Spectral Space Research Articles

Consensus Graph Learning for Multi-View Clustering

Multi-view clustering, which exploits the multi-view information to partition data into their clusters, has attracted intense attention. However, most existing methods directly learn a similarity graph from original multi-view features, which inevitably contain noises and redundancy information. The learned similarity graph is inaccurate and is insufficient to depict the underlying cluster structure of multi-view data. To address this issue, we propose a novel multi-view clustering method that is able to construct an essential similarity graph in a spectral embedding space instead of the original feature space. Concretely, we first obtain multiple spectral embedding matrices from the view-specific similarity graphs, and reorganize the gram matrices constructed by the inner product of the normalized spectral embedding matrices into a tensor. Then, we impose a weighted tensor nuclear norm constraint on the tensor to capture high-order consistent information among multiple views. Furthermore, we unify the spectral embedding and low rank tensor learning into a unified optimization framework to determine the spectral embedding matrices and tensor representation jointly. Finally, we obtain the consensus similarity graph from the gram matrices via an adaptive neighbor manner. An efficient optimization algorithm is designed to solve the resultant optimization problem. Extensive experiments on six benchmark datasets are conducted to verify the efficacy of the proposed method. The code is implemented by using MATLAB R2018a and MindSpore library <xref ref-type="bibr" rid="ref1">[1]</xref>: <uri>https://github.com/guanyuezhen/CGL</uri>.

Towards pseudo-spectral incompressible smoothed particle hydrodynamics (ISPH)

In this paper a pseudo-spectral incompressible smoothed particle hydrodynamics (FFT-ISPH) solver is presented. While the solution of the linear system arising from the pressure Poisson equation in physical space using iterative solvers in incompressible SPH is a viable solution, it is widely accepted that the computational cost of solving the pressure Poisson equation by iterative solvers is excessive and affects negatively on the efficiency of the solver. The proposed scheme is an intermediate between a fully spectral and a standard incompressible SPH solver. Herein, the solution of the pressure Poisson equation is performed in spectral space whereas the discretisation and time integration are performed in physical space. This results in a second and higher-order scheme with the classical first-order projection and a third-order Runge-Kutta time integration scheme, respectively. A detailed performance analysis shows gains in computational cost of two orders of magnitude. Further, it is demonstrated that the solution of the pressure Poisson equation in spectral space is independent of the number of neighbouring nodes, in contrast to the iterative solver whose cost increases by a factor of three with smoothing length to particle size ratio. Periodic, bounded, and mixed boundary conditions test cases have been used to demonstrate the applicability, accuracy and robustness of the scheme with second and fourth-order convergence rates. The scheme opens an avenue for simulations of high-order incompressible flows in SPH where filtering operations in the frequency domain can be performed straightforwardly.

Energy Partitioning Control in the PITM Hybrid RANS/LES Method for the Simulation of Turbulent Flows

The partially integrated transport modeling (PITM) method first introduced in Refs. Schiestel and Dejoan (Theor Comput Fluid Dyn 18:443, 2005) and in Chaouat and Schiestel (Phys Fluids 17:065106, 2005) provides a continuous approach for hybrid RANS-LES simulations. Inspired from the multiple scale approach, the basis of the development of the method is the spectral space in quasi-homogeneous turbulence. The PITM method embodies a partitioning control function that monitors the ratio of subfilter energy to total turbulent energy by reference to the cutoff wavenumber location. How this procedure behaves in inhomogeneous flows is an important question. The present paper demonstrates that the same control function can be used both in homogeneous and in non-homogeneous flows as well. Further on, an analysis of the effect of anisotropic filters generally used for wall flows is conducted for computing the equivalent cutoff wavenumber suitable for determining the subfilter energy of the spectrum and see how it interferes with control function. Illustrations in the turbulent plane channel flow are given that confirm the efficiency of the procedure and DNS data have been used to support and supplement the discussion.

