stress attributes, all evolved in line with continuum mechanics principles. A defining characteristic of our method is the seamless integration between physical simulation and visual rendering: both components utilize the same 3D Gaussian kernels as their discrete representations. This negates the necessity for triangle/tetrahedron meshing, marching cubes, "cage meshes," or any other geometry embedding, highlighting the principle of "what you see is what you simulate (WS$^2$)." Our method demonstrates exceptional versatility across a wide variety of materials--including elastic entities, metals, non-Newtonian fluids, and granular materials--showcasing its strong capabilities in creating diverse visual content with novel viewpoints and movements. Our project page is at: https://xpandora.github.io/PhysGaussian/, Comment: Accepted by CVPR 2024

Remote sensing images are essential for many applications of the earth's sciences, but their quality can usually be degraded due to limitations in sensor technology and complex imaging environments. To address this, various remote sensing image deblurring methods have been developed to restore sharp and high-quality images from degraded observational data. However, most traditional model-based deblurring methods usually require predefined {hand-crafted} prior assumptions, which are difficult to handle in complex applications. On the other hand, deep learning-based deblurring methods are often considered as black boxes, lacking transparency and interpretability. In this work, we propose a new blind deblurring learning framework that utilizes alternating iterations of shrinkage thresholds. This framework involves updating blurring kernels and images, with a theoretical foundation in network design. Additionally, we propose a learnable blur kernel proximal mapping module to improve the accuracy of the blur kernel reconstruction. Furthermore, we propose a deep proximal mapping module in the image domain, which combines a generalized shrinkage threshold with a multi-scale prior feature extraction block. This module also incorporates an attention mechanism to learn adaptively the importance of prior information, improving the flexibility and robustness of prior terms, and avoiding limitations similar to hand-crafted image prior terms. Consequently, we design a novel multi-scale generalized shrinkage threshold network (MGSTNet) that focuses specifically on learning deep geometric prior features to enhance image restoration. Experimental results on real and synthetic remote sensing image datasets demonstrate the superiority of our MGSTNet framework compared to existing deblurring methods., Comment: 16 pages,Accepted to IEEE Transactions on Geoscience and Remote Sensing,2024

The problem of phase retrieval (PR) involves recovering an unknown image from limited amplitude measurement data and is a challenge nonlinear inverse problem in computational imaging and image processing. However, many of the PR methods are based on black-box network models that lack interpretability and plug-and-play (PnP) frameworks that are computationally complex and require careful parameter tuning. To address this, we have developed PRISTA-Net, a deep unfolding network (DUN) based on the first-order iterative shrinkage thresholding algorithm (ISTA). This network utilizes a learnable nonlinear transformation to address the proximal-point mapping sub-problem associated with the sparse priors, and an attention mechanism to focus on phase information containing image edges, textures, and structures. Additionally, the fast Fourier transform (FFT) is used to learn global features to enhance local information, and the designed logarithmic-based loss function leads to significant improvements when the noise level is low. All parameters in the proposed PRISTA-Net framework, including the nonlinear transformation, threshold parameters, and step size, are learned end-to-end instead of being manually set. This method combines the interpretability of traditional methods with the fast inference ability of deep learning and is able to handle noise at each iteration during the unfolding stage, thus improving recovery quality. Experiments on Coded Diffraction Patterns (CDPs) measurements demonstrate that our approach outperforms the existing state-of-the-art methods in terms of qualitative and quantitative evaluations. Our source codes are available at \emph{https://github.com/liuaxou/PRISTA-Net}., Comment: 12 pages

Proximal gradient-based optimization is one of the most common strategies to solve inverse problem of images, and it is easy to implement. However, these techniques often generate heavy artifacts in image reconstruction. One of the most popular refinement methods is to fine-tune the regularization parameter to alleviate such artifacts, but it may not always be sufficient or applicable due to increased computational costs. In this work, we propose a deep geometric incremental learning framework based on the second Nesterov proximal gradient optimization. The proposed end-to-end network not only has the powerful learning ability for high-/low-frequency image features, but also can theoretically guarantee that geometric texture details will be reconstructed from preliminary linear reconstruction. Furthermore, it can avoid the risk of intermediate reconstruction results falling outside the geometric decomposition domains and achieve fast convergence. Our reconstruction framework is decomposed into four modules including general linear reconstruction, cascade geometric incremental restoration, Nesterov acceleration, and post-processing. In the image restoration step, a cascade geometric incremental learning module is designed to compensate for missing texture information from different geometric spectral decomposition domains. Inspired by the overlap-tile strategy, we also develop a post-processing module to remove the block effect in patch-wise-based natural image reconstruction. All parameters in the proposed model are learnable, an adaptive initialization technique of physical parameters is also employed to make model flexibility and ensure converging smoothly. We compare the reconstruction performance of the proposed method with existing state-of-the-art methods to demonstrate its superiority. Our source codes are available at https://github.com/fanxiaohong/Nest-DGIL., Comment: 15 pages,our source codes are available at https://github.com/fanxiaohong/Nest-DGIL

In this paper, we focus on the task of 3D shape completion from partial point clouds using deep implicit functions. Existing methods seek to use voxelized basis functions or the ones from a certain family of functions (e.g., Gaussians), which leads to high computational costs or limited shape expressivity. On the contrary, our method employs adaptive local basis functions, which are learned end-to-end and not restricted in certain forms. Based on those basis functions, a local-to-local shape completion framework is presented. Our algorithm learns sparse parameterization with a small number of basis functions while preserving local geometric details during completion. Quantitative and qualitative experiments demonstrate that our method outperforms the state-of-the-art methods in shape completion, detail preservation, generalization to unseen geometries, and computational cost. Code and data are at https://github.com/yinghdb/Adaptive-Local-Basis-Functions., Comment: In SIGGRAPH 2023

