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In uncertainty quantification, it is commonly required to solve a forward model consisting of a partial differential equation (PDE) with a spatially varying uncertain coefficient that is represented as an affine function of a set of random variables, or parameters. Discretizing such models using stochastic Galerkin finite element methods (SGFEMs) leads to very high-dimensional discrete problems that can be cast as linear multi-term matrix equations (LMTMEs). We develop efficient computational methods for approximating solutions of such matrix equations in low rank. To do this, we follow an alternating energy minimization (AEM) framework, wherein the solution is represented as a product of two matrices, and approximations to each component are sought by solving certain minimization problems repeatedly. Inspired by proper generalized decomposition methods, the iterative solution algorithms we present are based on a rank-adaptive variant of AEM methods that successively computes a rank-one solution component at each step. We introduce and evaluate new enhancement procedures to improve the accuracy of the approximations these algorithms deliver. The efficiency and accuracy of the enhanced AEM methods is demonstrated through numerical experiments with LMTMEs associated with SGFEM discretizations of parameterized linear elliptic PDEs. [ABSTRACT FROM AUTHOR]

Vertical, gigapascal-level mechanical stress (MS) is induced at different locations along the channel of 40-nm effective gate length planar CMOS field-effect transistor (FET) devices and electrical parameter variations are investigated. In both p-and n-channel devices, the threshold voltage, mobility, and ON-current are seen to change proportionally with the additional MS, while gate-induced drain-leakage current increases exponentially. A clear effect of the location of the applied force along the source–drain direction is observed on the transistor parameters. Simulations show that a mechanical load located closer to the FET source induces a stronger asymmetry between the source and drain stresses. This leads to asymmetric subband splitting/warping, which reduces the backscattering rate at the source, in line with theoretical predictions on the importance of the channel barrier near the source for current in quasi-ballistic transistors. [ABSTRACT FROM AUTHOR]

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter instances. Our extension is inspired by the concept of parameterized ODEs, which are widely investigated in computational science and engineering contexts, where characteristics of the governing equations vary over the input parameters. We apply the proposed parameterized NODEs (PNODEs) for learning latent dynamics of complex dynamical processes that arise in computational physics, which is an essential component for enabling rapid numerical simulations for time-critical physics applications. For this, we propose an encoder–decoder-type framework, which models latent dynamics as PNODEs. We demonstrate the effectiveness of PNODEs on benchmark problems from computational physics. [ABSTRACT FROM AUTHOR]

In this paper we investigate the utility of one-dimensional convolutional neural network (CNN) models in epidemiological forecasting. Deep learning models, in particular variants of recurrent neural networks (RNNs) have been studied for ILI (Influenza-Like Illness) forecasting, and have achieved a higher forecasting skill compared to conventional models such as ARIMA. In this study, we adapt two neural networks that employ one-dimensional temporal convolutional layers as a primary building block—temporal convolutional networks and simple neural attentive meta-learners—for epidemiological forecasting. We then test them with influenza data from the US collected over 2010-2019. We find that epidemiological forecasting with CNNs is feasible, and their forecasting skill is comparable to, and at times, superior to, plain RNNs. Thus CNNs and RNNs bring the power of nonlinear transformations to purely data-driven epidemiological models, a capability that heretofore has been limited to more elaborate mechanistic/compartmental disease models. [ABSTRACT FROM AUTHOR]

In this study, high‐performance few‐layered ReS2 field‐effect transistors (FETs), fabricated with hexagonal boron nitride (h‐BN) as top/bottom dual gate dielectrics, are presented. The performance of h‐BN dual gated ReS2 FET having a trade‐off of performance parameters is optimized using a compact model from analytical choice maps, which consists of three regions with different electrical characteristics. The bottom h‐BN dielectric has almost no defects and provides a physical distance between the traps in the SiO2 and the carriers in the ReS2 channel. Using a compact analyzing model and structural advantages, an excellent and optimized performance is introduced consisting of h‐BN dual‐gated ReS2 with a high mobility of 46.1 cm2 V−1 s−1, a high current on/off ratio of ≈106, a subthreshold swing of 2.7 V dec−1, and a low effective interface trap density (Nt,eff) of 7.85 × 1010 cm−2 eV−1 at a small operating voltage (<3 V). These phenomena are demonstrated through not only a fundamental current–voltage analysis, but also technology computer aided design simulations, time‐dependent current, and low‐frequency noise analysis. In addition, a simple method is introduced to extract the interlayer resistance of ReS2 channel through Y‐function method as a function of constant top gate bias. [ABSTRACT FROM AUTHOR]