The Predictability of the Extratropical Flow Response to Recurving Atlantic Tropical Cyclones

AbstractGiven the ability of recurving Atlantic tropical cyclones (TCs) to disturb the amplitude of Rossby waves on the extratropical jet, this study investigates whether the predictability of the synoptic-scale flow is significantly modified from climatology downstream from and after TC recurvature events. Predictability is evaluated as the standard deviation of isentropic potential vorticity among a 50-member ensemble and is compared to a model climatology. It is shown that forecast uncertainty is dependent upon the relative location of the nearest trough at the time of recurvature and the relative zonal speed between the aforementioned trough and the TC in the 72 hours after recurvature. Predictability is significantly degraded when recurvature occurs downstream of a trough; the elevated uncertainty subsequently propagates downstream along with the trough axis. Furthermore, this study evaluates predictability in spectral space in order to distinguish between uncertainty tied to the exact location of troughs and ridges and uncertainty in Rossby wave amplitude. The wavelet analysis demonstrates that the increase in uncertainty is not solely limited to the trough location, as there is also significantly elevated uncertainty in the Rossby wave amplitude that originates from the upstream trough and spans across downstream troughs and ridges. Uncertainty is also increased near the recurvature longitude in the subset of cases in which the Rossby wave train propagates zonally slower than the TC after recurvature, which is hypothesized to be linked to baroclinic growth processes.

Sheaf representations and locality of Riesz spaces with order unit

We present an algebraic study of Riesz spaces (=real vector lattices) with a (strong) order unit. We exploit a categorical equivalence between those structures and a variety of algebras called RMV-algebras. We prove two different sheaf representations for Riesz spaces with order unit: the first represents them as sheaves of linearly ordered Riesz spaces over a spectral space, the second represent them as sheaves of "local" Riesz spaces over a compact Hausdorff space. Motivated by the latter representation we study the class of local RMV-algebras. We study the algebraic properties of local RMV-algebra and provide a characterisation of them as special retracts of the real interval [0,1]. Finally, we prove that the category of local RMV-algebras is equivalent to the category of all Riesz spaces.

Evaluating three calibration transfer methods for predictions of soil properties using mid‐infrared spectroscopy

AbstractMid‐infrared (MIR) spectroscopy models have been developed for rapid assessment of soils but are often soil and instrument specific because of differences in laboratory conditions and sensor setup. Calibration transfer is required to apply a spectral model such as partial least squares (PLS) regression developed from a primary instrument to a spectral dataset measured by a secondary instrument with statistically retained accuracy and precision. The study aimed to compare the performance of three transfer methods (i.e., direct standardization [DS], piecewise direct standardization [PDS], and spectral space transfer [SST]) and investigate the effects of transfer sample size and sample selection methods. The transfer methods were developed for predicting total C, clay, silt, and sand contents, cation exchange capacity (CEC), pH in water (pHW) and CaCl2, CaCO3 equivalent, and −1,500‐kPa water retention using spectral measurements of a secondary instrument. Calibration transfer methods of three PLS models for estimating soil properties with a high (total C), intermediate (clay content), and low (pHW) predictability were discussed. The effect of sample size required for the development of the calibration transfer and the selection method of the transferred samples were investigated. It was found that SST was most favorable for a relatively small sample size used in calibration transfer (≤12 samples). The performance of transfer methods was optimal when the transfer samples accounted for the variability of MIR spectra from the secondary instrument. We conclude that SST and PDS have the potential to be applied in spectroscopy for predicting soil properties using secondary instruments.

