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This paper addresses the inverse optimal control for the linear quadratic tracking problem with a fixed but unknown target state, which aims to estimate the possible triplets comprising the target state, the state weight matrix, and the input weight matrix from observed optimal control input and the corresponding state trajectories. Sufficient conditions have been provided for the unique determination of both the linear quadratic cost function as well as the target state. A computationally efficient and numerically reliable parameter identification algorithm is proposed by equating optimal control strategies with a system of linear equations, and the associated relative error upper bound is derived in terms of data volume and signal-to-noise ratio. Moreover, the proposed inverse optimal control algorithm is applied for the joint cluster coordination and intent identification of a multi-agent system. By incorporating the structural constraint of the Laplace matrix, the relative error upper bound can be reduced accordingly. Finally, the algorithm's efficiency and accuracy are validated by a vehicle-on-a-lever example and a multi-agent formation control example.

Laser-directed-energy deposition (DED) offers advantages in additive manufacturing (AM) for creating intricate geometries and material grading. Yet, challenges like material inconsistency and part variability remain, mainly due to its layer-wise fabrication. A key issue is heat accumulation during DED, which affects the material microstructure and properties. While closed-loop control methods for heat management are common in DED research, few integrate real-time monitoring, physics-based modeling, and control in a unified framework. Our work presents a digital twin (DT) framework for real-time predictive control of DED process parameters to meet specific design objectives. We develop a surrogate model using Long Short-Term Memory (LSTM)-based machine learning with Bayesian Inference to predict temperatures in DED parts. This model predicts future temperature states in real time. We also introduce Bayesian Optimization (BO) for Time Series Process Optimization (BOTSPO), based on traditional BO but featuring a unique time series process profile generator with reduced dimensions. BOTSPO dynamically optimizes processes, identifying optimal laser power profiles to attain desired mechanical properties. The established process trajectory guides online optimizations, aiming to enhance performance. This paper outlines the digital twin framework's components, promoting its integration into a comprehensive system for AM., Comment: 12 Pages, 10 Figures, 1 Table, NAMRC Conference

We investigate the emergence of unconventional corner mode in a two-dimensional topolectrical circuits induced by asymmetric couplings. The non-Hermitian skin effect of two kinked one-dimensional lattices with multiple asymmetric couplings are explored. Then we extend to the two-dimensional model, derive conditions for the non-Hermitian hybrid skin effect and show how the corner modes are formed by non-reciprocal pumping based on one-dimensional topological modes. We provide explicit electrical circuit setups for realizing our observations via realistic LTspice simulation. Moreover, we show the time varying behaviors of voltage distributions to confirm our results. Our study may help to extend the knowledge on building the topological corner modes in the non-Hermitian presence.

Bayesian optimization has been successfully applied to optimize black-box functions where the number of evaluations is severely limited. However, in many real-world applications, it is hard or impossible to know in advance which designs are feasible due to some physical or system limitations. These issues lead to an even more challenging problem of optimizing an unknown function with unknown constraints. In this paper, we observe that in such scenarios optimal solution typically lies on the boundary between feasible and infeasible regions of the design space, making it considerably more difficult than that with interior optima. Inspired by this observation, we propose BE-CBO, a new Bayesian optimization method that efficiently explores the boundary between feasible and infeasible designs. To identify the boundary, we learn the constraints with an ensemble of neural networks that outperform the standard Gaussian Processes for capturing complex boundaries. Our method demonstrates superior performance against state-of-the-art methods through comprehensive experiments on synthetic and real-world benchmarks. Code available at: https://github.com/yunshengtian/BE-CBO, Comment: Accepted at International Conference on Machine Learning (ICML) 2024

In this paper, we consider the well-posedness of stochastic S-KdV driven by multiplicative noises in $H_x^1\times H_x^1$. To get the local well-posedness, we first develop the bilinear and trilinear Bourgain norm estimates of the nonlinear terms with $b\in\left(0,1/2\right)$. Then, to overcome the lack of the maximum functional estimate, we introduce a series of approximation equations with localized nonlinear terms, which are also cutted-off in both the physical and the Fourier space. By limitations, these approximation equations will help us get a priori estimate in the Bourgain space and finish the proof of the global well-posedness of the initial system., Comment: 41 pages

Multiview clustering (MVC) segregates data samples into meaningful clusters by synthesizing information across multiple views. Moreover, deep learning-based methods have demonstrated their strong feature learning capabilities in MVC scenarios. However, effectively generalizing feature representations while maintaining consistency is still an intractable problem. In addition, most existing deep clustering methods based on contrastive learning overlook the consistency of the clustering representations during the clustering process. In this paper, we show how the above problems can be overcome and propose a consistent enhancement-based deep MVC method via contrastive learning (CCEC). Specifically, semantic connection blocks are incorporated into a feature representation to preserve the consistent information among multiple views. Furthermore, the representation process for clustering is enhanced through spectral clustering, and the consistency across multiple views is improved. Experiments conducted on five datasets demonstrate the effectiveness and superiority of our method in comparison with the state-of-the-art (SOTA) methods. The code for this method can be accessed at https://anonymous.4open.science/r/CCEC-E84E/., Comment: There are multiple errors that need to be corrected, including some formulas and concept descriptions. We will re upload the paper after the modifications are completed

