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 present a novel framework for the development of fourth-order lattice Boltzmann schemes to tackle multidimensional nonlinear systems of conservation laws. Our numerical schemes preserve two fundamental characteristics inherent in classical lattice Boltzmann methods: a local relaxation phase and a transport phase composed of elementary shifts on a Cartesian grid. Achieving fourth-order accuracy is accomplished through the composition of second-order time-symmetric basic schemes utilizing rational weights. This enables the representation of the transport phase in terms of elementary shifts. Introducing local variations in the relaxation parameter during each stage of relaxation ensures the entropic nature of the schemes. This not only enhances stability in the long-time limit but also maintains fourth-order accuracy. To validate our approach, we conduct comprehensive testing on scalar equations and systems in both one and two spatial dimensions.

The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric variables of solutions. For the corresponding spatial approximations, an independently refined finite element mesh is used for each polynomial coefficient. The method relies on multilevel expansions of input random fields and achieves error reduction with uniform rate. In particular, the saturation property for the refinement process is ensured by the algorithm. The results are illustrated by numerical experiments, including cases with random fields of low regularity.

We propose a material design method via gradient-based optimization on compositions, overcoming the limitations of traditional methods: exhaustive database searches and conditional generation models. It optimizes inputs via backpropagation, aligning the model's output closely with the target property and facilitating the discovery of unlisted materials and precise property determination. Our method is also capable of adaptive optimization under new conditions without retraining. Applying to exploring high-Tc superconductors, we identified potential compositions beyond existing databases and discovered new hydrogen superconductors via conditional optimization. This method is versatile and significantly advances material design by enabling efficient, extensive searches and adaptability to new constraints.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

Regent is an implicitly parallel programming language that allows the development of a single codebase for heterogeneous platforms targeting CPUs and GPUs. This paper presents the development of a parallel meshfree solver in Regent for two-dimensional inviscid compressible flows. The meshfree solver is based on the least squares kinetic upwind method. Example codes are presented to show the difference between the Regent and CUDA-C implementations of the meshfree solver on a GPU node. For CPU parallel computations, details are presented on how the data communication and synchronisation are handled by Regent and Fortran+MPI codes. The Regent solver is verified by applying it to the standard test cases for inviscid flows. Benchmark simulations are performed on coarse to very fine point distributions to assess the solver's performance. The computational efficiency of the Regent solver on an A100 GPU is compared with an equivalent meshfree solver written in CUDA-C. The codes are then profiled to investigate the differences in their performance. The performance of the Regent solver on CPU cores is compared with an equivalent explicitly parallel Fortran meshfree solver based on MPI. Scalability results are shown to offer insights into performance.

In sound event detection (SED), convolution neural networks (CNNs) are widely used to extract time-frequency patterns from the input spectrogram. However, features extracted by CNN can be insensitive to the shift of time-frequency patterns along the frequency axis. To address this issue, frequency dynamic convolution (FDY) has been proposed, which applies different kernels to different frequency components. Compared to the vannila CNN, FDY requires several times more parameters. In this paper, a more efficient solution named frequency-aware convolution (FAC) is proposed. In FAC, frequency-positional information is encoded in a vector and added to the input spectrogram. To match the amplitude of input, the encoding vector is scaled adaptively and channel-independently. Experiments are carried out in the context of DCASE 2022 task 4, and the results demonstrate that FAC can achieve comparable performance to that of FDY with only 515 additional parameters, while FDY requires 8.02 million additional parameters. The ablation study shows that scaling the encoding vector adaptively and channel-independently is critical to the performance of FAC.

Image codecs are typically optimized to trade-off bitrate \vs distortion metrics. At low bitrates, this leads to compression artefacts which are easily perceptible, even when training with perceptual or adversarial losses. To improve image quality and remove dependency on the bitrate, we propose to decode with iterative diffusion models. We condition the decoding process on a vector-quantized image representation, as well as a global image description to provide additional context. We dub our model PerCo for 'perceptual compression', and compare it to state-of-the-art codecs at rates from 0.1 down to 0.003 bits per pixel. The latter rate is more than an order of magnitude smaller than those considered in most prior work, compressing a 512x768 Kodak image with less than 153 bytes. Despite this ultra-low bitrate, our approach maintains the ability to reconstruct realistic images. We find that our model leads to reconstructions with state-of-the-art visual quality as measured by FID and KID. As predicted by rate-distortion-perception theory, visual quality is less dependent on the bitrate than previous methods.

To date, most methods for simulating conditioned diffusions are limited to the Euclidean setting. The conditioned process can be constructed using a change of measure known as Doob's $h$-transform. The specific type of conditioning depends on a function $h$ which is typically unknown in closed form. To resolve this, we extend the notion of guided processes to a manifold $M$, where one replaces $h$ by a function based on the heat kernel on $M$. We consider the case of a Brownian motion with drift, constructed using the frame bundle of $M$, conditioned to hit a point $x_T$ at time $T$. We prove equivalence of the laws of the conditioned process and the guided process with a tractable Radon-Nikodym derivative. Subsequently, we show how one can obtain guided processes on any manifold $N$ that is diffeomorphic to $M$ without assuming knowledge of the heat kernel on $N$. We illustrate our results with numerical simulations and an example of parameter estimation where a diffusion process on the torus is observed discretely in time.

The direct parametrisation method for invariant manifold is a model-order reduction technique that can be applied to nonlinear systems described by PDEs and discretised e.g. with a finite element procedure in order to derive efficient reduced-order models (ROMs). In nonlinear vibrations, it has already been applied to autonomous and non-autonomous problems to propose ROMs that can compute backbone and frequency-response curves of structures with geometric nonlinearity. While previous developments used a first-order expansion to cope with the non-autonomous term, this assumption is here relaxed by proposing a different treatment. The key idea is to enlarge the dimension of the parametrising coordinates with additional entries related to the forcing. A new algorithm is derived with this starting assumption and, as a key consequence, the resonance relationships appearing through the homological equations involve multiple occurrences of the forcing frequency, showing that with this new development, ROMs for systems exhibiting a superharmonic resonance, can be derived. The method is implemented and validated on academic test cases involving beams and arches. It is numerically demonstrated that the method generates efficient ROMs for problems involving 3:1 and 2:1 superharmonic resonances, as well as converged results for systems where the first-order truncation on the non-autonomous term showed a clear limitation.

We compute the minimum distance of the parameterized code of order 1 over an even cycle.