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Semi-Lagrangian (SL) schemes are highly efficient for simulating transport equations and are widely used across various applications. Despite their success, designing genuinely multi-dimensional and conservative SL schemes remains a significant challenge. Building on our previous work [Chen et al., J. Comput. Phys., V490 112329, (2023)], we introduce a conservative machine-learning-based SL finite difference (FD) method that allows for extra-large time step evolution. At the core of our approach is a novel dynamical graph neural network designed to handle the complexities associated with tracking accurately upstream points along characteristics. This proposed neural transport solver learns the conservative SL FD discretization directly from data, improving accuracy and efficiency compared to traditional numerical schemes, while significantly simplifying algorithm implementation. We validate the method' s effectiveness and efficiency through numerical tests on benchmark transport equations in both one and two dimensions, as well as the nonlinear Vlasov-Poisson system.

This paper focuses on the distributed online convex optimization problem with time-varying inequality constraints over a network of agents, where each agent collaborates with its neighboring agents to minimize the cumulative network-wide loss over time. To reduce communication overhead between the agents, we propose a distributed event-triggered online primal-dual algorithm over a time-varying directed graph. With several classes of appropriately chose decreasing parameter sequences and non-increasing event-triggered threshold sequences, we establish dynamic network regret and network cumulative constraint violation bounds. Finally, a numerical simulation example is provided to verify the theoretical results.

We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where no structural assumption is made on the system matrix $A^* \in \mathbb{R}^{n \times n}$, and have consequently analyzed the ordinary least squares (OLS) estimator in detail. We assume prior structural information on $A^*$ is available, which can be captured in the form of a convex set $\mathcal{K}$ containing $A^*$. For the solution of the ensuing constrained least squares estimator, we derive non-asymptotic error bounds in the Frobenius norm that depend on the local size of $\mathcal{K}$ at $A^*$. To illustrate the usefulness of these results, we instantiate them for four examples, namely when (i) $A^*$ is sparse and $\mathcal{K}$ is a suitably scaled $\ell_1$ ball; (ii) $\mathcal{K}$ is a subspace; (iii) $\mathcal{K}$ consists of matrices each of which is formed by sampling a bivariate convex function on a uniform $n \times n$ grid (convex regression); (iv) $\mathcal{K}$ consists of matrices each row of which is formed by uniform sampling (with step size $1/T$) of a univariate Lipschitz function. In all these situations, we show that $A^*$ can be reliably estimated for values of $T$ much smaller than what is needed for the unconstrained setting.

The goal of multi-objective optimisation is to identify a collection of points which describe the best possible trade-offs between the multiple objectives. In order to solve this vector-valued optimisation problem, practitioners often appeal to the use of scalarisation functions in order to transform the multi-objective problem into a collection of single-objective problems. This set of scalarised problems can then be solved using traditional single-objective optimisation techniques. In this work, we formalise this convention into a general mathematical framework. We show how this strategy effectively recasts the original multi-objective optimisation problem into a single-objective optimisation problem defined over sets. An appropriate class of objective functions for this new problem are the R2 utilities, which are utility functions that are defined as a weighted integral over the scalarised optimisation problems. As part of our work, we show that these utilities are monotone and submodular set functions which can be optimised effectively using greedy optimisation algorithms. We then analyse the performance of these greedy algorithms both theoretically and empirically. Our analysis largely focusses on Bayesian optimisation, which is a popular probabilistic framework for black-box optimisation.

Capturing the extremal behaviour of data often requires bespoke marginal and dependence models which are grounded in rigorous asymptotic theory, and hence provide reliable extrapolation into the upper tails of the data-generating distribution. We present a toolbox of four methodological frameworks, motivated by modern extreme value theory, that can be used to accurately estimate extreme exceedance probabilities or the corresponding level in either a univariate or multivariate setting. Our frameworks were used to facilitate the winning contribution of Team Yalla to the EVA (2023) Conference Data Challenge, which was organised for the 13$^\text{th}$ International Conference on Extreme Value Analysis. This competition comprised seven teams competing across four separate sub-challenges, with each requiring the modelling of data simulated from known, yet highly complex, statistical distributions, and extrapolation far beyond the range of the available samples in order to predict probabilities of extreme events. Data were constructed to be representative of real environmental data, sampled from the fantasy country of "Utopia"

Biological nervous systems constitute important sources of inspiration towards computers that are faster, cheaper, and more energy efficient. Neuromorphic disciplines view the brain as a coevolved system, simultaneously optimizing the hardware and the algorithms running on it. There are clear efficiency gains when bringing the computations into a physical substrate, but we presently lack theories to guide efficient implementations. Here, we present a principled computational model for neuromorphic systems in terms of spatio-temporal receptive fields, based on affine Gaussian kernels over space and leaky-integrator and leaky integrate-and-fire models over time. Our theory is provably covariant to spatial affine and temporal scaling transformations, and with close similarities to the visual processing in mammalian brains. We use these spatio-temporal receptive fields as a prior in an event-based vision task, and show that this improves the training of spiking networks, which otherwise is known as problematic for event-based vision. This work combines efforts within scale-space theory and computational neuroscience to identify theoretically well-founded ways to process spatio-temporal signals in neuromorphic systems. Our contributions are immediately relevant for signal processing and event-based vision, and can be extended to other processing tasks over space and time, such as memory and control.

The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.

While deep learning strategies achieve outstanding results in computer vision tasks, one issue remains. The current strategies rely heavily on a huge amount of labeled data. In many real-world problems it is not feasible to create such an amount of labeled training data. Therefore, researchers try to incorporate unlabeled data into the training process to reach equal results with fewer labels. Due to a lot of concurrent research, it is difficult to keep track of recent developments. In this survey we provide an overview of often used techniques and methods in image classification with fewer labels. We compare 21 methods. In our analysis we identify three major trends. 1. State-of-the-art methods are scaleable to real world applications based on their accuracy. 2. The degree of supervision which is needed to achieve comparable results to the usage of all labels is decreasing. 3. All methods share common techniques while only few methods combine these techniques to achieve better performance. Based on all of these three trends we discover future research opportunities.