Sparse Systems Research Articles

A new fast and robust thermo-hydraulic code for ITER superconducting magnet simulation

A new software is being developed for plasma pulse scenario validation of the ITER magnet system behaviour and prediction of the margin to quench in superconductors. The principal idea behind this project has been to develop a software tool for the thermo-hydraulic simulation of superconducting magnets that is able to simulate different operations scenarios for the magnets at least an order of magnitude faster than real time. To achieve this level of performance, a tight coupling between the Cable-In-Conduit-Conductors and the structure of the magnet is performed. All the equations for the flow and heat conduction parts of the global model are put in a single sparse system that is integrated in time. Such tight coupling in combination with implicit time stepping allows much longer time steps whilst keeping high accuracy of the solution. The code named REIMS (Riemann Explicit Implicit Magnet Simulator) is still under development. Both central solenoid (CS) and toroidal field (TF) ITER magnets are available at this stage. The development of the different intermediate steps that led to the current version of the code required verification/validation against exact solutions, experimental data and/or comparisons with existing codes. In the same way, results obtained with REIMS for the simulation of both CS and TF loops after application of a short plasma pulse scenario have been compared to results from existing reference codes, showing a good agreement.

Mid-frequency contrast compensation for sparse aperture imaging systems by increasing the size of a sub-aperture

Mid-frequency contrast compensation for sparse aperture imaging systems by increasing the size of a sub-aperture

Compilation of Shape Operators on Sparse Arrays

We show how to build a compiler for a sparse array language that supports shape operators such as reshaping or concatenating arrays, in addition to compute operators. Existing sparse array programming systems implement generic shape operators for only some sparse data structures, reduce shape operators on other data structures to those, and do not support fusion. Our system compiles sparse array expressions to code that efficiently iterates over reshaped views of irregular sparse data structures, without needing to materialize temporary storage for intermediates. Our evaluation shows that our approach generates sparse array code competitive with popular sparse array libraries: our generated shape operators achieve geometric mean speed-ups of 1.66×–15.3× when compared to hand-written kernels in scipy.sparse and 1.67×–651× when compared to generic implementations in pydata/sparse. For operators that require data structure conversions in these libraries, our generated code achieves geometric mean speed-ups of 7.29×–13.0× when compared to scipy.sparse and 21.3×–511× when compared to pydata/sparse. Finally, our evaluation demonstrates that fusing shape and compute operators improves the performance of several expressions by geometric mean speed-ups of 1.22×–2.23×.

Localized space-time Trefftz method for diffusion equations in complex domains

This paper introduces an advanced localized space-time Trefftz method tackling boundary value predicaments within complex two-dimensional domains governed by diffusion equations. In contrast to the widespread space-time collocation Trefftz method, which typically produces dense and ill-conditioned matrices, the proposed strategy employs a localized collocation scheme to remove these constraints. In particular, this is beneficial in multi-connected configurations or when dealing with significant variations in field values. To the best of our knowledge, this is the first space-time collocation Trefftz method adaptation, which is referred to as the localized space-time Trefftz method in this paper. The latter combines the space-time collocation Trefftz method principles, which allows to eliminate the need for mesh and numerical quadrature in its application. The localized space-time Trefftz method represents each interior node expressed as a linear blend of its immediate neighbors, while the space-time collocation Trefftz method applies numerical techniques within distinct subdomains. A sparse system of linear algebraic equations with internal points satisfying the governing equation, and boundary points satisfying the boundary conditions, allows to obtain numerical solutions using matrix systems. The localized space-time Trefftz method retains the easy-to-use properties and mesh-free structure of the space-time collocation Trefftz method, and it mitigates its ill-conditioning characteristics. Due to the localization principle and the consideration of overlapping subdomains, the solutions in the proposed localized space-time Trefftz method are more simply and compactly expressed compared with those in the space-time collocation Trefftz method, especially when dealing with multiply-connected domains. Numerical examples for simply-connected and multiply-connected domains are then provided to demonstrate the high precision and simplicity of the proposed localized space-time Trefftz method. The obtained results show that the latter has very high accuracy in solving two-dimensional diffusion problems. Compared with the traditional space-time collocation Trefftz method, the proposed mesh-free strategy yields solutions with higher precision while significantly reducing the instability.

