The focus of this paper is to develop a methodology that enables an unmanned surface vehicle (USV) to efficiently track a planned path. The introduction of a vector field-based adaptive line-of-sight guidance law (VFALOS) for accurate trajectory tracking and minimizing the overshoot response time during USV tracking of curved paths improves the overall line-of-sight (LOS) guidance method. These improvements contribute to faster convergence to the desired path, reduce oscillations, and can mitigate the effects of persistent external disturbances. It is shown that the proposed guidance law exhibits k-exponential stability when converging to the desired path consisting of straight and curved lines. The results in the paper show that the proposed method effectively improves the accuracy of the USV tracking the desired path while ensuring the safety of the USV work.
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We present the learned harmonic mean estimator with normalizing flows - a robust, scalable and flexible estimator of the Bayesian evidence for model comparison. Since the estimator is agnostic to sampling strategy and simply requires posterior samples, it can be applied to compute the evidence using any Markov chain Monte Carlo (MCMC) sampling technique, including saved down MCMC chains, or any variational inference approach. The learned harmonic mean estimator was recently introduced, where machine learning techniques were developed to learn a suitable internal importance sampling target distribution to solve the issue of exploding variance of the original harmonic mean estimator. In this article we present the use of normalizing flows as the internal machine learning technique within the learned harmonic mean estimator. Normalizing flows can be elegantly coupled with the learned harmonic mean to provide an approach that is more robust, flexible and scalable than the machine learning models considered previously. We perform a series of numerical experiments, applying our method to benchmark problems and to a cosmological example in up to 21 dimensions. We find the learned harmonic mean estimator is in agreement with ground truth values and nested sampling estimates. The open-source harmonic Python package implementing the learned harmonic mean, now with normalizing flows included, is publicly available.
This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the parametric regularity of multivariate double integration problems over high-dimensional parameter and data domains arising in Bayesian optimal design problems. We provide a detailed analysis for these double integration problems using two approaches: a full tensor product and a sparse tensor product combination of quasi-Monte Carlo (QMC) cubature rules over the parameter and data domains. Specifically, we show that the latter approach significantly improves the convergence rate, exhibiting performance comparable to that of QMC integration of a single high-dimensional integral. Furthermore, we numerically verify the predicted convergence rates for an elliptic PDE problem with an unknown diffusion coefficient in two spatial dimensions, offering empirical evidence supporting the theoretical results and highlighting practical applicability.
This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the algorithm design process for a class of PDEs through training, which requires only training data of coefficient distributions. The proposed method is anchored by three core principles: (1) a multilevel hierarchy to promote rapid convergence, (2) adherence to linearity concerning the right-hand-side of equations, and (3) weights sharing across different levels to facilitate adaptability to various problem sizes. Built on these foundational principles and considering the similar computation pattern of the convolutional neural network (CNN) as multigrid components, we introduce a network adept at solving linear systems from PDEs with heterogeneous coefficients, discretized on structured grids. Notably, our proposed solver possesses the ability to generalize over right-hand-side terms, PDE coefficients, and grid sizes, thereby ensuring its training is purely offline. To evaluate its effectiveness, we train the solver on convection-diffusion equations featuring heterogeneous diffusion coefficients. The solver exhibits swift convergence to high accuracy over a range of grid sizes, extending from $31 \times 31$ to $4095 \times 4095$. Remarkably, our method outperforms the classical Geometric Multigrid (GMG) solver, demonstrating a speedup of approximately 3 to 8 times. Furthermore, our numerical investigation into the solver's capacity to generalize to untrained coefficient distributions reveals promising outcomes.
Channels with noisy duplications have recently been used to model the nanopore sequencer. This paper extends some foundational information-theoretic results to this new scenario. We prove the asymptotic equipartition property (AEP) for noisy duplication processes based on ergodic Markov processes. A consequence is that the noisy duplication channel is information stable for ergodic Markov sources, and therefore the channel capacity constrained to Markov sources is the Markov-constrained Shannon capacity. We use the AEP to estimate lower bounds on the capacity of the binary symmetric channel with Bernoulli and geometric duplications using Monte Carlo simulations. In addition, we relate the AEP for noisy duplication processes to the AEP for hidden semi-Markov processes.