Through time-dependent defect spectroscopy and low-frequency noise measurements, we investigate and characterize the differences of carrier trapping processes occurred by different interfaces (top/sidewall) of the gate-all-around silicon nanosheet field-effect transistor (GAA SiNS FET). In a GAA SiNS FET fabricated by the top-down process, the traps at the sidewall interface significantly affect the device performance as the width decreases. Compare to expectations, as the width of the device decreases, the subthreshold swing (SS) increases from 120 to 230 mV/dec, resulting in less gate controllability. In narrow-width devices, the effect of traps located at the sidewall interface is significantly dominant, and the 1/f2 noise, also known as generation–recombination (G–R) noise, is clearly appeared with an increased time constant (τi). In addition, the probability density distributions for the normalized current fluctuations (ΔID) show only one Gaussian in wide-width devices, whereas they are separated into four Gaussians with increased in narrow-width devices. Therefore, fitting is performed through the carrier number fluctuation-correlated with mobility fluctuations model that separately considered the effects of sidewall. In narrow-width GAA SiNS FETs, consequently, the extracted interface trap densities (NT) distribution becomes more dominant, and the scattering parameter () distribution increases by more than double. [ABSTRACT FROM AUTHOR]

Irradiation of MoS2 field-effect transistors (FETs) fabricated on Si/SiO2 substrates with electron beams (e-beams) below 30 keV creates electron–hole pairs (EHP) in the SiO2, which increase the interface trap density (Nit) and change the current path in the channel, resulting in performance changes. In situ measurements of the electrical characteristics of the FET performed using a nano-probe system mounted inside a scanning electron microscope show that e-beam irradiation enables both multilayer and monolayer MoS2 channels act as conductors. The e-beams mostly penetrate the channel owing to their large kinetic energy, while the EHPs formed in the SiO2 layer can contribute to the conductance by flowing into the MoS2 channel or inducing the gate bias effect. The analysis of the device parameters in the initial state and the vent-evacuation state after e-beam irradiation can clarify the effect of the interplay between the e-beam-induced EHPs and ambient adsorbates on the carrier behavior, which depends on the thickness of the MoS2 layer. DC and low frequency noise analysis reveals that the e-beam-induced EHPs increase Nit from 109–1010 to 1011 cm−2 eV−1 in both monolayer and multilayer devices, while the interfacial Coulomb scattering parameter αSC increases by three times in the monolayer and decreases to one-tenth of its original value in the multilayer. In other words, an MoS2 layer with a thickness of ∼30 nm is less sensitive to adsorbates by surface screening. Thus, the carrier mobility in the monolayer device decreases from 45.7 to 40 cm2 V−1 s−1, while in the 30 nm-thick multilayer device, it increases from 4.9 to 5.6 cm2 V−1 s−1. This is further evidenced by simulations of the distribution of interface traps and channel carriers in the MoS2 FET before and after e-beam irradiation, demonstrating that Coulomb scattering decreases as the effective channel moves away from the interface. [ABSTRACT FROM AUTHOR]

We study linear stability of solutions to the Navier-Stokes equations with stochastic viscosity. Specifically, we assume that the viscosity is given in the form of a stochastic expansion. Stability analysis requires a solution of the steady-state Navier-Stokes equation and then leads to a generalized eigenvalue problem, from which we wish to characterize the real part of the rightmost eigenvalue. While this can be achieved by Monte Carlo simulation, due to its computational cost we study three surrogates based on generalized polynomial chaos, Gaussian process regression and a shallow neural network. The results of linear stability analysis assessment obtained by the surrogates are compared to that of Monte Carlo simulation using a set of numerical experiments. [ABSTRACT FROM AUTHOR]