Optimization of Sparse Camera Array Arrangement using Grid-based Method

—This study explores the application of multi-camera array technology in super-resolution (SR) imaging system. We propose an innovative method based on grid representation to optimize camera arrangements using sparse Gaussian processes and variational inference. This approach significantly enhances the image reconstruction quality of sparse camera arrays. Unlike conventional techniques that provide only qualitative conclusions, our grid-based method precisely optimizes camera positions and effectively simulates the impact of assembly errors. The optimized camera arrangement substantially improves the SR reconstruction quality of sparse array imaging systems, reducing contour jaggedness and high-frequency aliasing. Extensive simulations and experimental validations confirm the robustness and practical applicability of our method. The results demonstrate that the optimized camera arrangements can achieve high-resolution imaging with enhanced robustness against assembly errors, indicating their potential for various applications such as biological microscopy, remote sensing, and smartphone photography. This work presents a new and effective strategy for designing sparse camera array imaging systems, offering significant improvements in both image quality and system reliability.

High-order energy stable discrete variational derivative schemes for gradient flows

Abstract The existing discrete variational derivative method is fully implicit and only second-order accurate for gradient flow. In this paper, we propose a framework to construct high-order implicit (original) energy stable schemes and second-order semi-implicit (modified) energy stable schemes. Combined with the Runge–Kutta process, we can build high-order and unconditionally (original) energy stable schemes based on the discrete variational derivative method. The new energy stable schemes are implicit and leads to a large sparse nonlinear algebraic system at each time step, which can be efficiently solved by using an inexact Newton-type solver. To avoid solving nonlinear algebraic systems, we then present a relaxed discrete variational derivative method, which can construct second-order, linear and unconditionally (modified) energy stable schemes. Several numerical simulations are performed to investigate the efficiency, stability and accuracy of the newly proposed schemes.

Hysteretic response to different modes of ramping an external field in sparse and dense Ising spin glasses

We consider the hysteretic behavior of Ising spin glasses at T=0 for various modes of driving. Previous studies mostly focused on an infinitely slow speed Ḣ by which the external field H was ramped to trigger avalanches of spin flips by starting with destabilizing a single spin while few have focused on the effect of different driving methods. First, we show that this conventional protocol imposes a system size dependence. Then, we numerically analyze the response of Ising spin glasses at rates Ḣ that are fixed as well, to elucidate the differences in the response. Specifically, we compare three different modes of ramping (Ḣ=c/N, Ḣ=c/N, and Ḣ=c for constant c) for two types of spin glass systems of size N, representing dense networks by the Sherrington–Kirkpatrick model and sparse networks by the lattice spin glass in d=3 dimensions known as the Edwards Anderson model. Depending on the mode of ramping, we find that the response of each system, in form of spin-flip avalanches and other observables, can vary considerably. In particular, in the N-independent mode applied to the lattice spin glass, which is closest to experimental reality, we observe a percolation transition with a broad avalanche distribution between phases of localized and system-spanning responses. We explore implications for combinatorial optimization problems pertaining to sparse systems.

Multi-state Markovian-random walk adaptive filter for time-varying block sparse system identification

This paper presents a higher order multi-state Markov model for block sparsity model of a system impulse response. To capture the time-varying behavior of the system, a random walk model for temporal evolution is incorporated; resulting in a two-dimensional multi-state Markov-Random walk model across spatial and temporal domains. Additionally, a block batch data structure is utilized for the adaptive filter design. The proposed adaptive filter is aimed to find the Maximum A Posteriori (MAP) estimator of the batch time-varying impulse response. The associated optimization problem is demonstrated to be convex and efficiently solvable through the Steepest-Descent (SD) approach. Furthermore, the final recursion of the proposed adaptive filter is derived and a mean convergence analysis of the algorithm is provided. Simulation results show the effectiveness of the proposed algorithm under severe time-varying conditions of the system impulse response, where alternative algorithms may exhibit divergence or poor convergence. Synthetic experiments and real-world experiments using acoustic channel estimation further validate the superiority of the proposed algorithm.

