Machine Learning methods belong to the group of most up-to-date approaches for solving partial differential equations. The current work investigates two classes, Neural FEM and Neural Operator Methods, for the use in elastostatics by means of numerical experiments. The Neural Operator methods require expensive training but then allow for solving multiple boundary value problems with the same Machine Learning model. Main differences between the two classes are the computational effort and accuracy. Especially the accuracy requires more research for practical applications.
相關內容
We consider the solution to the biharmonic equation in mixed form discretized by the Hybrid High-Order (HHO) methods. The two resulting second-order elliptic problems can be decoupled via the introduction of a new unknown, corresponding to the boundary value of the solution of the first Laplacian problem. This technique yields a global linear problem that can be solved iteratively via a Krylov-type method. More precisely, at each iteration of the scheme, two second-order elliptic problems have to be solved, and a normal derivative on the boundary has to be computed. In this work, we specialize this scheme for the HHO discretization. To this aim, an explicit technique to compute the discrete normal derivative of an HHO solution of a Laplacian problem is proposed. Moreover, we show that the resulting discrete scheme is well-posed. Finally, a new preconditioner is designed to speed up the convergence of the Krylov method. Numerical experiments assessing the performance of the proposed iterative algorithm on both two- and three-dimensional test cases are presented.
Face parsing infers a pixel-wise label map for each semantic facial component. Previous methods generally work well for uncovered faces, however overlook the facial occlusion and ignore some contextual area outside a single face, especially when facial occlusion has become a common situation during the COVID-19 epidemic. Inspired by the illumination theory of image, we propose a novel homogeneous tanh-transforms for image preprocessing, which made up of four tanh-transforms, that fuse the central vision and the peripheral vision together. Our proposed method addresses the dilemma of face parsing under occlusion and compresses more information of surrounding context. Based on homogeneous tanh-transforms, we propose an occlusion-aware convolutional neural network for occluded face parsing. It combines the information both in Tanh-polar space and Tanh-Cartesian space, capable of enhancing receptive fields. Furthermore, we introduce an occlusion-aware loss to focus on the boundaries of occluded regions. The network is simple and flexible, and can be trained end-to-end. To facilitate future research of occluded face parsing, we also contribute a new cleaned face parsing dataset, which is manually purified from several academic or industrial datasets, including CelebAMask-HQ, Short-video Face Parsing as well as Helen dataset and will make it public. Experiments demonstrate that our method surpasses state-of-art methods of face parsing under occlusion.
Due to the high similarity between camouflaged instances and the background, the recently proposed camouflaged instance segmentation (CIS) faces challenges in accurate localization and instance segmentation. To this end, inspired by query-based transformers, we propose a unified query-based multi-task learning framework for camouflaged instance segmentation, termed UQFormer, which builds a set of mask queries and a set of boundary queries to learn a shared composed query representation and efficiently integrates global camouflaged object region and boundary cues, for simultaneous instance segmentation and instance boundary detection in camouflaged scenarios. Specifically, we design a composed query learning paradigm that learns a shared representation to capture object region and boundary features by the cross-attention interaction of mask queries and boundary queries in the designed multi-scale unified learning transformer decoder. Then, we present a transformer-based multi-task learning framework for simultaneous camouflaged instance segmentation and camouflaged instance boundary detection based on the learned composed query representation, which also forces the model to learn a strong instance-level query representation. Notably, our model views the instance segmentation as a query-based direct set prediction problem, without other post-processing such as non-maximal suppression. Compared with 14 state-of-the-art approaches, our UQFormer significantly improves the performance of camouflaged instance segmentation. Our code will be available at //github.com/dongbo811/UQFormer.
We propose and analyse an explicit boundary-preserving scheme for the strong approximations of some SDEs with non-globally Lipschitz drift and diffusion coefficients whose state-space is bounded. The scheme consists of a Lamperti transform followed by a Lie--Trotter splitting. We prove $L^{p}(\Omega)$-convergence of order $1$, for every $p \in \mathbb{N}$, of the scheme and exploit the Lamperti transform to confine the numerical approximations to the state-space of the considered SDE. We provide numerical experiments that confirm the theoretical results and compare the proposed Lamperti-splitting scheme to other numerical schemes for SDEs.