Numerical investigation of instability and transition to chaos in electro-convection of dielectric liquids between concentric cylinders

The two-dimensional (2D) electro-convection (EC) flow of dielectric liquids between two concentric cylindrical electrodes driven by unipolar injection of ions is investigated numerically. The finite volume method is used to resolve the spatiotemporal distributions of the flow field, electric field, and charge density. The flow transition routes from steady laminar to chaotic flow states are studied in various scenarios where the mobility parameter M of the dielectric liquids varies from 5 to 200. The dynamic characteristics and bifurcation routes of the EC flow depend on the electric Rayleigh number T, a ratio of the electric force to viscous force, and the mobility parameter M. For increasing T, three different transition routes from a convective steady-state to chaos via different intermediate states are observed. The flow states have been quantified by the power spectral density distribution and phase space trajectory of the velocity. The fractal dimensions and Lyapunov exponents are calculated to identify the chaotic flow. The increase in the mobility parameter M leads to a shorter and more direct route with fewer intermediate states when bifurcating to chaos. In addition, the power scale of charge transport that is defined by the electric Nusselt number Ne and T is discussed when the EC flow develops into electro-turbulence.

A new linear forcing method for isotropic turbulence with controlled integral length scale

Turbulence is a common feature to all flows that surround us. Despite its ubiquity, particularly in industrial flows, it is very difficult to provide a mathematical framework for the generation of turbulent eddies. Several methods have been proposed which are able to reproduce realistic features for velocity fluctuations, exhibiting proper space- and time-correlations. Focusing on physical space forcing, these methods are usually first evaluated upon sustained homogeneous isotropic turbulence by introducing a body force to the Navier–Stokes equations. Since the pioneering work of Lundgren, these techniques usually experience difficulties in predicting the integral length scale. The present study provides a forcing through a reconstruction approach which consists in building velocity fluctuations with a prescribed energy spectrum model. The proposed approach is assessed by performing large-eddy simulations of a sustained homogeneous isotropic turbulence in a triply periodic box. Properties of this forcing technique are discussed, drawing on both spatial and time correlations and also on the shape of energy spectrum together with the level of resolved turbulent kinetic energy. A special attention is put on the control of resolved turbulent energy. In this framework, an efficient selective forcing technique is derived, making use of spectral space features. The results show that the proposed approach allows to drive efficiently the resolved kinetic energy toward its target value while preserving the integral length scale independent of the domain size. It is observed that the resulting longitudinal length scale is overestimated by 13%, while the two-time correlations are recovered when using stochastic frequencies.

Comparative assessment of drought monitoring index susceptibility using geospatial techniques.

There are two main categories of dryness monitoring indices based on spectral feature space. One category uses the vertical distance from any point to a line passing through the coordinate origin, which is perpendicular to a soil line, to monitor the dryness conditions. The most popular indices are the Perpendicular Dryness Index (PDI) and the modified perpendicular dryness index (MPDI). The other category uses the distance from any point in feature space to the coordinate origin to represent the dryness status, for instance, the soil moisture (SM) monitoring index (SMMI) and the modified soil moisture monitoring index (MSMMI). In this study, the performances and differences of these four indicators were evaluated using field-measured SM (FSM) data based on Gaofen-1 (GF-1) wide field of view (WFV), Landsat-8 Operational Land Imager (OLI), and Sentinel-2 Multi-Spectral Instrument (MSI) sensors. Performance evaluations were conducted in two study areas, namely an arid and semi-arid region of northwest China and a humid agricultural region of southwest Canada. We employed gradient-based structural similarity (GSSIM) to quantitatively assess the similarity of the structural information and structural characteristics among these four indicators. Monitoring SM in bare soil or low vegetation-covered areas in the semi-arid region, the SMMI, PDI, MSMMI, and MPDI from Near-Infrared (NIR)-Red had significantly negative linear correlations with the FSM at 0-5-cm depth (P < 0.01). However, SMMI was better than PDI in estimating SM in bare soil, which was better than MSMMI and MPDI for GF-1. Moreover, the PDI and SMMI had similar SM evaluation abilities, which were better than those of MPDI and MSMMI for Landsat-8. The GSSIM map of the SMMI/PDI and the MSMMI/MPDI showed that the low change areas accounted for 99.89% and 98.89% for GF-1, respectively, and 95.78% and 94.45% for Landsat-8, respectively. This result indicated that the SMMI, PDI, MSMMI, and MPDI values from NIR-Red in low vegetation cover were similar. In monitoring SM in agricultural vegetation areas, the accuracy of the four indices from Short-Wave Infrared (SWIR) feature space was higher than that from NIR-Red feature space for Sentinel-2. The SM monitoring effect of MSMMI and MPDI was better than that of SMMI and PDI. Due to the lack of SWIR band, GF-1 was limited in monitoring SM in vegetation-covered areas. The SMMI and MSMMI, which do not rely on the soil line, were more suitable than PDI and MPDI for retrieving SM in the complex surface environment depending on the soil line and the number of parameters. GF-1 with 16-m resolution had higher accuracy in SM assessment than Landsat-8 with 30-m resolution and had almost the same accuracy as Sentinel-2 with 20 m.

