Stochastic Domain Research Articles

Graphene-enhanced ferroelectric domain wall high-output memristor

Recent studies on memristive materials and technologies have expanded beyond conventional memory elements, driven by their potential application in novel information processing concepts. Among these materials, conductive domain walls in ferroics are especially promising, offering conductive tunability suitable for reconfigurable multi-state devices. However, challenges such as domain stability, time-dependent conductivity, and low current output have impeded progress in the field. Here, we study the graphene/Pb(Zr,Ti)O3/SrRuO3 system, which demonstrates robust domain wall conduction up to 100 nA/μm2 for 2 V bias, while addressing the critical issue of stability of switched domains. The introduction of graphene electrodes enhances low-voltage stochastic domain formation with limited domain expansion that promotes the emergence of multi-domain states. The developed micrometer sized capacitor devices enable electrically programmable multiple distinct conduction states with robust retention combined with high current output and low operation voltage. These features are highly desirable for memristors and mark the significant potential of domain wall electronics for neuromorphic computing.

Stochastic assessment of 3‐D tunnels in near‐fault ground motion using modified domain reduction method

AbstractA robust assessment of tunnels due to uncertainties present in soil and ground motion properties can affect the dynamic response of these structures. In this paper, a stochastic analysis considering an aleatory variability in shear velocity Vs by performing Monte Carlo simulations and assessing its influence on underground tunnels. To numerically assess the response of the soil‐tunnel system to near‐fault earthquake ground motion, the required computational domain usually spans multiple kilometers including both earthquake fault and the structure. Thus, these simulations are computationally expensive. An efficient alternative method, that is, the Domain Reduction Method (DRM), in which a modular two‐step methodology for reducing the computational costs in the large domain analysis is employed. A 3‐D soil‐tunnel structure interaction is modeled to simulate the response of tunnel subjected to an inclined earthquake fault. The numerical simulation of the soil‐tunnel‐fault system is conducted in an open‐source FE package called Multi‐hazard Analysis for STOchastic time DOmaiN phenomena (MASTODON) based on MOOSE framework. The interactive analyses are carried out for three distinct types of soils based on National Earthquake Hazards Reduction Program (NEHRP) provision, that is, soft, medium, and hard, by generating 130 realizations. The results provide many insights into the influence of local site effects, that is, frequency shift for the peak response and the importance of input ground motion characteristics that govern the response of underground structures. The dynamic response of the structure is very sensitive to the uncertainty in rock material properties, especially, the stiffness of the rock sample and the shear wave velocity.

Stochastic Spin‐Orbit‐Torque Synapse and its Application in Uncertainty Quantification

AbstractStochasticity plays a significant role in the low‐power operation of a biological neural network. In an artificial neural network, stochasticity also contributes to critical functions such as the uncertainty quantification (UQ) for estimating the probability for the correctness of prediction. This UQ is vital for cutting‐edge applications, including medical diagnostics, autopilots, and large language models. Thanks to nonlinear variation of analogous Hall resistance with high computing velocity and low dissipation, a stochastic spin‐orbit‐torque (SOT) device exhibits significant potential for implementing the UQ. However, up until now, the application of UQ for stochastic SOT devices remains unexplored. In this study, based on SOT‐induced stochastic magnetic domain wall (DW) motion with varying velocity, a SOT synapse is fabricated that can emulate stochastic weight update following the Spike‐Timing‐Dependent‐Plasticity (STDP) rule. Furthermore, a stochastic SNN is set up, which, when compared to its deterministic counterpart, demonstrates a clear advantage in quantifying uncertainty for diagnosing the type of breast tumor (benign or malignant).

