An Efficient Localized Meshless Method Based on the Space–Time Gaussian RBF for High-Dimensional Space Fractional Wave and Damped Equations

In this paper, an efficient localized meshless method based on the space–time Gaussian radial basis functions is discussed. We aim to deal with the left Riemann–Liouville space fractional derivative wave and damped wave equation in high-dimensional space. These significant problems as anomalous models could arise in several research fields of science, engineering, and technology. Since an explicit solution to such equations often does not exist, the numerical approach to solve this problem is fascinating. We propose a novel scheme using the space–time radial basis function with advantages in time discretization. Moreover this approach produces the (n + 1)-dimensional spatial-temporal computational domain for n-dimensional problems. Therefore the local feature, as a remarkable and efficient property, leads to a sparse coefficient matrix, which could reduce the computational costs in high-dimensional problems. Some benchmark problems for wave models, both wave and damped, have been considered, highlighting the proposed method performances in terms of accuracy, efficiency, and speed-up. The obtained experimental results show the computational capabilities and advantages of the presented algorithm.

Reduced-Order Modeling for Multiphase Flow Using a Physics-Based Deep Learning

Reservoir simulation is the most widely used tool for oil and gas production forecasting and reservoir management. Solving a large-scale system of nonlinear differential equations every timestep can be computationally expensive. In this work, we present a two-phase physics-constrained deep-learning reduced-order model as a surrogate model for subsurface flow production forecast. The implemented deep learning model is a physics-guided encoder-decoder, constructed based on the Embed-to-Control (E2C) framework. In our implementation, the E2C works in a way analogous to Proper Orthogonal Decomposition combined with Discrete Empirical Interpolation Method (POD-DEIM) or Trajectory Piece-Wise Linearization approach (POD-TPWL). The E2C-Reduced-order model (ROM) involves projecting the system from a high-dimensional space into a low-dimensional subspace using the encoder-decoder, approximating the progression of the system from one timestep to the next using a linear transition model, and finally projecting the system back to high-dimensional space using the encoder-decoder. To guarantee mass conservation, we adopt the Finite Elements Mixed Formulation in the neural network's loss function combined with the original data-based loss function. Training simulations are generated using a full-physics reservoir simulator (IPARS). High-fidelity pressure, velocity, and saturation solution snapshot at constant time intervals are taken as training input to the neural network. After training, the model is tested over large variations of well control settings. Accurate pressure and saturation solutions are predicted along with the injection and production well quantities using the proposed approach. Errors in the predicted quantities of interest are reduced with the increase in the number of training simulations used. Although it required a large number of training simulations for the offline (training) step, the model achieved a significant speedup in the online stage compared to the full physics model. Considering the overall computational cost, this ROM model is proper for cases when a large number of simulations are required like in the case of production optimization and uncertainty assessments. The proposed approach shows the capability of the deep-learning reduced-order model to accurately predict multiphase flow behavior such as well quantities, and global pressure and saturation fields. The model honors mass conservation and the underlying physics laws, which many existing approaches don't take into direct consideration.

On Carr’s Eleven-Dimensional Dramaturgy

Contemporary Irish playwright Marina Carr integrates eleven-dimension theory into her post dramatic art creation, forming a unique eleven-dimensional dramaturgy. This unique eleven-dimensional dramaturgy runs through Carr's whole drama creation career, and has different focuses in different periods: in her early drama, Carr concentrated on the expression of the concept of “non-linear time”. In the mid-land drama, she focuses on the creation of “high dimensional space”, while in the later drama of death and fantasy, she focuses on the presentation of “multidimensional worlds”. Finally, with the connection of the eleven-dimensional dramaturgy, Carr created a “non-linear”, “high dimensional” and “multi-dimensional” dynamic post-dramatic theater, and conveyed the eleven-dimensional philosophy of life beyond time and space.

Difference Curvature Multidimensional Network for Hyperspectral Image Super-Resolution

In recent years, convolutional-neural-network-based methods have been introduced to the field of hyperspectral image super-resolution following their great success in the field of RGB image super-resolution. However, hyperspectral images appear different from RGB images in that they have high dimensionality, implying a redundancy in the high-dimensional space. Existing approaches struggle in learning the spectral correlation and spatial priors, leading to inferior performance. In this paper, we present a difference curvature multidimensional network for hyperspectral image super-resolution that exploits the spectral correlation to help improve the spatial resolution. Specifically, we introduce a multidimensional enhanced convolution (MEC) unit into the network to learn the spectral correlation through a self-attention mechanism. Meanwhile, it reduces the redundancy in the spectral dimension via a bottleneck projection to condense useful spectral features and reduce computations. To remove the unrelated information in high-dimensional space and extract the delicate texture features of a hyperspectral image, we design an additional difference curvature branch (DCB), which works as an edge indicator to fully preserve the texture information and eliminate the unwanted noise. Experiments on three publicly available datasets demonstrate that the proposed method can recover sharper images with minimal spectral distortion compared to state-of-the-art methods. PSNR/SAM is 0.3–0.5 dB/0.2–0.4 better than the second best methods.

Semantics in High-Dimensional Space

Geometric models are used for modelling meaning in various semantic-space models. They are seductive in their simplicity and their imaginative qualities, and for that reason, their metaphorical power risks leading our intuitions astray: human intuition works well in a three-dimensional world but is overwhelmed by higher dimensionalities. This note is intended to warn about some practical pitfalls of using high-dimensional geometric representation as a knowledge representation and a memory model—challenges that can be met by informed design of the representation and its application.