Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on heuristics, e.g., the solution operators of partial differential equations (PDE), such as the Laplace or biharmonic equation. Especially the latter, which shows good numerical performance for large displacements, is expensive. Moreover, from a continuous perspective, choosing the mesh motion technique is to a certain extent arbitrary and has no influence on the physically relevant quantities. Therefore, we consider approaches inspired by machine learning. We present a hybrid PDE-NN approach, where the neural network (NN) serves as parameterization of a coefficient in a second order nonlinear PDE. We ensure existence of solutions for the nonlinear PDE by the choice of the neural network architecture. Moreover, we present an approach where a neural network corrects the harmonic extension such that the boundary displacement is not changed. In order to avoid technical difficulties in coupling finite element and machine learning software, we work with a splitting of the monolithic FSI system into three smaller subsystems. This allows to solve the mesh motion equation in a separate step. We assess the quality of the learned mesh motion technique by applying it to a FSI benchmark problem.
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IFIP TC13 Conference on Human-Computer Interaction是人機交互領域的研究者和實踐者展示其工作的重要平臺。多年來，這些會議吸引了來自幾個國家和文化的研究人員。官網鏈接： ·
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To promote the generalization ability of breast tumor segmentation models, as well as to improve the segmentation performance for breast tumors with smaller size, low-contrast amd irregular shape, we propose a progressive dual priori network (PDPNet) to segment breast tumors from dynamic enhanced magnetic resonance images (DCE-MRI) acquired at different sites. The PDPNet first cropped tumor regions with a coarse-segmentation based localization module, then the breast tumor mask was progressively refined by using the weak semantic priori and cross-scale correlation prior knowledge. To validate the effectiveness of PDPNet, we compared it with several state-of-the-art methods on multi-center datasets. The results showed that, comparing against the suboptimal method, the DSC, SEN, KAPPA and HD95 of PDPNet were improved 3.63\%, 8.19\%, 5.52\%, and 3.66\% respectively. In addition, through ablations, we demonstrated that the proposed localization module can decrease the influence of normal tissues and therefore improve the generalization ability of the model. The weak semantic priors allow focusing on tumor regions to avoid missing small tumors and low-contrast tumors. The cross-scale correlation priors are beneficial for promoting the shape-aware ability for irregual tumors. Thus integrating them in a unified framework improved the multi-center breast tumor segmentation performance.
We introduce two new stochastic conjugate frameworks for a class of nonconvex and possibly also nonsmooth optimization problems. These frameworks are built upon Stochastic Recursive Gradient Algorithm (SARAH) and we thus refer to them as Acc-Prox-CG-SARAH and Acc-Prox-CG-SARAH-RS, respectively. They are efficiently accelerated, easy to implement, tune free and can be smoothly extended and modified. We devise a deterministic restart scheme for stochastic optimization and apply it in our second stochastic conjugate framework, which serves the key difference between the two approaches. In addition, we apply the ProbAbilistic Gradient Estimator (PAGE) and further develop a practical variant, denoted as Acc-Prox-CG-SARAH-ST, in order to reduce potential computational overhead. We provide comprehensive and rigorous convergence analysis for all three approaches and establish linear convergence rates for unconstrained minimization problem with nonconvex and nonsmooth objective functions. Experiments have demonstrated that Acc-Prox-CG-SARAH and Acc-Prox-CG-SARAH-RS both outperform state-of-art methods consistently and Acc-Prox-CG-SARAH-ST can as well achieve comparable convergence speed. In terms of theory and experiments, we verify the strong computational efficiency of the deterministic restart scheme in stochastic optimization methods.
Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty. Gibbs posteriors provide a principled framework for likelihood-free Bayesian inference, but in many situations, including a single tuning parameter inevitably leads to poor uncertainty quantification. In particular, regardless of the value of the parameter, credible regions have far from the nominal frequentist coverage even in large samples. We propose a sequential extension to Gibbs posteriors to address this problem. We prove the proposed sequential posterior exhibits concentration and a Bernstein-von Mises theorem, which holds under easy to verify conditions in Euclidean space and on manifolds. As a byproduct, we obtain the first Bernstein-von Mises theorem for traditional likelihood-based Bayesian posteriors on manifolds. All methods are illustrated with an application to principal component analysis.