Digital watermarking is the process of embedding secret information by altering images in a way that is undetectable to the human eye. To increase the robustness of the model, many deep learning-based watermarking methods use the encoder-decoder architecture by adding different noises to the noise layer. The decoder then extracts the watermarked information from the distorted image. However, this method can only resist weak noise attacks. To improve the robustness of the algorithm against stronger noise, this paper proposes to introduce a denoise module between the noise layer and the decoder. The module is aimed at reducing noise and recovering some of the information lost during an attack. Additionally, the paper introduces the SE module to fuse the watermarking information pixel-wise and channel dimensions-wise, improving the encoder's efficiency. Experimental results show that our proposed method is comparable to existing models and outperforms state-of-the-art under different noise intensities. In addition, ablation experiments show the superiority of our proposed module.
In this paper, we introduce the design of HackCar, a testing platform for replicating attacks and defenses on a generic automotive system without requiring access to a complete vehicle. This platform empowers security researchers to illustrate the consequences of attacks targeting an automotive system on a realistic platform, facilitating the development and testing of security countermeasures against both existing and novel attacks. The HackCar platform is built upon an F1-10th model, to which various automotive-grade microcontrollers are connected through automotive communication protocols. This solution is crafted to be entirely modular, allowing for the creation of diverse test scenarios. Researchers and practitioners can thus develop innovative security solutions while adhering to the constraints of automotive-grade microcontrollers. We showcase our design by comparing it with a real, licensed, and unmodified vehicle. Additionally, we analyze the behavior of the HackCar in both an attack-free scenario and a scenario where an attack on in-vehicle communication is deployed.
A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High order local maximum entropy approximants are used for metamodelling, which take advantage of boundary-corrected kernel density estimation to increase accuracy and robustness on highly clumped datasets, as well as conferring the resulting metamodel with some robustness against data noise in the common case of unreplicated experiments. Two-dimensional test cases are analyzed against full factorial and latin hypercube designs and compare favourably. The proposed method is then applied in a unique manner to the problem of adaptive spatial resolution in time-varying non-linear functions, opening up the possibility to adapt the method to solve partial differential equations.
Interests in the value of digital technologies for its potential uses to increase supply chain resilience (SCRes) are increasing in light to the industry 4.0 and the global pandemic. Utilization of Recommender systems (RS) as a supply chain (SC) resilience measure is neglected although RS is a capable tool to enhance SC resilience from a reactive aspect. To address this problem, this research proposed a novel data-driven supply chain disruption response framework based on the intelligent recommender system techniques and validated the conceptual model through a practical use case. Results show that our framework can be implemented as an effective SC disruption mitigation measure in the very first response phrase and help SC participants get better reaction performance after the SC disruption.
Some hyperbolic systems are known to include implicit preservation of differential constraints: these are for example the time conservation of the curl or the divergence of a vector that appear as an implicit constraint. In this article, we show that this kind of constraint can be easily conserved at the discrete level with the classical discontinuous Galerkin method, provided the right approximation space is used for the vectorial space, and under some mild assumption on the numerical flux. For this, we develop a discrete differential geometry framework for some well chosen piece-wise polynomial vector approximation space. More precisely, we define the discrete Hodge star operator, the exterior derivative, and their adjoints. The discrete adjoint divergence and curl are proven to be exactly preserved by the discontinuous Galerkin method under a small assumption on the numerical flux. Numerical tests are performed on the wave system, the two dimensional Maxwell system and the induction equation, and confirm that the differential constraints are preserved at machine precision while keeping the high order of accuracy.
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The algorithm is derived by combining a proximal method of multipliers (PMM) with a standard semismooth Newton method (SSN), and is shown to be globally convergent under minimal assumptions. Further local linear (and potentially superlinear) convergence is shown under standard additional conditions. The major computational bottleneck of the proposed approach arises from the solution of the associated SSN linear systems. These are solved using a Krylov-subspace method, accelerated by certain novel general-purpose preconditioners which are shown to be optimal with respect to the proximal penalty parameters. The preconditioners are easy to store and invert, since they exploit the structure of the nonsmooth terms appearing in the problem's objective to significantly reduce their memory requirements. We showcase the efficiency, robustness, and scalability of the proposed solver on a variety of problems arising in risk-averse portfolio selection, $L^1$-regularized partial differential equation constrained optimization, quantile regression, and binary classification via linear support vector machines. We provide computational evidence, on real-world datasets, to demonstrate the ability of the solver to efficiently and competitively handle a diverse set of medium- and large-scale optimization instances.
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