A distributed memory parallel randomized Kaczmarz for sparse system of equations

AbstractKaczmarz algorithm is an iterative projection method for solving system of linear equations that arise in science and engineering problems in various application domains. In addition to classical Kaczmarz, there are randomized and parallel variants. The main challenge of the parallel implementation is the dependency of each Kaczmarz iteration on its predecessor. Because of this dependency, frequent communication is required which results in a substantial overhead. In this study, a new distributed parallel method that reduces the communication overhead is proposed. The proposed method partitions the problem so that the Kaczmarz iterations on different blocks are less dependent. A frequency parameter is introduced to see the effect of communication frequency on the performance. The communication overhead is also decreased by allowing communication between processes only if they have shared non‐zero columns. The experiments are performed using problems from various domains to compare the effects of different partitioning methods on the communication overhead and performance. Finally, parallel speedups of the proposed method on larger problems are presented.

Sparsity-aware complex-valued least mean kurtosis algorithms

Complex-valued least mean kurtosis (CLMK) algorithm and its augmented version (ACLMK) have recently become popular as workhorse tools in the processing of complex-valued signals due to their superior performances. Unfortunately, they are not yet suitable for sparse system identification problems. In this paper, combining the well-known sparsity-promoting strategies into the cost function based on the negated kurtosis of the error signal, we introduce a suit of sparsity-aware CLMK algorithms, named l0-norm CLMK (l0-CLMK), l0-ACLMK, zero-attraction CLMK (ZA-CLMK), ZA-ACLMK, reweighted ZA-CLMK (RZA-CLMK), and RZA-ACLMK. Simulation results on synthetic and real-world sparse system identification scenarios in the complex domain show that the proposed algorithms outperform the existing sparsity-aware algorithms in terms of convergence rate, tracking, and steady-state error.

Sparse reservoir computing with vertically coupled vortex spin-torque oscillators for time series prediction

Spin torque nano-oscillators possessing fast nonlinear dynamics and short-term memory functions are potentially able to achieve energy-efficient neuromorphic computing. In this study, we introduce an activation-state controllable spin neuron unit composed of vertically coupled vortex spin torque oscillators and a V–I source circuit is proposed and used to build an energy-efficient sparse reservoir computing (RC) system to solve nonlinear dynamic system prediction task. Based on micromagnetic and electronic circuit simulation, the Mackey–Glass chaotic time series and the real motor vibration signal series can be predicted by the RC system with merely 20 and 100 spin neuron units, respectively. Further study shows that the proposed sparse reservoir system could reduce energy consumption without significantly compromising performance, and a minimal response from inactivated neurons is crucial for maintaining the system’s performance. The accuracy and signal processing speed show the potential of the proposed sparse RC system for high-performance and low-energy neuromorphic computing.

Hermite polynomial based affine projection Blake Zisserman algorithm for identification of robust sparse nonlinear system

Hermite polynomial based affine projection Blake Zisserman algorithm for identification of robust sparse nonlinear system

Neural Networks to Find the Optimal Forcing for Offsetting the Anthropogenic Climate Change Effects

Abstract Of great relevance to climate engineering is the systematic relationship between the radiative forcing to the climate system and the response of the system, a relationship often represented by the linear response function (LRF) of the system. However, estimating the LRF often becomes an ill-posed inverse problem due to high-dimensionality and nonunique relationships between the forcing and response. Recent advances in machine learning make it possible to address the ill-posed inverse problem through regularization and sparse system fitting. Here, we develop a convolutional neural network (CNN) for regularized inversion. The CNN is trained using the surface temperature responses from a set of Green’s function perturbation experiments as imagery input data together with data sample densification. The resulting CNN model can infer the forcing pattern responsible for the temperature response from out-of-sample forcing scenarios. This promising proof of concept suggests a possible strategy for estimating the optimal forcing to negate certain undesirable effects of climate change. The limited success of this effort underscores the challenges of solving an inverse problem for a climate system with inherent nonlinearity. Significance Statement Predicting the climate response for a given climate forcing is a direct problem, while inferring the forcing for a given desired climate response is often an inverse, ill-posed, problem, posing a new challenge to the climate community. This study makes the first attempt to infer the radiative forcing for a given target pattern of global surface temperature response using a deep learning approach. The resulting deeply trained convolutional neural network inversion model shows promise in capturing the forcing pattern corresponding to a given surface temperature response, with a significant implication on the design of an optimal solar radiation management strategy for curbing global warming. This study also highlights the technical challenges that future research should prioritize in seeking feasible solutions to the inverse climate problem.