Identification of Short and Long‐Lived Atmospheric Trace Gases From IASI Space Observations

AbstractIn recent years, major progress has been made in measuring weakly absorbing atmospheric trace gases from high spectral resolution space observations. In this paper, we apply the so‐called whitening transformation on spectra of the Infrared Atmospheric Sounding Interferometer, and show that it allows removing most of the climatological background from spectra, leaving a residual that contains those spectral signatures that depart from normality. These can subsequently be attributed to changes in the abundance of trace species. This is illustrated for two diverging cases: (1) a biomass burning plume from the 2019/2020 Australian bushfires, leading to the unambiguous identification of nine reactive trace gases, including a first observation of glycolaldehyde; (2) spectra observed a decade apart, from which changes in eight long‐lived halogenated substances are identified; three of them never observed before by a nadir sounder.

Two level simulation of Schmidt number effect on passive scalar transport in wall-bounded turbulent flows

In this study, the two-level simulation (TLS) modeling strategy developed earlier for momentum mixing is assessed in turbulent flows with passive scalar mixing and transport. Compared to the conventional algebraic and transport equation based subgrid-scale closures for large-eddy simulation (LES), where the effects of the unresolved small scales (SS) of motion on the large scales (LS) are modeled, in the TLS model, both large and small scales are explicitly evolved in a coupled two-scale decomposition method called TLS. Earlier studies demonstrated the ability of the SS model in the TLS to simulate high Reynolds number wall-bounded flows with a reasonable LS grid resolution. In the present study, this two-scale strategy is extended to model passive scalar mixing in turbulent channel flows. A comprehensive a priori assessment of the scalar SS model is performed using direct numerical simulation datasets for passive scalar transport in a fully developed turbulent channel flow at frictional Reynolds number Reτ=395 and at Schmidt numbers Sc= 1 and 4. This assessment is carried out to study the evolution of the large and the small scales of the scalar field in physical and spectral space and also to assess the SS prediction of quantities relevant for modeling of scalars such as scalar dissipation rate, counter-gradient transport, and backscatter. A TLS model is, then, used in a posteriori near-wall study using a hybrid TLS–LES approach to assess the two-scale scalar model.

One-Pot Hydrothermal Synthesis of Victoria Green (Ca3Cr2Si3O12) Nanoparticles in Alkaline Fluids and Its Colour Hue Characterisation