• Two model-reduction methods that project dynamical systems on nonlinear manifolds. • Analysis including conditions under which the two methods are equivalent. • A novel convolutional autoencoder architecture to construct the nonlinear manifold. • Numerical experiments demonstrating the method outperforms linear subspaces. Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the reduced-basis method, and (balanced) proper orthogonal decomposition (POD). Unfortunately, restricting the state to evolve in a linear subspace imposes a fundamental limitation to the accuracy of the resulting reduced-order model (ROM). In particular, linear-subspace ROMs can be expected to produce low-dimensional models with high accuracy only if the problem admits a fast decaying Kolmogorov n -width (e.g., diffusion-dominated problems). Unfortunately, many problems of interest exhibit a slowly decaying Kolmogorov n -width (e.g., advection-dominated problems). To address this, we propose a novel framework for projecting dynamical systems onto nonlinear manifolds using minimum-residual formulations at the time-continuous and time-discrete levels; the former leads to manifold Galerkin projection, while the latter leads to manifold least-squares Petrov–Galerkin (LSPG) projection. We perform analyses that provide insight into the relationship between these proposed approaches and classical linear-subspace reduced-order models; we also derive a posteriori discrete-time error bounds for the proposed approaches. In addition, we propose a computationally practical approach for computing the nonlinear manifold, which is based on convolutional autoencoders from deep learning. Finally, we demonstrate the ability of the method to significantly outperform even the optimal linear-subspace ROM on benchmark advection-dominated problems, thereby demonstrating the method's ability to overcome the intrinsic n -width limitations of linear subspaces. [ABSTRACT FROM AUTHOR]

Experimental research was conducted to study the combustion characteristics of clouds composed of micrometer-sized aluminum particles with an oxidizer blend of oxygen and superheated steam. Both ignition and combustion of an aluminum particle are difficult because it is enveloped by an oxide layer that has a high melting point (above 2300 K). To overcome the problem, we induced a particular shape of the combustor that can keep a stable flame of aluminum dust clouds at a lower feeding-rate. The combustion characteristics were examined using a system applied combustor involving a variety of parameters affecting the burning of the dust clouds. Based on these attempts, the aluminum dust clouds had an upper flammability limit above the equivalence ratio (Ф) 1.9 for oxygen diluted by air. Varying the lower limit of flammability, we found, crucially, that the feeding-rate and velocity of the particles are more effective than the equivalence ratio or combustor length. Furthermore, we could confirm the changing of the lower limit from 0.3 to 0.26 because the steam was additionally fed in the combustion of aluminum-oxygen. • Designed Combustor that Al dust can be terminated the burning without depositing. • Variation of the lower limit of flammability depending on Al dust feeding conditions. • Confirming the changing of a lower limit owing to feeding steam in Al–O 2 flame. [ABSTRACT FROM AUTHOR]

In this paper we study the efficacy of combining machine-learning methods with projection-based model reduction techniques for creating data-driven surrogate models of computationally expensive, high-fidelity physics models. Such surrogate models are essential for many-query applications e.g., engineering design optimization and parameter estimation, where it is necessary to invoke the high-fidelity model sequentially, many times. Surrogate models are usually constructed for individual scalar quantities. However there are scenarios where a spatially varying field needs to be modeled as a function of the model's input parameters. We develop a method to do so, using projections to represent spatial variability while a machine-learned model captures the dependence of the model's response on the inputs. The method is demonstrated on modeling the heat flux and pressure on the surface of the HIFiRE-1 geometry in a Mach 7.16 turbulent flow. The surrogate model is then used to perform Bayesian estimation of freestream conditions and parameters of the SST (Shear Stress Transport) turbulence model embedded in the high-fidelity (Reynolds-Averaged Navier–Stokes) flow simulator, using shock-tunnel data. The paper provides the first-ever Bayesian calibration of a turbulence model for complex hypersonic turbulent flows. We find that the primary issues in estimating the SST model parameters are the limited information content of the heat flux and pressure measurements and the large model-form error encountered in a certain part of the flow. • We study data-driven ROM-based surrogate model construction for application in hypersonic flows. • Complementary software compatible with scikit-learn is available here: https://www.github.com/kennychowdhary/tesuract. • First-ever Bayesian calibration of a hypersonic flow model using data-driven ROM surrogates. [ABSTRACT FROM AUTHOR]