SPECTRAL METHOD FOR ONE DIMENSIONAL BENJAMIN-BONA-MAHONY-BURGERS EQUATION USING THE TRANSFORMED GENERALIZED JACOBI POLYNOMIAL

The Benjamin-Bona-Mahony-Burgers equation (BBMBE) plays a fundemental role in many application scenarios. In this paper, we study a spectral method for the BBMBE with homogeneous boundary conditions. We propose a spectral scheme using the transformed generalized Jacobi polynomial in combination of the explicit fourth-order Runge-Kutta method in time. The boundedness, the generalized stability and the convergence of the proposed scheme are proved. The extensive numerical examples show the efficiency of the new proposed scheme and coincide well with the theoretical analysis. The advantages of our new approach are as follows: (i) the use of the transformed generalized Jacobi polynomial simplifies the theoretical analysis and brings a sparse discrete system; (ii) the numerical solution is spectral accuracy in space.

Convex regularized recursive kernel risk-sensitive loss adaptive filtering algorithm and its performance analysis

In the context of channel estimation amid non-Gaussian impulse noise, traditional non-kernel-space methods face challenges of divergence, while many kernel-space methods fail to fully exploit the a priori information embedded in the channel. To address this, we introduce a robust sparse recursive adaptive filtering algorithm named convex regularized recursive kernel risk-sensitive loss (CR-RKRSL) in this paper. By combining the KRSL with a convex function constraint term, our proposed algorithm maximizes the utilization of channel a priori information. Furthermore, we delve into the theoretical aspects of the proposed algorithm, presenting expressions for the convergence and steady-state error. Through extensive simulation results, we demonstrate that CR-RKRSL outperforms the APSA, LHCAF, PRMCC, CR-RMC, RZAMCC algorithms. In comparison to existing algorithms, CR-RKRSL exhibits superior robustness and faster convergence, particularly in scenarios involving highly sparse systems.

Generalized sparse and outlier-robust broad learning systems for multi-dimensional output problems

Broad learning systems (BLSs) are becoming increasingly popular due to their fast and superior learning capabilities. However, their performances are susceptible to outliers and dense networks. The Elastic-net robust BLS (ER-BLS), which employs an ℓ1-norm loss function along with Elastic-net regularization, attempts to mitigate these issues by promoting network sparsity. Nevertheless, even ER-BLS fails to achieve satisfactory robustness and sparsity in multi-dimensional output tasks because the ℓ1-norm ignores the correlations between the output dimensions and output weights. Therefore, we propose a generalized Elastic-net robust BLS (GER-BLS) by generalizing the ℓ1-norm to the L2,1-norm. The L2,1-norm enhances robustness by treating the residuals across all output dimensions as a whole and induces node-level sparsity by penalizing all output weights connected to a single hidden node. The alternating direction method of multipliers (ADMM) algorithm was employed to solve GER-BLS efficiently, circumventing the non-differentiable issue of the objective function. Moreover, we developed DGER-BLS, a distributed variant of GER-BLS, tailored to handle data with distributed storage. The convergence analysis of our proposed algorithms and a large number of numerical experiments on multi-dimensional output datasets demonstrated the effectiveness of GER-BLS and DGER-BLS in dealing with outliers, distributed stored data, and sparsity.

MATRICS: The implicit matrix-free Eulerian hydrodynamics solver

Context. There exists a zoo of different astrophysical fluid dynamics solvers, most of which are based on an explicit formulation and hence stability-limited to small time steps dictated by the Courant number expressing the local speed of sound. With this limitation, the modeling of low-Mach-number flows requires small time steps that introduce significant numerical diffusion, and a large amount of computational resources are needed. On the other hand, implicit methods are often developed to exclusively model the fully incompressible or 1D case since they require the construction and solution of one or more large (non)linear systems per time step, for which direct matrix inversion procedures become unacceptably slow in two or more dimensions. Aims. In this work, we present a globally implicit 3D axisymmetric Eulerian solver for the compressible Navier–Stokes equations including the energy equation using conservative formulation and a fully simultaneous approach. We use the second-order-in-time backward differentiation formula for temporal discretization as well as the κ scheme for spatial discretization. We implement different limiter functions to prohibit the occurrence of spurious oscillations in the vicinity of discontinuities. Our method resembles the well-known monotone upwind scheme for conservation laws (MUSCL). We briefly present efficient solution methods for the arising sparse and nonlinear system of equations. Methods. To deal with the nonlinearity of the Navier–Stokes equations we used a Newton iteration procedure in which the required Jacobian matrix-vector product was reconstructed with a first-order finite difference approximation to machine precision in a matrix-free way. The resulting linear system was solved either completely matrix-free with a combination of a sufficient Krylov solver and an approximate Jacobian preconditioner or semi-matrix-free with the incomplete lower upper factorization technique as a preconditioner. The latter was dependent on a standalone approximation of the Jacobian matrix, which was optionally calculated and needed solely for the purpose of preconditioning. Results. We show our method to be capable of damping sound waves and resolving shocks even at Courant numbers larger than one. Furthermore, we prove the method’s ability to solve boundary value problems like the cylindrical Taylor-Couette flow (TC), including viscosity, and to model transition flows. To show the latter, we recover predicted growth rates for the vertical shear instability, while choosing a time step orders of magnitude larger than the explicit one. Finally, we verify that our method is second order in space by simulating a simplistic, stationary solar wind.