Sequential transfer optimization (STO), which aims to improve the optimization performance on a task of interest by exploiting the knowledge captured from several previously-solved optimization tasks stored in a database, has been gaining increasing research attention over the years. However, despite the remarkable advances in algorithm design, the development of a systematic benchmark suite for comprehensive comparisons of STO algorithms received far less attention. Existing test problems are either simply generated by assembling other benchmark functions or extended from specific practical problems with limited scalability. The relationships between the optimal solutions of the source and target tasks in these problems are also often manually configured, limiting their ability to model different similarity relationships presented in real-world problems. Consequently, the good performance achieved by an algorithm on these problems might be biased and hard to be generalized to other problems. In light of the above, in this study, we first introduce four concepts for characterizing STO problems and present an important problem feature, namely similarity distribution, which quantitatively delineates the relationship between the optima of the source and target tasks. Then, we present the general design guidelines of STO problems and a particular STO problem generator with good scalability. Specifically, the similarity distribution of a problem can be easily customized, enabling a continuous spectrum of representation of the diverse similarity relationships of real-world problems. Lastly, a benchmark suite with 12 STO problems featured by a variety of customized similarity relationships is developed using the proposed generator. The source code of the problem generator is available at //github.com/XmingHsueh/STOP-G.
We consider rather a general class of multi-level optimization problems, where a convex objective function is to be minimized subject to constraints of optimality of nested convex optimization problems. As a special case, we consider a trilevel optimization problem, where the objective of the two lower layers consists of a sum of a smooth and a non-smooth term.~Based on fixed-point theory and related arguments, we present a natural first-order algorithm and analyze its convergence and rates of convergence in several regimes of parameters.
Explainable recommender systems (RS) have traditionally followed a one-size-fits-all approach, delivering the same explanation level of detail to each user, without considering their individual needs and goals. Further, explanations in RS have so far been presented mostly in a static and non-interactive manner. To fill these research gaps, we aim in this paper to adopt a user-centered, interactive explanation model that provides explanations with different levels of detail and empowers users to interact with, control, and personalize the explanations based on their needs and preferences. We followed a user-centered approach to design interactive explanations with three levels of detail (basic, intermediate, and advanced) and implemented them in the transparent Recommendation and Interest Modeling Application (RIMA). We conducted a qualitative user study (N=14) to investigate the impact of providing interactive explanations with varying level of details on the users' perception of the explainable RS. Our study showed qualitative evidence that fostering interaction and giving users control in deciding which explanation they would like to see can meet the demands of users with different needs, preferences, and goals, and consequently can have positive effects on different crucial aspects in explainable recommendation, including transparency, trust, satisfaction, and user experience.
The ability to measure the satisfaction of (groups of) voters is a crucial prerequisite for formulating proportionality axioms in approval-based participatory budgeting elections. Two common - but very different - ways to measure the satisfaction of a voter consider (i) the number of approved projects and (ii) the total cost of approved projects, respectively. In general, it is difficult to decide which measure of satisfaction best reflects the voters' true utilities. In this paper, we study proportionality axioms with respect to large classes of approval-based satisfaction functions. We establish logical implications among our axioms and related notions from the literature, and we ask whether outcomes can be achieved that are proportional with respect to more than one satisfaction function. We show that this is impossible for the two commonly used satisfaction functions when considering proportionality notions based on extended justified representation, but achievable for a notion based on proportional justified representation. For the latter result, we introduce a strengthening of priceability and show that it is satisfied by several polynomial-time computable rules, including the Method of Equal Shares and Phragm\`en's sequential rule.
Natural gradient methods have been used to optimise the parameters of probability distributions in a variety of settings, often resulting in fast-converging procedures. Unfortunately, for many distributions of interest, computing the natural gradient has a number of challenges. In this work we propose a novel technique for tackling such issues, which involves reframing the optimisation as one with respect to the parameters of a surrogate distribution, for which computing the natural gradient is easy. We give several examples of existing methods that can be interpreted as applying this technique, and propose a new method for applying it to a wide variety of problems. Our method expands the set of distributions that can be efficiently targeted with natural gradients. Furthermore, it is fast, easy to understand, simple to implement using standard autodiff software, and does not require lengthy model-specific derivations. We demonstrate our method on maximum likelihood estimation and variational inference tasks.
Graphs are used widely to model complex systems, and detecting anomalies in a graph is an important task in the analysis of complex systems. Graph anomalies are patterns in a graph that do not conform to normal patterns expected of the attributes and/or structures of the graph. In recent years, graph neural networks (GNNs) have been studied extensively and have successfully performed difficult machine learning tasks in node classification, link prediction, and graph classification thanks to the highly expressive capability via message passing in effectively learning graph representations. To solve the graph anomaly detection problem, GNN-based methods leverage information about the graph attributes (or features) and/or structures to learn to score anomalies appropriately. In this survey, we review the recent advances made in detecting graph anomalies using GNN models. Specifically, we summarize GNN-based methods according to the graph type (i.e., static and dynamic), the anomaly type (i.e., node, edge, subgraph, and whole graph), and the network architecture (e.g., graph autoencoder, graph convolutional network). To the best of our knowledge, this survey is the first comprehensive review of graph anomaly detection methods based on GNNs.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
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