Breaking safety constraints in control systems can lead to potential risks, resulting in unexpected costs or catastrophic damage. Nevertheless, uncertainty is ubiquitous, even among similar tasks. In this paper, we develop a novel adaptive safe control framework that integrates meta learning, Bayesian models, and control barrier function (CBF) method. Specifically, with the help of CBF method, we learn the inherent and external uncertainties by a unified adaptive Bayesian linear regression (ABLR) model, which consists of a forward neural network (NN) and a Bayesian output layer. Meta learning techniques are leveraged to pre-train the NN weights and priors of the ABLR model using data collected from historical similar tasks. For a new control task, we refine the meta-learned models using a few samples, and introduce pessimistic confidence bounds into CBF constraints to ensure safe control. Moreover, we provide theoretical criteria to guarantee probabilistic safety during the control processes. To validate our approach, we conduct comparative experiments in various obstacle avoidance scenarios. The results demonstrate that our algorithm significantly improves the Bayesian model-based CBF method, and is capable for efficient safe exploration even with multiple uncertain constraints.

In this paper, the semileptonic decays $D_s^+ \to \pi^0\ell^+ \nu_\ell$ with $\ell=(e,\mu)$ are investigated by using the light-cone sum rule approach. Firstly, the neutral meson mixing scheme between $\pi^0$, $\eta$, $\eta^\prime$ and pseudoscalar gluonium $G$ is discussed in a unified way, which leads to the direct connection between two different channels for $D_s^+\to \pi^0\ell^+\nu_\ell$ and $D_s^+ \to \eta\ell^+\nu_\ell$ by the $\pi^0-\eta$ mixing angle. Then we calculated the $D_s\to \pi^0$ transition form factors (TFFs) within QCD light-cone sum rule approach up to next-to-leading order correction. At the large recoil point, we have $f_+^{D_s^+\pi^0}(0)=0.0113_{-0.0019}^{+0.0024}$ and $f_-^{D_s^+\pi^0}(0)=0.0020_{-0.0009}^{+0.0008}$. Furthermore, the TFFs are extrapolated to the whole physical $q^2$-region by using the simplified $z(q^2)$-series expansion. The behaviors of TFFs and related three angular coefficient functions $a_{\theta_\ell}(q^2)$, $b_{\theta_\ell}(q^2)$ and $c_{\theta_\ell}(q^2)$ are given. The differential decay widths for $D_s^+ \to \pi^0\ell^+ \nu_\ell$ with respect to $q^2$ and $\cos\theta_\ell$ are presented, and also lead to the branching fractions ${\cal B}(D_s^+\to \pi ^0e^+\nu_e) =2.60_{-0.51}^{+0.57}\times 10^{-5}$ and ${\cal B}(D_s^+\to \pi ^0\mu^+\nu _\mu )= 2.58_{-0.51}^{+0.56}\times 10^{-5}$. These results show well agreement with the recent BESIII measurements and theoretical predictions. Then the differential distributions and integrated predictions for three angular observables, {\it i.e.} forward-backward asymmetries, $q^2$-differential flat terms and lepton polarization asymmetries are given separately. Lastly, we estimate the ratio for different decay channels ${\cal R}_{\pi ^0/\eta}^{\ell}=1.108_{-0.071}^{+0.039}\times 10^{-3}$., Comment: 10 pages, 5 figures. Matches version accepted for publication in PRD

Clustering continues to be a significant and challenging task. Recent studies have demonstrated impressive results by applying clustering to feature representations acquired through self-supervised learning, particularly on small datasets. However, when dealing with datasets containing a large number of clusters, such as ImageNet, current methods struggle to achieve satisfactory clustering performance. In this paper, we introduce a novel method called Contrastive representation Disentanglement for Clustering (CDC) that leverages contrastive learning to directly disentangle the feature representation for clustering. In CDC, we decompose the representation into two distinct components: one component encodes categorical information under an equipartition constraint, and the other component captures instance-specific factors. To train our model, we propose a contrastive loss that effectively utilizes both components of the representation. We conduct a theoretical analysis of the proposed loss and highlight how it assigns different weights to negative samples during the process of disentangling the feature representation. Further analysis of the gradients reveals that larger weights emphasize a stronger focus on hard negative samples. As a result, the proposed loss exhibits strong expressiveness, enabling efficient disentanglement of categorical information. Through experimental evaluation on various benchmark datasets, our method demonstrates either state-of-the-art or highly competitive clustering performance. Notably, on the complete ImageNet dataset, we achieve an accuracy of 53.4%, surpassing existing methods by a substantial margin of +10.2%., Comment: 10 pages, 7 tables, 4 figures

We present a robust and efficient method for simulating Lagrangian solid-fluid coupling based on a new operator splitting strategy. We use variational formulations to approximate fluid properties and solid-fluid interactions, and introduce a unified two-way coupling formulation for SPH fluids and FEM solids using interior point barrier-based frictional contact. We split the resulting optimization problem into a fluid phase and a solid-coupling phase using a novel time-splitting approach with augmented contact proxies, and propose efficient custom linear solvers. Our technique accounts for fluids interaction with nonlinear hyperelastic objects of different geometries and codimensions, while maintaining an algorithmically guaranteed non-penetrating criterion. Comprehensive benchmarks and experiments demonstrate the efficacy of our method., Comment: 14 pages, 13 figures