This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and displacement fields. The proposed methodology develops a low-dimensional parametrization of these quantities of interest using space–time bases combined with machine learning methods. In particular, the space–time solutions are sought in a low-dimensional space–time linear trial subspace that can be obtained by computing tensor decompositions of usual state-snapshots data. The mapping between the input parameters and the basis expansion coefficients (or generalized coordinates) is approximated using four different machine learning techniques: multivariate polynomial regression, k -nearest-neighbors, random forests and neural networks. The relative costs and effectiveness of the four machine learning techniques are explored through three engineering problems: steady heat conduction, unsteady heat conduction and unsteady advective–diffusive–reactive system. Numerical results demonstrate that the proposed method performs well in terms of both accuracy and computational cost, and highlights the important point that the amount of model training data available in an engineering setting is often much less than it is in other machine learning applications, making it essential to incorporate knowledge from physical models. • A novel non-intrusive reduced-order model (ROM) method to solve systems of parameterized unsteady nonlinear algebraic equations is developed. • Various machine learning techniques to approximate the mapping between input parameters and output space–time bases expansion coefficients are examined: multivariate polynomial regression, k-nearest neighbors, random forest and neural network. • In the offline stage, we collect usual (space–time) state snapshots to build space–time bases and train the machine learning surrogate models. • In the online stage, for an arbitrary input parameter we express the space–time solution as linear combinations of those space–time bases and compute the coefficients using the trained surrogate models. • The space–time basis expansion coefficients only depend on input parameters and not on time. • The proposed method is verified on three benchmark problems: parameterized steady heat conduction PDE, parameterized unsteady heat conduction PDE and parameterized advective–diffusive–reactive problem. • Numerical results show that the online computation of machine learning surrogate models is extremely fast and the relative solution error is less than 1% on average. • We show that while our proposed approach is less accurate than the least-square Petrov–Galerkin (LSPG) model reduction (without hyper-reduction), it is significantly faster. [ABSTRACT FROM AUTHOR]

Thickness-dependent bandgap and carrier mobility of two-dimensional (2D) van der Waals (vdW) layered materials make them a promising material as a phototransistor that detects light signals and converts them to electrical signals. Thus far, to achieve a high photoresponsivity of 2D materials, enormous efforts have been made via material and dielectric engineering, as well as modifying device structure. Nevertheless, understanding the effect of interplay between the thickness and the carrier mobility to photoresponsivity is little known. Here, we demonstrate the tunable photoresponsivity (R) of 2D multilayer rhenium disulfide (ReS2), which is an attractive candidate for photodetection among 2D vdW materials owing to its layer-independent direct bandgap and decoupled vdW interaction. The gate bias (VG)-dependent photocurrent generation mechanism and R are presented for the channel thickness range of 1.7–27.5 nm. The high similarity between VG-dependent photocurrent and transconductance features in the ReS2 phototransistors clearly implies the importance of the channel thickness and the operating VG bias condition. Finally, the maximum R was found to be 4.1 × 105 A/W at 14.3 nm with the highest carrier mobility of ∼15.7 cm2⋅V−1⋅s−1 among the fabricated devices after excluding the contact resistance effect. This work sheds light on the strategy of how to obtain the highest R in 2D vdW-based phototransistors. [ABSTRACT FROM AUTHOR]