亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

We consider the scalar anisotropic wave equation. Recently a convergence analysis for radial perfectly matched layers (PML) in the frequency domain was reported and in the present article we continue this approach into the time domain. First we explain why there is a good hope that radial complex scalings can overcome the instabilities of PML methods caused by anisotropic materials. Next we discuss some sensitive details, which seem like a paradox at the first glance: if the absorbing layer and the inhomogeneities are sufficiently separated, then the solution is indeed stable. However, for more general data the problem becomes unstable. In numerical computations we observe instabilities regardless of the position of the inhomogeneities, although the instabilities arise only for fine enough discretizations. As a remedy we propose a complex frequency shifted scaling and discretizations by Hardy space infinite elements or truncation-free PMLs. We show numerical experiments which confirm the stability and convergence of these methods.

Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some problems, this simulation is infeasible, leading to the discretization of state variable space and the need to train one neural network for each data point. This approach becomes computationally inefficient when dealing with large state variable spaces. In this paper, we consider a class of this type of stochastic optimal control problems and introduce an effective solution employing multitask neural networks. To train our multitask neural network, we introduce a novel scheme that dynamically balances the learning across tasks. Through numerical experiments on real-world derivatives pricing problems, we prove that our method outperforms state-of-the-art approaches.

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural networks, PINNs are trained as surrogate models to approximate solutions without the need for label data. Nevertheless, even though PINNs have shown remarkable performance, they can face difficulties, especially when dealing with equations featuring rapidly changing solutions. These difficulties encompass slow convergence, susceptibility to becoming trapped in local minima, and reduced solution accuracy. To address these issues, we propose a binary structured physics-informed neural network (BsPINN) framework, which employs binary structured neural network (BsNN) as the neural network component. By leveraging a binary structure that reduces inter-neuron connections compared to fully connected neural networks, BsPINNs excel in capturing the local features of solutions more effectively and efficiently. These features are particularly crucial for learning the rapidly changing in the nature of solutions. In a series of numerical experiments solving Burgers equation, Euler equation, Helmholtz equation, and high-dimension Poisson equation, BsPINNs exhibit superior convergence speed and heightened accuracy compared to PINNs. From these experiments, we discover that BsPINNs resolve the issues caused by increased hidden layers in PINNs resulting in over-smoothing, and prevent the decline in accuracy due to non-smoothness of PDEs solutions.

When extreme weather events affect large areas, their regional to sub-continental spatial scale is important for their impacts. We propose a novel methodology that combines spatial extreme-value theory with a machine learning (ML) algorithm to model weather extremes and quantify probabilities associated with the occurrence, intensity and spatial extent of these events. The model is here applied to Western European summertime heat extremes. Using new loss functions adapted to extreme values, we fit a theoretically-motivated spatial model to extreme positive temperature anomaly fields from 1959-2022, using the daily 500-hpa geopotential height fields across the Euro-Atlantic region and the local soil moisture as predictors. Our generative model reveals the importance of individual circulation features in determining different facets of heat extremes, thereby enriching our process understanding of them from a data-driven perspective. The occurrence, intensity, and spatial extent of heat extremes are sensitive to the relative position of individual ridges and troughs that are part of a large-scale wave pattern. Heat extremes in Europe are thus the result of a complex interplay between local and remote physical processes. Our approach is able to extrapolate beyond the range of the data to make risk-related probabilistic statements, and applies more generally to other weather extremes. It also offers an attractive alternative to physical model-based techniques, or to ML approaches that optimise scores focusing on predicting well the bulk instead of the tail of the data distribution.

Optimization under uncertainty is important in many applications, particularly to inform policy and decision making in areas such as public health. A key source of uncertainty arises from the incorporation of environmental variables as inputs into computational models or simulators. Such variables represent uncontrollable features of the optimization problem and reliable decision making must account for the uncertainty they propagate to the simulator outputs. Often, multiple, competing objectives are defined from these outputs such that the final optimal decision is a compromise between different goals. Here, we present emulation-based optimization methodology for such problems that extends expected quantile improvement (EQI) to address multi-objective optimization. Focusing on the practically important case of two objectives, we use a sequential design strategy to identify the Pareto front of optimal solutions. Uncertainty from the environmental variables is integrated out using Monte Carlo samples from the simulator. Interrogation of the expected output from the simulator is facilitated by use of (Gaussian process) emulators. The methodology is demonstrated on an optimization problem from public health involving the dispersion of anthrax spores across a spatial terrain. Environmental variables include meteorological features that impact the dispersion, and the methodology identifies the Pareto front even when there is considerable input uncertainty.

We consider Maxwell eigenvalue problems on uncertain shapes with perfectly conducting TESLA cavities being the driving example. Due to the shape uncertainty, the resulting eigenvalues and eigenmodes are also uncertain and it is well known that the eigenvalues may exhibit crossings or bifurcations under perturbation. We discuss how the shape uncertainties can be modelled using the domain mapping approach and how the deformation mapping can be expressed as coefficients in Maxwell's equations. Using derivatives of these coefficients and derivatives of the eigenpairs, we follow a perturbation approach to compute approximations of mean and covariance of the eigenpairs. For small perturbations, these approximations are faster and more accurate than Monte Carlo or similar sampling-based strategies. Numerical experiments for a three-dimensional 9-cell TESLA cavity are presented.

We study the complexity (that is, the weight of the multiplication table) of the elliptic normal bases introduced by Couveignes and Lercier. We give an upper bound on the complexity of these elliptic normal bases, and we analyze the weight of some special vectors related to the multiplication table of those bases. This analysis leads us to some perspectives on the search for low complexity normal bases from elliptic periods.

During multiple testing, researchers often adjust their alpha level to control the familywise error rate for a statistical inference about a joint union alternative hypothesis (e.g., "H1 or H2"). However, in some cases, they do not make this inference and instead make separate inferences about each of the individual hypotheses that comprise the joint hypothesis (e.g., H1 and H2). For example, a researcher might use a Bonferroni correction to adjust their alpha level from the conventional level of 0.050 to 0.025 when testing H1 and H2, find a significant result for H1 (p < 0.025) and not for H2 (p > .0.025), and so claim support for H1 and not for H2. However, these separate individual inferences do not require an alpha adjustment. Only a statistical inference about the union alternative hypothesis "H1 or H2" requires an alpha adjustment because it is based on "at least one" significant result among the two tests, and so it depends on the familywise error rate. When a researcher corrects their alpha level during multiple testing but does not make an inference about the union alternative hypothesis, their correction is redundant. In the present article, I discuss this redundant correction problem, including its associated loss of statistical power and its potential causes vis-\`a-vis error rate confusions and the alpha adjustment ritual. I also provide three illustrations of redundant corrections from recent psychology studies. I conclude that redundant corrections represent a symptom of statisticism, and I call for a more nuanced and context-specific approach to multiple testing corrections.

Neural network with quadratic decision functions have been introduced as alternatives to standard neural networks with affine linear one. They are advantageous when the objects to be identified are of compact basic geometries like circles, ellipsis etc. In this paper we investigate the use of such ansatz functions for classification. In particular we test and compare the algorithm on the MNIST dataset for classification of handwritten digits and for classification of subspecies. We also show, that the implementation can be based on the neural network structure in the software Tensorflow and Keras, respectively.