Abnormal Traffic Detection System Based on Feature Fusion and Sparse Transformer

This paper presents a feature fusion and sparse transformer-based anomalous traffic detection system (FSTDS). FSTDS utilizes a feature fusion network to encode the traffic data sequences and extracting features, fusing them into coding vectors through shallow and deep convolutional networks, followed by deep coding using a sparse transformer to capture the complex relationships between network flows; finally, a multilayer perceptron is used to classify the traffic and achieve anomaly traffic detection. The feature fusion network of FSTDS improves feature extraction from small sample data, the deep encoder enhances the understanding of complex traffic patterns, and the sparse transformer reduces the computational and storage overhead and improves the scalability of the model. Experiments demonstrate that the number of FSTDS parameters is reduced by up to nearly half compared to the baseline, and the success rate of anomalous flow detection is close to 100%.

Optimal policies for nutrition administration to very low birth weight infants

AbstractVery low birth weight (VLBW) infants (birth weight 1500 grams) are at risk of postnatal growth restriction. Understanding how nutrition is associated with growth and how these associations vary based on infant characteristics and comorbidities is important to reduce postnatal growth restriction. We propose a three‐step analytical framework: (i) We use unsupervised Clustering techniques to identify subgroups within a cohort of VLBW infants based on infant characteristics, diagnoses, and treatments. (ii) For each cluster, we use Multilevel Modeling to explore the associations between calorie or protein intake and growth velocity (GV) for varying time windows. (iii) We build Mixed‐Integer Programming Models to achieve simple rule‐based policies that physicians can use to classify infants into one of the identified subgroups. We use electronic health records from VLBW infants at Lurie Children's Hospital in Chicago, IL, born between 2011 and 2014. We find that clustering separates infants into two clusters, with Cluster 1 having smaller infants with more comorbidities than Cluster 2. Initial clustering on only sex and birth weight provides results similar to clustering on later‐life diagnoses and treatments. Multilevel models with Clustering provide better model fit than models without clustering. For Cluster 1, there is a significant association between GV and protein but not calories. For Cluster 2, both protein and calories are individually associated with growth. We develop accurate and sparse scoring systems to help clinicians identify infants at higher risk of growth restriction and consider nutrition regimens accordingly.

Constrained Normalized Subband Adaptive Filter Algorithm and Its Performance Analysis

Constrained least mean square (CLMS) algorithm is the most popular constrained adaptive filtering algorithm due to its simple structure and easy implementation. However, its convergence slows down when the input signal is colored. To address this issue, this paper firstly introduces the normalized subband adaptive filter (NSAF) into the constrained filtering problem and derives a constrained NSAF (CNSAF) algorithm using the Lagrange multiplier method. Benefiting from the good decorrelation capability of the NSAF, the proposed CNSAF algorithm significantly improves the convergence performance of the CLMS algorithm under colored inputs. Then, the mean and mean-square stability of the CNSAF algorithm is analyzed, and the theoretical models to characterize the transient and steady-state mean square deviation (MSD) behaviors of the CNSAF algorithm are derived utilizing the Kronecker product property and vectorization method. Further to extend the CNSAF algorithm to the problem of sparse system identification, a sparse version of the CNSAF algorithm (S-CNSAF) is derived. Finally, the validity of the derived theoretical MSD prediction models and the superiority of the proposed algorithms are confirmed by extensive computer simulations on system identification with colored inputs.