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In this paper, we propose a general numerical framework to derive structure-preserving reduced order models for thermodynamically consistent PDEs. Our numerical framework has two primary features: (a) a systematic way to extract reduced order models for thermodynamically consistent PDE systems while maintaining their inherent thermodynamic principles and (b) a strategic process to devise accurate, efficient, and structure-preserving numerical algorithms to solve the forehead reduced-order models. The platform's generality extends to various PDE systems governed by embedded thermodynamic laws. The proposed numerical platform is unique from several perspectives. First, it utilizes the generalized Onsager principle to transform the thermodynamically consistent PDE system into an equivalent one, where the transformed system's free energy adopts a quadratic form of the state variables. This transformation is named energy quadratization (EQ). Through EQ, we gain a novel perspective on deriving reduced order models. The reduced order models derived through our method continue to uphold the energy dissipation law. Secondly, our proposed numerical approach automatically provides numerical algorithms to discretize the reduced order models. The proposed algorithms are always linear, easy to implement and solve, and uniquely solvable. Furthermore, these algorithms inherently ensure the thermodynamic laws. In essence, our platform offers a distinctive approach to derive structure-preserving reduced-order models for a wide range of PDE systems abiding by thermodynamic principles.

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In this study, we harness the information-theoretic Privacy Funnel (PF) model to develop a method for privacy-preserving representation learning using an end-to-end training framework. We rigorously address the trade-off between obfuscation and utility. Both are quantified through the logarithmic loss, a measure also recognized as self-information loss. This exploration deepens the interplay between information-theoretic privacy and representation learning, offering substantive insights into data protection mechanisms for both discriminative and generative models. Importantly, we apply our model to state-of-the-art face recognition systems. The model demonstrates adaptability across diverse inputs, from raw facial images to both derived or refined embeddings, and is competent in tasks such as classification, reconstruction, and generation.

In this paper, we study zeroth-order algorithms for nonconvex-concave minimax problems, which have attracted widely attention in machine learning, signal processing and many other fields in recent years. We propose a zeroth-order alternating randomized gradient projection (ZO-AGP) algorithm for smooth nonconvex-concave minimax problems, and its iteration complexity to obtain an $\varepsilon$-stationary point is bounded by $\mathcal{O}(\varepsilon^{-4})$, and the number of function value estimation is bounded by $\mathcal{O}(d_{x}+d_{y})$ per iteration. Moreover, we propose a zeroth-order block alternating randomized proximal gradient algorithm (ZO-BAPG) for solving block-wise nonsmooth nonconvex-concave minimax optimization problems, and the iteration complexity to obtain an $\varepsilon$-stationary point is bounded by $\mathcal{O}(\varepsilon^{-4})$ and the number of function value estimation per iteration is bounded by $\mathcal{O}(K d_{x}+d_{y})$. To the best of our knowledge, this is the first time that zeroth-order algorithms with iteration complexity gurantee are developed for solving both general smooth and block-wise nonsmooth nonconvex-concave minimax problems. Numerical results on data poisoning attack problem and distributed nonconvex sparse principal component analysis problem validate the efficiency of the proposed algorithms.

In this study, we introduce three distinct testing methods for testing alpha in high dimensional linear factor pricing model that deals with dependent data. The first method is a sum-type test procedure, which exhibits high performance when dealing with dense alternatives. The second method is a max-type test procedure, which is particularly effective for sparse alternatives. For a broader range of alternatives, we suggest a Cauchy combination test procedure. This is predicated on the asymptotic independence of the sum-type and max-type test statistics. Both simulation studies and practical data application demonstrate the effectiveness of our proposed methods when handling dependent observations.

In this paper, we present a novel approach for detecting the discontinuity interfaces of a discontinuous function. This approach leverages Graph-Informed Neural Networks (GINNs) and sparse grids to address discontinuity detection also in domains of dimension larger than 3. GINNs, trained to identify troubled points on sparse grids, exploit graph structures built on the grids to achieve efficient and accurate discontinuity detection performances. We also introduce a recursive algorithm for general sparse grid-based detectors, characterized by convergence properties and easy applicability. Numerical experiments on functions with dimensions n = 2 and n = 4 demonstrate the efficiency and robust generalization of GINNs in detecting discontinuity interfaces. Notably, the trained GINNs offer portability and versatility, allowing integration into various algorithms and sharing among users.