One-pot hydrothermal preparation of Ca3Cr2Si3O12 uvarovite nanoparticles under alkaline conditions was investigated for the first time. The experimental parameters selected for the study considered the concentration of the KOH solvent solution (0.01 to 5.0 M), the agitation of the autoclave (50 rpm), and the nominal content of Si4+ (2.2–3.0 mole). Fine uvarovite particles were synthesised at 200 °C after a 3 h interval in a highly concentrated 5.0 M KOH solution. The crystallisation of single-phase Ca3Cr2Si3O12 particles proceeded free of by-products via a one-pot process involving a single-step reaction. KOH solutions below 2.5 M and water hindered the crystallisation of the Ca3Cr2Si3O12 particles. The hydrothermal treatments carried out with stirring (50 rpm) and non-stirring triggered the crystallisation of irregular anhedral particles with average sizes of 8.05 and 12.25 nm, respectively. These particles spontaneously assembled into popcorn-shaped agglomerates with sizes varying from 66 to 156 nm. All the powders prepared by the present method exhibited CIE-L*a*b* values that correspond to the Victoria green colour spectral space and have a high near infrared reflectance property. The particle size and structural crystallinity are factors affecting the Victoria pigment optical properties, such as CIE-L*a*b* values, green tonality, and near-infrared reflectance.

Endmember Estimation with Maximum Distance Analysis

Endmember estimation plays a key role in hyperspectral image unmixing, often requiring an estimation of the number of endmembers and extracting endmembers. However, most of the existing extraction algorithms require prior knowledge regarding the number of endmembers, being a critical process during unmixing. To bridge this, a new maximum distance analysis (MDA) method is proposed that simultaneously estimates the number and spectral signatures of endmembers without any prior information on the experimental data containing pure pixel spectral signatures and no noise, being based on the assumption that endmembers form a simplex with the greatest volume over all pixel combinations. The simplex includes the farthest pixel point from the coordinate origin in the spectral space, which implies that: (1) the farthest pixel point from any other pixel point must be an endmember, (2) the farthest pixel point from any line must be an endmember, and (3) the farthest pixel point from any plane (or affine hull) must be an endmember. Under this scenario, the farthest pixel point from the coordinate origin is the first endmember, being used to create the aforementioned point, line, plane, and affine hull. The remaining endmembers are extracted by repetitively searching for the pixel points that satisfy the above three assumptions. In addition to behaving as an endmember estimation algorithm by itself, the MDA method can co-operate with existing endmember extraction techniques without the pure pixel assumption via generalizing them into more effective schemes. The conducted experiments validate the effectiveness and efficiency of our method on synthetic and real data.

Spectral signatures of soil horizons and soil orders – An exploratory study of 270 soil profiles

Soil mid-infrared (MIR) spectra contain absorption features related to soil physical, chemical, and biological properties. In this study, we explored the use of soil MIR spectra (7500 to 600 cm−1) to characterize and classify soil horizons and soil orders and identified the important features in the MIR spectra. The dataset consisted of 1167 soil samples collected from soil horizons of 270 soil profiles encompassing eight soil orders across 12 National Ecological Observatory Network (NEON) domains in the USA. The spectral features of the soil samples were qualitatively explored on the five master horizons (O, A, E, B, and C) and five B horizons (Bhs, Bs, Bk, Bt, and Bw). Random forest models were developed to investigate the predictability of soil MIR spectra on the soil master horizons and B horizons. Organic soils had different absorption features in the MIR spectra compared to mineral soils. Many absorption features in the MIR spectra were caused by organic functional groups, clay minerals, quartz, and carbonates in soils. The random forest models had an overall accuracy of 0.74 and 0.72 in classifying the five master horizons and the five B horizons for the validation, respectively. Hierarchical clustering analysis was applied on the concatenated topsoil (averaged from O and A horizons) and subsoil (averaged from E, B, and C horizons) MIR spectra of the 270 soil profiles to investigate the similarity of soil profiles in the spectral space. The MIR spectra of Spodosols had strong features of O horizons and Bhs and Bs horizons and thus Spodosols were well distinguished from other soil orders. Mollisols, Ultisols, Aridisols, and Inceptisols were not easily differentiated using MIR spectra. The random forest model to classify eight soil orders had an overall accuracy of 0.72 in the validation. The Alfisols, Aridisols, and Spodosols were fairly well classified by the MIR spectra, whereas the MIR spectra could not be used to differentiate Entisols, Inceptisols, Mollisols, and Ultisols. Soil MIR spectra can be used for characterizing and classifying soil horizons and soil orders when there are distinct spectral features in the soils. Soils with similar features cannot be easily distinguished using soil MIR spectra.

