In this paper, we propose a method to improve the accuracy of speech emotion recognition (SER) by using vision transformer (ViT) to attend to the correlation of frequency (y-axis) with time (x-axis) in spectrogram and transferring positional information between ViT through knowledge transfer. The proposed method has the following originality i) We use vertically segmented patches of log-Mel spectrogram to analyze the correlation of frequencies over time. This type of patch allows us to correlate the most relevant frequencies for a particular emotion with the time they were uttered. ii) We propose the use of image coordinate encoding, an absolute positional encoding suitable for ViT. By normalizing the x, y coordinates of the image to -1 to 1 and concatenating them to the image, we can effectively provide valid absolute positional information for ViT. iii) Through feature map matching, the locality and location information of the teacher network is effectively transmitted to the student network. Teacher network is a ViT that contains locality of convolutional stem and absolute position information through image coordinate encoding, and student network is a structure that lacks positional encoding in the basic ViT structure. In feature map matching stage, we train through the mean absolute error (L1 loss) to minimize the difference between the feature maps of the two networks. To validate the proposed method, three emotion datasets (SAVEE, EmoDB, and CREMA-D) consisting of speech were converted into log-Mel spectrograms for comparison experiments. The experimental results show that the proposed method significantly outperforms the state-of-the-art methods in terms of weighted accuracy while requiring significantly fewer floating point operations (FLOPs). Overall, the proposed method offers an promising solution for SER by providing improved efficiency and performance.
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In this paper, we present a randomized extension of the deep splitting algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)] using random neural networks suitable to approximately solve both high-dimensional nonlinear parabolic PDEs and PIDEs with jumps having (possibly) infinite activity. We provide a full error analysis of our so-called random deep splitting method. In particular, we prove that our random deep splitting method converges to the (unique viscosity) solution of the nonlinear PDE or PIDE under consideration. Moreover, we empirically analyze our random deep splitting method by considering several numerical examples including both nonlinear PDEs and nonlinear PIDEs relevant in the context of pricing of financial derivatives under default risk. In particular, we empirically demonstrate in all examples that our random deep splitting method can approximately solve nonlinear PDEs and PIDEs in 10'000 dimensions within seconds.
In this paper, we introduce the design of HackCar, a testing platform for replicating attacks and defenses on a generic automotive system without requiring access to a complete vehicle. This platform empowers security researchers to illustrate the consequences of attacks targeting an automotive system on a realistic platform, facilitating the development and testing of security countermeasures against both existing and novel attacks. The HackCar platform is built upon an F1-10th model, to which various automotive-grade microcontrollers are connected through automotive communication protocols. This solution is crafted to be entirely modular, allowing for the creation of diverse test scenarios. Researchers and practitioners can thus develop innovative security solutions while adhering to the constraints of automotive-grade microcontrollers. We showcase our design by comparing it with a real, licensed, and unmodified vehicle. Additionally, we analyze the behavior of the HackCar in both an attack-free scenario and a scenario where an attack on in-vehicle communication is deployed.
This paper deals with a numerical analysis of plastic deformation under various conditions, utilizing Radial Basis Function (RBF) approximation. The focus is on the elasto-plastic von Mises problem under plane-strain assumption. Elastic deformation is modelled using the Navier-Cauchy equation. In regions where the von Mises stress surpasses the yield stress, corrections are applied locally through a return mapping algorithm. The non-linear deformation problem in the plastic domain is solved using the Picard iteration. The solutions for the Navier-Cauchy equation are computed using the Radial Basis Function-Generated Finite Differences (RBF-FD) meshless method using only scattered nodes in a strong form. Verification of the method is performed through the analysis of an internally pressurized thick-walled cylinder subjected to varying loading conditions. These conditions induce states of elastic expansion, perfectly-plastic yielding, and plastic yielding with linear hardening. The results are benchmarked against analytical solutions and traditional Finite Element Method (FEM) solutions. The paper also showcases the robustness of this approach by solving case of thick-walled cylinder with cut-outs. The results affirm that the RBF-FD method produces results comparable to those obtained through FEM, while offering substantial benefits in managing complex geometries without the necessity for conventional meshing, along with other benefits of meshless methods.
In the present paper, we consider one-hidden layer ANNs with a feedforward architecture, also referred to as shallow or two-layer networks, so that the structure is determined by the number and types of neurons. The determination of the parameters that define the function, called training, is done via the resolution of the approximation problem, so by imposing the interpolation through a set of specific nodes. We present the case where the parameters are trained using a procedure that is referred to as Extreme Learning Machine (ELM) that leads to a linear interpolation problem. In such hypotheses, the existence of an ANN interpolating function is guaranteed. The focus is then on the accuracy of the interpolation outside of the given sampling interpolation nodes when they are the equispaced, the Chebychev, and the randomly selected ones. The study is motivated by the well-known bell-shaped Runge example, which makes it clear that the construction of a global interpolating polynomial is accurate only if trained on suitably chosen nodes, ad example the Chebychev ones. In order to evaluate the behavior when growing the number of interpolation nodes, we raise the number of neurons in our network and compare it with the interpolating polynomial. We test using Runge's function and other well-known examples with different regularities. As expected, the accuracy of the approximation with a global polynomial increases only if the Chebychev nodes are considered. Instead, the error for the ANN interpolating function always decays and in most cases we observe that the convergence follows what is observed in the polynomial case on Chebychev nodes, despite the set of nodes used for training.