In this paper, we present a novel deep image clustering approach termed PICI, which enforces the partial information discrimination and the cross-level interaction in a joint learning framework. In particular, we leverage a Transformer encoder as the backbone, through which the masked image modeling with two paralleled augmented views is formulated. After deriving the class tokens from the masked images by the Transformer encoder, three partial information learning modules are further incorporated, including the PISD module for training the auto-encoder via masked image reconstruction, the PICD module for employing two levels of contrastive learning, and the CLI module for mutual interaction between the instance-level and cluster-level subspaces. Extensive experiments have been conducted on six real-world image datasets, which demononstrate the superior clustering performance of the proposed PICI approach over the state-of-the-art deep clustering approaches. The source code is available at //github.com/Regan-Zhang/PICI.

In this paper, a comparison analysis between geometric impedance controls (GICs) derived from two different potential functions on SE(3) for robotic manipulators is presented. The first potential function is defined on the Lie group, utilizing the Frobenius norm of the configuration error matrix. The second potential function is defined utilizing the Lie algebra, i.e., log-map of the configuration error. Using a differential geometric approach, the detailed derivation of the distance metric and potential function on SE(3) is introduced. The GIC laws are respectively derived from the two potential functions, followed by extensive comparison analyses. In the qualitative analysis, the properties of the error function and control laws are analyzed, while the performances of the controllers are quantitatively compared using numerical simulation.

In this study, we introduce an optimization framework aimed at enhancing the efficiency of motion priority design in scenarios involving automated and teleoperated robots within an industrial recovery context. The escalating utilization of industrial robots at manufacturing sites has been instrumental in mitigating human workload. Nevertheless, the challenge persists in achieving effective human-robot collaboration/cooperation where human workers and robots share a workspace for collaborative tasks. In the event of an industrial robot encountering a failure, it necessitates the suspension of the corresponding factory cell for safe recovery. Given the limited capacity of pre-programmed robots to rectify such failures, human intervention becomes imperative, requiring entry into the robot workspace to address the dropped object while the robot system is halted. This non-continuous manufacturing process results in productivity loss. Robotic teleoperation has emerged as a promising technology enabling human workers to undertake high-risk tasks remotely and safely. Our study advocates for the incorporation of robotic teleoperation in the recovery process during manufacturing failure scenarios, which is referred to as "Cooperative Tele-Recovery". Our proposed approach involves the formulation of priority rules designed to facilitate collision avoidance between manufacturing and recovery robots. This, in turn, ensures a continuous manufacturing process with minimal production loss within a configurable risk limitation. We present a comprehensive motion priority optimization framework, encompassing an HRC simulator-based priority optimization and a cooperative multi-robot controller, to identify optimal parameters for the priority function. The framework dynamically adjusts the allocation of motion priorities for manufacturing and recovery robots while adhering to predefined risk limitations.

Link prediction is a very fundamental task on graphs. Inspired by traditional path-based methods, in this paper we propose a general and flexible representation learning framework based on paths for link prediction. Specifically, we define the representation of a pair of nodes as the generalized sum of all path representations, with each path representation as the generalized product of the edge representations in the path. Motivated by the Bellman-Ford algorithm for solving the shortest path problem, we show that the proposed path formulation can be efficiently solved by the generalized Bellman-Ford algorithm. To further improve the capacity of the path formulation, we propose the Neural Bellman-Ford Network (NBFNet), a general graph neural network framework that solves the path formulation with learned operators in the generalized Bellman-Ford algorithm. The NBFNet parameterizes the generalized Bellman-Ford algorithm with 3 neural components, namely INDICATOR, MESSAGE and AGGREGATE functions, which corresponds to the boundary condition, multiplication operator, and summation operator respectively. The NBFNet is very general, covers many traditional path-based methods, and can be applied to both homogeneous graphs and multi-relational graphs (e.g., knowledge graphs) in both transductive and inductive settings. Experiments on both homogeneous graphs and knowledge graphs show that the proposed NBFNet outperforms existing methods by a large margin in both transductive and inductive settings, achieving new state-of-the-art results.

In this paper, we propose a deep reinforcement learning framework called GCOMB to learn algorithms that can solve combinatorial problems over large graphs. GCOMB mimics the greedy algorithm in the original problem and incrementally constructs a solution. The proposed framework utilizes Graph Convolutional Network (GCN) to generate node embeddings that predicts the potential nodes in the solution set from the entire node set. These embeddings enable an efficient training process to learn the greedy policy via Q-learning. Through extensive evaluation on several real and synthetic datasets containing up to a million nodes, we establish that GCOMB is up to 41% better than the state of the art, up to seven times faster than the greedy algorithm, robust and scalable to large dynamic networks.

In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.

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