A nonlinear calibration transfer method based on joint kernel subspace

A nonlinear strategy is proposed to develop calibration transfer method with the available joint spectral data composed of the master and slave spectra of standard samples. Its core idea is to minimize the instrument-induced spectral variation in the reproducing kernel Hilbert space (RKHS) where the joint spectral data is implicitly mapped by proper kernel function. The nonlinear feature representation of master or slave spectra are reconstructed by singular value decomposition (SVD) in the RKHS. Then the transferred feature of slave spectra approaching the reconstructed feature of master spectra in the RKHS can be acquired by the procedure that (1) calculates the transfer matrix to match the maser and slave kernel features in the joint kernel subspace and (2) utilizes the transferred slave kernel feature to reconstruct the nonlinear feature representation of slave spectra. As a better feature representation suited for multivariate calibration, both the reconstructed feature of master calibration spectra and the transferred feature of slave test spectra are derived in the RKHS. A kernel partial least squares (KPLS) model built on the former is applied to the latter. The KPLS master calibration model is equivalent to a partial least squares (PLS) model built with the corresponding reconstructed master kernel feature in the joint kernel subspace. By exploiting the kernel eigenvector representations and kernel trick, a series of computationally less demanding formulas with linear operation is derived to realize the nonlinear calibration model, termed as joint kernel subspace based calibration transfer (JKSCT). JKSCT is compared with boxcar signal transfer (BST), piecewise direct standardization (PDS), multi-level simultaneous component analysis (MSCA), canonical correlation analysis based calibration transfer (CCACT), generalized least squares (GLS), slope and bias correction (SBC), spectral space transformation (SST), external parameter orthogonalization (EPO) and double competitive adaptive reweighted sampling (DCARS) on three spectral datasets. Experimental results show that JKSCT performs at least comparable with the DCARS or SST, and frequently better than the other methods.

Rota's Fubini lectures: The first problem

In his 1998 Fubini Lectures, Rota discusses twelve problems in probability that “no one likes to bring up”. The first problem calls for a revision of the notion of a sample space, guided by the belief that mention of sample points in a probabilistic argument is bad form and that a “pointless” foundation of probability should be provided by algebras of random variables.In 1958 Chang introduced MV-algebras to prove the completeness theorem of Łukasiewicz logic Ł∞. The aim of this paper is to show that MV-algebras provide a solution of Rota's first problem.The adjunction between MV-algebras and unital commutative C*-algebras equips every MV-algebra A with a natural ring structure, as advocated by Nelson for algebras of random variables. The closed compact set S(A)⊆[0,1]A of finitely additive probability measures on A (the states of A) coincides with the set of [0,1]-valued functions on A whose finite restrictions are consistent in de Finetti's sense. MV-algebras and Ł∞ thus provide the framework for a generalization (known as ŁIPSAT) of Boole's probabilistic inference problem, and its modern reformulation known as probabilistic satisfiability, PSAT. We construct an affine homeomorphism γA of S(A) onto the weakly compact space of regular Borel probability measures on the maximal spectral space μ(A). The latter is the most general compact Hausdorff space. As a consequence, for every Kolmogorov probability space (Ω,FΩ,P), with FΩ the sigma-algebra of Borel sets of a compact Hausdorff space Ω, and P a regular probability measure on FΩ, there is an MV-algebra A and a state σ of A such that (Ω,FΩ,P)≅(μ(A),Fμ(A),γA(σ)).

Extension groups between atoms in abelian categories

We introduce the extension groups between atoms in an abelian category. For a locally noetherian Grothendieck category, the localizing subcategories closed under injective envelopes are characterized in terms of those extension groups. We also introduce the virtual duals of the extension groups between atoms to measure the global dimension of the category. A new topological property of atom spectra is revealed and it is used to relate the projective dimensions of atoms with the Krull-Gabriel dimensions. As a byproduct of the topological observation, we show that there exists a spectral space that is not homeomorphic to the atom spectrum of any abelian category.