Fighting misinformation is a challenging, yet crucial, task. Despite the growing number of experts being involved in manual fact-checking, this activity is time-consuming and cannot keep up with the ever-increasing amount of Fake News produced daily. Hence, automating this process is necessary to help curb misinformation. Thus far, researchers have mainly focused on claim veracity classification. In this paper, instead, we address the generation of justifications (textual explanation of why a claim is classified as either true or false) and benchmark it with novel datasets and advanced baselines. In particular, we focus on summarization approaches over unstructured knowledge (i.e. news articles) and we experiment with several extractive and abstractive strategies. We employed two datasets with different styles and structures, in order to assess the generalizability of our findings. Results show that in justification production summarization benefits from the claim information, and, in particular, that a claim-driven extractive step improves abstractive summarization performances. Finally, we show that although cross-dataset experiments suffer from performance degradation, a unique model trained on a combination of the two datasets is able to retain style information in an efficient manner.
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its hyperbolic structure. This new system can be written as a quasi linear system in time and horizontal variables and involves no more vertical derivatives. However, the coefficients in front of the horizontal derivatives include an integral operator acting on the new vertical variable. The spectrum of these operators is studied in detail, in particular it includes a continuous part. Riemann invariants are then determined as conserved quantities along the characteristic curves. Examples of solutions are provided, in particular stationary solutions and solutions blowing-up in finite time. Eventually, we propose an exact multi-layer $\mathbb{P}_0$-discretization, which could be used to solve numerically this semi-Lagrangian system, and analyze the eigenvalues of the corresponding discretized operator to investigate the hyperbolic nature of the approximated system.
The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian simple groups to cryptography and discuss different scenarios in which this theory is clearly central, providing the relevant definitions to make the material accessible to both cryptographers and group theorists, in the hope of stimulating further interaction between these two (non-disjoint) communities. In particular, we look at constructions based on various group-theoretic factorization problems, review group theoretical hash functions, and discuss fully homomorphic encryption using simple groups. The Hidden Subgroup Problem is also briefly discussed in this context.
The composition theorems of differential privacy (DP) allow data curators to combine different algorithms to obtain a new algorithm that continues to satisfy DP. However, new granularity notions (i.e., neighborhood definitions), data domains, and composition settings have appeared in the literature that the classical composition theorems do not cover. For instance, the parallel composition theorem does not apply to general granularity notions. This complicates the opportunity of composing DP mechanisms in new settings and obtaining accurate estimates of the incurred privacy loss after composition. To overcome these limitations, we study the composability of DP in a general framework and for any kind of data domain or neighborhood definition. We give a general composition theorem in both independent and adaptive versions and we provide analogous composition results for approximate, zero-concentrated, and Gaussian DP. Besides, we study the hypothesis needed to obtain the best composition bounds. Our theorems cover both parallel and sequential composition settings. Importantly, they also cover every setting in between, allowing us to compute the final privacy loss of a composition with greatly improved accuracy.
The parallel alternating direction method of multipliers (ADMM) algorithms have become popular in statistics and machine learning due to their ability to efficiently handle large sample data problems. However, the parallel structure of the ADMM algorithms are all based on consensus structure, which can cause too many auxiliary variables for high-dimensional data. In this paper, we focus on nonconvex penalized smooth quantile regression peoblems and develop a parallel linearized ADMM (LADMM) algorithm to solve it. Compared with existing parallel ADMM algorithms, our algorithm does not rely on consensus structure, resulting in a significant reduction in the number of variables that need to be updated at each iteration. It is worth noting that the solution of our algorithm remains unchanged regardless of how the total sample is divided. Furthermore, under some mild assumptions, we prove that the iterative sequence generated by the LADMM converges to a critical point of the nonconvex optimization problem. Numerical experiments on synthetic and real datasets demonstrate the feasibility and validity of the proposed algorithm.
Denoising diffusion models have emerged as the go-to framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution (OOD) tasks, which remains an under-explored challenge. Realistic reconstructions inconsistent with the measured data can be generated, hallucinating image features that are uniquely present in the training dataset. To simultaneously enforce data-consistency and leverage data-driven priors, we introduce a novel sampling framework called Steerable Conditional Diffusion. This framework adapts the denoising network specifically to the available measured data. Utilising our proposed method, we achieve substantial enhancements in OOD performance across diverse imaging modalities, advancing the robust deployment of denoising diffusion models in real-world applications.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191