We treat disordered Heisenberg model in 1D as the "standard model" of many-body localization (MBL). Two independent order parameters stemming purely from the half-chain von Neumann entanglement entropy $S_{\textrm{vN}}$ are introduced to probe its eigenstate transition. From symmetry-endowed entropy decomposition, they are probability distribution deviation $|d(p_n)|$ and von Neumann entropy $S_{\textrm{vN}}^{n}(D_n\!=\!\mbox{max})$ of the maximum-dimensional symmetry subdivision. Finite-size analyses reveal that $\{p_n\}$ drives the localization transition, preceded by a thermalization breakdown transition governed by $\{S_{\textrm{vN}}^{n}\}$. For noninteracting case, these transitions coincide, but in interacting situation they separate. Such separability creates an intermediate phase region and may help discriminate between the Anderson and MBL transitions. An obstacle whose solution eludes community to date is the violation of Harris criterion in nearly all numeric investigations of MBL so far. Upon elucidating the mutually independent components in $S_{\textrm{vN}}$, it is clear that previous studies of eigenspectra, $S_{\textrm{vN}}$, and the like lack resolution to pinpoint (thus completely overlook) the crucial internal structures of the transition. We show, for the first time, that after this necessary decoupling, the universal critical exponents for both transitions of $|d(p_n)|$ and $S_{\textrm{vN}}^{n}(D_n\!=\!\mbox{max})$ fulfill the Harris criterion: $\nu\approx2.0\ (\nu\approx1.5)$ for quench (quasirandom) disorder. Our work puts forth "symmetry combined with entanglement" as the missing organization principle for the generic eigenstate matter and transition.

Neutron star (NS) binaries can be potentially intriguing gravitational wave (GW) sources, with both high- and low-frequency radiations from the possibly aspherical individual stars and the binary orbit, respectively. The successful detection of such a dual-line source could provide fresh insights into binary geometry and NS physics. In the absence of electromagnetic observations, we develop a strategy for inferring the spin-orbit misalignment angle using the tight dual-line double NS system under the spin-orbit coupling. Based on the four-year joint detection of a typical dual-line system with LISA and Cosmic Explorer, we find that the misalignment angle and the NS moment of inertia can be measured with sub-percentage and 5% accuracy, respectively., Comment: 8 pages, 3 figures. Accepted by PRD

Current language models tailored for code tasks often adopt the pre-training-then-fine-tuning paradigm from natural language processing, modeling source code as plain text. This approach, however, overlooks the unambiguous structures inherent in programming languages. In this work, we explore data-efficient adaptation of pre-trained code models by further pre-training and fine-tuning them with program structures. Specifically, we represent programs as parse trees -- also known as concrete syntax trees (CSTs) -- and adapt pre-trained models on serialized CSTs. Although the models that we adapt have been pre-trained only on the surface form of programs, we find that a small amount of continual pre-training and fine-tuning on CSTs without changing the model architecture yields improvements over the baseline approach across various code tasks. The improvements are found to be particularly significant when there are limited training examples, demonstrating the effectiveness of integrating program structures with plain-text representation even when working with backbone models that have not been pre-trained with structures.

In recent years, drones have found increased applications in a wide array of real-world tasks. Model predictive control (MPC) has emerged as a practical method for drone flight control, owing to its robustness against modeling errors/uncertainties and external disturbances. However, MPC's sensitivity to manually tuned parameters can lead to rapid performance degradation when faced with unknown environmental dynamics. This paper addresses the challenge of controlling a drone as it traverses a swinging gate characterized by unknown dynamics. This paper introduces a parameterized MPC approach named hyMPC that leverages high-level decision variables to adapt to uncertain environmental conditions. To derive these decision variables, a novel policy search framework aimed at training a high-level Gaussian policy is presented. Subsequently, we harness the power of neural network policies, trained on data gathered through the repeated execution of the Gaussian policy, to provide real-time decision variables. The effectiveness of hyMPC is validated through numerical simulations, achieving a 100\% success rate in 20 drone flight tests traversing a swinging gate, demonstrating its capability to achieve safe and precise flight with limited prior knowledge of environmental dynamics., Comment: To be published in Unmanned Systems

In the era of large language models (LLMs), hallucination (i.e., the tendency to generate factually incorrect content) poses great challenge to trustworthy and reliable deployment of LLMs in real-world applications. To tackle the LLM hallucination, three key questions should be well studied: how to detect hallucinations (detection), why do LLMs hallucinate (source), and what can be done to mitigate them (mitigation). To address these challenges, this work presents a systematic empirical study on LLM hallucination, focused on the the three aspects of hallucination detection, source and mitigation. Specially, we construct a new hallucination benchmark HaluEval 2.0, and designs a simple yet effective detection method for LLM hallucination. Furthermore, we zoom into the different training or utilization stages of LLMs and extensively analyze the potential factors that lead to the LLM hallucination. Finally, we implement and examine a series of widely used techniques to mitigate the hallucinations in LLMs. Our work has led to several important findings to understand the hallucination origin and mitigate the hallucinations in LLMs. Our code and data can be accessed at https://github.com/RUCAIBox/HaluEval-2.0., Comment: 24 pages, 8 figures, 13 tables