Numerical Modelling of the Effects of the Gulf Stream on the Wave Characteristics

The influence of the Gulf Stream on the wind wave characteristics is investigated. Wave–current interaction inside the current field can result in significant inhomogeneities of the wave field that change the wave spectrum and wave statistics. This study relies on regional realistic simulations using high resolution in time, space and in the spectral space that allow to solve small scale features of the order of 5 km. Wave model simulations are performed with and without ocean currents to understand the impact of the Gulf Stream. Modelled wave spectra are examined along the main axis of the Gulf Stream, and also along a transect that crosses the current. The behavior of significant wave height (Hs), the current speed, as well as the mean wave propagation and the current direction are analyzed at the selected transect locations. It is shown that inside the current the spectral wave energy grows if the wave and the current are aligned and opposed which result in a very peaked and elongated spectrum. The Gulf Stream causes a widening of the spectrum angular distribution. The results indicate that the Hs increases with the current velocity once the waves are inside the Gulf Stream. Most of the time, waves travelled in opposite direction to the current that flows from the SW to the NE, which could explain why inside the Gulf Stream waves are high. The validation of the numerical simulations is performed for Hs using different wave buoy data available in the study region for the winter period of 2019. In addition, one-dimensional wave spectra measured by an NDBC (National Data Buoy Center) wave buoy are compared with the WAM (Wave Advanced Modeling) modelled 1d spectra showing a good correlation. Accounting for ocean currents improves the quality of the simulated results, which is more realistic than only considering waves.

Feature Extraction via Joint Adaptive Structure Density for Hyperspectral Imagery Classification

Feature extraction is known to be an effective way in both reducing computational complexity and increasing accuracy in hyperspectral imagery (HSI) classification. In this article, we propose a novel HSI feature extraction based on joint adaptive structure density (JASD), which can make full use of the texture feature of feature level and effectively utilize the spatial structure feature of pixel level. Specifically, the proposed JASD method considers two weak assumptions when exploiting the structure information contained in the HSI: 1) close pixels in spectral space have the same label and 2) all the pixels in a subregion belong to the same class. The JASD method consists of the following steps. First, a principal component analysis method is applied to the original high-dimensional HSI to obtain low-dimensional features in order to promote the separability of pixels between different classes and improve the execution efficiency of the proposed method. Then, the local density peak-assisted $k$ nearest neighbor idea is introduced into oversegmentation-based regions to define the structural spatial information of the HSI and overcome the aforementioned weak assumptions. Meanwhile, recursive filtering in the transform domain is applied to the above low-dimensional HSI to preserve global edge details. Next, the global edge details and the local spatial structure feature are fused based on the stacking method. Finally, the composite hyperspectral feature is fed into the supervised classifier to obtain the classification results. Experimental results on three widely used real HSI data sets demonstrated that the proposed JASD method is superior to several comparative classification methods in terms of classification accuracy and computational burden.

Schwarz Waveform Relaxation Physics Informed Neural Networks for Solving Advection-Diffusion-Reaction Equations

This paper develops a physics-informed neural network (PINN) based on the Schwarz waveform relaxation (SWR) method for solving local and nonlocal advection-diffusion-reaction equations. Specifically, we derive the formulation by constructing subdomain-dependent local solutions by minimizing local loss functions, allowing the decomposition of the training process in different domains in an embarrassingly parallel procedure. Provided the convergence of PINN, the overall proposed algorithm is convergent. By constructing local solutions, one can, in particular, adapt the depth of the deep neural networks, depending on the solution's spectral space and time complexity in each subdomain. We present some numerical experiments based on classical and Robin-SWR to illustrate the performance and comment on the convergence of the proposed method.