Water Quality Prediction Method Based on OVMD and Spatio-Temporal Dependence

Water quality changes at one monitoring spot are not only related to local historical data but also spatially to the water quality of the adjacent spots. Additionally, the non-linear and non-stationary nature of water quality data has a significant impact on prediction results. To improve the accuracy of water quality prediction models, a comprehensive water quality prediction model has been initially established that takes into account both data complexity and spatio-temporal dependencies. The Optimal Variational Mode Decomposition (OVMD) technology is used to effectively decompose water quality data into several simple and stable time series, highlighting short-term and long-term features and enhancing the model\u27s learning ability. The component sequence and spot adjacency matrix are used as the input of Graph Convolutional Network (GCN) to extract the spatial characteristics of the data, and the spatio-temporal dependencies of water quality data at different spots are obtained by combining GCN into the neurons of Gated Recurrent Unit (GRU). The attention model is added to automatically adjust the importance of each time node to further improve the accuracy of the training model and obtain a multi-step prediction output that more closely aligns with the characteristics of water quality change. The proposed model has been validated with real monitoring data for ammonia nitrogen (NH3-N) and total phosphorus (TP), and the results show that the proposed model is better than ARIMA, GRU and GCN+GRU models in terms of prediction results and it shows obvious advantages in the benchmark comparison experiment, which can provide reliable evidence for water pollution source traceability or early warning

A generalized multi-polaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system

We develop a systematic variational coherent state expansion for the many-body ground state of the spin-boson model, in which a quantum two-level system is coupled to a continuum of harmonic oscillators. Energetic constraints at the heart of this technique are rationalized in terms of polarons (displacements of the bath states in agreement with classical expectations) and antipolarons (counter-displacements due to quantum tunneling effects). We present a comprehensive study of the ground state two-level system population and coherence as a function of tunneling amplitude, dissipation strength, and bias (akin to asymmetry of the double well potential defining the two-state system). The entanglement among the different environmental modes is investigated by looking at spectroscopic signatures of the bipartite entanglement entropy between a given environmental mode and all the other modes. We observe a drastic change in behavior of this entropy for increasing dissipation, indicative of the entangled nature of the environmental states. In addition, the entropy spreads over a large energy range at strong dissipation, a testimony to the wide entanglement window characterizing the underlying Kondo state. Finally, comparisons to accurate numerical renormalization group calculations and to the exact Bethe Ansatz solution of the model demonstrate the rapid convergence of our variationally-optimized multi-polaron expansion, suggesting that it should also be a useful tool for dissipative models of greater complexity, as relevant for numerous systems of interest in quantum physics and chemistry.Comment: 17 pages, 14 figure

Finite element surface registration incorporating curvature, volume preservation, and statistical model information

We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models

Dimensionality Reduction and Dynamical Mode Recognition of Circular Arrays of Flame Oscillators Using Deep Neural Network

Oscillatory combustion in aero engines and modern gas turbines often has significant adverse effects on their operation, and accurately recognizing various oscillation modes is the prerequisite for understanding and controlling combustion instability. However, the high-dimensional spatial-temporal data of a complex combustion system typically poses considerable challenges to the dynamical mode recognition. Based on a two-layer bidirectional long short-term memory variational autoencoder (Bi-LSTM-VAE) dimensionality reduction model and a two-dimensional Wasserstein distance-based classifier (WDC), this study proposes a promising method (Bi-LSTM-VAE-WDC) for recognizing dynamical modes in oscillatory combustion systems. Specifically, the Bi-LSTM-VAE dimension reduction model was introduced to reduce the high-dimensional spatial-temporal data of the combustion system to a low-dimensional phase space; Gaussian kernel density estimates (GKDE) were computed based on the distribution of phase points in a grid; two-dimensional WD values were calculated from the GKDE maps to recognize the oscillation modes. The time-series data used in this study were obtained from numerical simulations of circular arrays of laminar flame oscillators. The results show that the novel Bi-LSTM-VAE method can produce a non-overlapping distribution of phase points, indicating an effective unsupervised mode recognition and classification. Furthermore, the present method exhibits a more prominent performance than VAE and PCA (principal component analysis) for distinguishing dynamical modes in complex flame systems, implying its potential in studying turbulent combustion.Comment: research paper (18 pages, 1 table 10 figures) with supplementary material (8 pages, 1 table, 5 figures

A Hybrid Approach Based on Variational Mode Decomposition for Analyzing and Predicting Urban Travel Speed

Predicting travel speeds on urban road networks is a challenging subject due to its uncertainty stemming from travel demand, geometric condition, traffic signals, and other exogenous factors. This uncertainty appears as nonlinearity, nonstationarity, and volatility in traffic data, and it also creates a spatiotemporal heterogeneity of link travel speed by interacting with neighbor links. In this study, we propose a hybrid model using variational mode decomposition (VMD) to investigate and mitigate the uncertainty of urban travel speeds. The VMD allows the travel speed data to be divided into orthogonal and oscillatory sub-signals, called modes. The regular components are extracted as the low-frequency modes, and the irregular components presenting uncertainty are transformed into a combination of modes, which is more predictable than the original uncertainty. For the prediction, the VMD decomposes the travel speed data into modes, and these modes are predicted and summed to represent the predicted travel speed. The evaluation results on urban road networks show that, the proposed hybrid model outperforms the benchmark models both in the congested and in the overall conditions. The improvement in performance increases significantly over specific link-days, which generally are hard to predict. To explain the significant variance of the prediction performance according to each link and each day, the correlation analysis between the properties of modes and the performance of the model are conducted. The results on correlation analysis show that the more variance of nondaily pattern is explained through the modes, the easier it was to predict the speed. Based on the results, discussions on the interpretation on the correlation analysis and future research are presented. Document type: Articl