In this study, we propose a novel surrogate modelling approach to efficiently and accurately approximate the response of complex dynamical systems driven by time-varying Recently, there has been increased interest in assessing the seismic fragility of industrial plants and process equipment. This is reflected in the growing number of studies, community-funded research projects and experimental campaigns on the matter.Nonetheless, the complexity of the problem and its inherent modelling, coupled with a general scarcity of available data on process equipment, has limited the development of risk assessment methods. In fact, these limitations have led to the creation of simplified and quick-to-run models. In this context, we propose an innovative framework for developing state-dependent fragility functions. This new methodology combines limited data with the power of metamodelling and statistical techniques, namely polynomial chaos expansions (PCE) and bootstrapping. Therefore, we validated the framework on a simplified and inexpensive-to-run MDoF system endowed with Bouc-Wen hysteresis.Then, we tested it on a real nonstructural industrial process component. Specifically, we applied the state-dependent fragility framework to a critical vertical tank of a multicomponent full-scale 3D steel braced frame (BF). The seismic performance of the BF endowed with process components was captured by means of shake table campaign within the European SPIF project. Finally, we derived state-dependent fragility functions based on the combination of PCE and bootstrap at a greatly reduced computational cost.
In this paper we present a novel algorithm developed for computing the QR factorisation of extremely ill-conditioned tall-and-skinny matrices on distributed memory systems. The algorithm is based on the communication-avoiding CholeskyQR2 algorithm and its block Gram-Schmidt variant. The latter improves the numerical stability of the CholeskyQR2 algorithm and significantly reduces the loss of orthogonality even for matrices with condition numbers up to $10^{15}$. Currently, there is no distributed GPU version of this algorithm available in the literature which prevents the application of this method to very large matrices. In our work we provide a distributed implementation of this algorithm and also introduce a modified version that improves the performance, especially in the case of extremely ill-conditioned matrices. The main innovation of our approach lies in the interleaving of the CholeskyQR steps with the Gram-Schmidt orthogonalisation, which ensures that update steps are performed with fully orthogonalised panels. The obtained orthogonality and numerical stability of our modified algorithm is equivalent to CholeskyQR2 with Gram-Schmidt and other state-of-the-art methods. Weak scaling tests performed with our test matrices show significant performance improvements. In particular, our algorithm outperforms state-of-the-art Householder-based QR factorisation algorithms available in ScaLAPACK by a factor of $6$ on CPU-only systems and up to $80\times$ on GPU-based systems with distributed memory.
In this study, we develop a novel multi-fidelity deep learning approach that transforms low-fidelity solution maps into high-fidelity ones by incorporating parametric space information into a standard autoencoder architecture. This method's integration of parametric space information significantly reduces the need for training data to effectively predict high-fidelity solutions from low-fidelity ones. In this study, we examine a two-dimensional steady-state heat transfer analysis within a highly heterogeneous materials microstructure. The heat conductivity coefficients for two different materials are condensed from a 101 x 101 grid to smaller grids. We then solve the boundary value problem on the coarsest grid using a pre-trained physics-informed neural operator network known as Finite Operator Learning (FOL). The resulting low-fidelity solution is subsequently upscaled back to a 101 x 101 grid using a newly designed enhanced autoencoder. The novelty of the developed enhanced autoencoder lies in the concatenation of heat conductivity maps of different resolutions to the decoder segment in distinct steps. Hence the developed algorithm is named microstructure-embedded autoencoder (MEA). We compare the MEA outcomes with those from finite element methods, the standard U-Net, and various other upscaling techniques, including interpolation functions and feedforward neural networks (FFNN). Our analysis shows that MEA outperforms these methods in terms of computational efficiency and error on test cases. As a result, the MEA serves as a potential supplement to neural operator networks, effectively upscaling low-fidelity solutions to high fidelity while preserving critical details often lost in traditional upscaling methods, particularly at sharp interfaces like those seen with interpolation.
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The algorithm is derived by combining a proximal method of multipliers (PMM) with a standard semismooth Newton method (SSN), and is shown to be globally convergent under minimal assumptions. Further local linear (and potentially superlinear) convergence is shown under standard additional conditions. The major computational bottleneck of the proposed approach arises from the solution of the associated SSN linear systems. These are solved using a Krylov-subspace method, accelerated by certain novel general-purpose preconditioners which are shown to be optimal with respect to the proximal penalty parameters. The preconditioners are easy to store and invert, since they exploit the structure of the nonsmooth terms appearing in the problem's objective to significantly reduce their memory requirements. We showcase the efficiency, robustness, and scalability of the proposed solver on a variety of problems arising in risk-averse portfolio selection, $L^1$-regularized partial differential equation constrained optimization, quantile regression, and binary classification via linear support vector machines. We provide computational evidence, on real-world datasets, to demonstrate the ability of the solver to efficiently and competitively handle a diverse set of medium- and large-scale optimization instances.
In this paper, we develop a new weak Galerkin finite element scheme for the Stokes interface problem with curved interfaces. We take a unique vector-valued function at the interface and reflect the interface condition in the variational problem. Theoretical analysis and numerical experiments show that the errors can reach the optimal convergence order under the energy norm and $L^2$ norm.
In this paper, we study the Boltzmann equation with uncertainties and prove that the spectral convergence of the semi-discretized numerical system holds in a combined velocity and random space, where the Fourier-spectral method is applied for approximation in the velocity space whereas the generalized polynomial chaos (gPC)-based stochastic Galerkin (SG) method is employed to discretize the random variable. Our proof is based on a delicate energy estimate for showing the well-posedness of the numerical solution as well as a rigorous control of its negative part in our well-designed functional space that involves high-order derivatives of both the velocity and random variables. This paper rigorously justifies the statement proposed in [Remark 4.4, J. Hu and S. Jin, J. Comput. Phys., 315 (2016), pp. 150-168].
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