PSNN-TADA: Prototype and Stochastic Neural Network-Based Twice Adversarial Domain Adaptation for Fault Diagnosis Under Varying Working Conditions

PSNN-TADA: Prototype and Stochastic Neural Network-Based Twice Adversarial Domain Adaptation for Fault Diagnosis Under Varying Working Conditions

The stochastic stability and H∞‐fuzzy control of stochastic bifurcation of a doubly‐fed induction generator

AbstractConsidering the dynamic behavior of doubly‐fed induction generators (DFIGs) under the influence of random factors, this paper not only analyzes the phenomenon of stochastic instability and bifurcation of a DFIG dynamic variable in its random space when they are affected by environmental noise, but also proposes a method based on the Tkagi–Sugneo (T–S) fuzzy control strategy to control its stochastic bifurcation. First, a four‐dimensional stochastic dynamic DFIG model is established by using multiplicative white noise to simulate the influence of environmental noise on electrical variables, and stochastic central manifold theory is used to reduce the dimensionality of a planar model in the bifurcation neighborhood. Then, the stochastic stability of the model is investigated based on singular boundary theory, while the steady‐state probability density of the stochastic DFIG is determined using the Fokker–Plank–Kolmogorov equation to obtain the location and probability density of its stochastic P‐bifurcation. Finally, the influence of stochastic bifurcation behavior is eliminated by H∞‐fuzzy output feedback control. The numerical simulation results indicate that the location and probability of stochastic bifurcation in a DFIG will vary with the change in noise intensity, and the bifurcation parameter values and stochastic stability domain are obtained. The harm caused by random factors can be solved based on H∞‐fuzzy output feedback, which provides a theoretical basis for the stable operation of the DFIG system.

Accuracy Analysis on Design of Stochastic Computing in Arithmetic Components and Combinational Circuit

Stochastic circuits are used in applications that require low area and power consumption. The computing performed using these circuits is referred to as Stochastic computing (SC). The arithmetic operations in this computing can be realized using minimum logic circuits. The SC system allows a tradeoff of computational accuracy and area; thereby, the challenge in SC is improving the accuracy. The accuracy depends on the SC system’s stochastic number generator (SNG) part. SNGs provide the appropriate stochastic input required for stochastic computation. Hence we explore the accuracy in SC for various arithmetic operations performed using stochastic computing with the help of logic circuits. The contributions in this paper are; first, we have performed stochastic computing for arithmetic components using two different SNGs. The SNGs considered are Linear Feed-back Shift Register (LFSR) -based traditional stochastic number generators and S-box-based stochastic number generators. Second, the arithmetic components are implemented in a combinational circuit for algebraic expression in the stochastic domain using two different SNGs. Third, computational analysis for stochastic arithmetic components and the stochastic algebraic equation has been conducted. Finally, accuracy analysis and measurement are performed between LFSR-based computation and S-box-based computation. The novel aspect of this work is the use of S-box-based SNG in the development of stochastic computing in arithmetic components. Also, the implementation of stochastic computing in the combinational circuit using the developed basic arithmetic components, and exploration of accuracy with respect to stochastic number generators used is presented.

Stochastic domain decomposition based on variable-separation method

This work proposes a stochastic domain decomposition method for solving steady-state partial differential equations (PDEs) with random inputs. Specifically, based on the efficiency of the variable-separation (VS) method in simulating stochastic partial differential equations (SPDEs), we extend it to stochastic algebraic systems and employ it in the context of stochastic domain decomposition. The resulting method, termed stochastic domain decomposition based on variable-separation (SDD-VS) alleviates the challenge commonly known as the “curse of dimensionality” notably by leveraging explicit representations of stochastic functions derived from physical systems. The primary objective of the proposed SDD-VS method is to obtain a separate representation of the solution for the stochastic interface problem. To enhance computational efficiency, we introduce a two-phase approach consisting of offline and online computation. In the offline phase, we establish an affine representation of stochastic algebraic systems by systematically applying the VS method. During the online phase, we estimate the interface unknowns of SPDEs using a quasi-optimal separated representation, facilitating the construction of efficient surrogate models for subproblems. We substantiate the effectiveness of our proposed approach through numerical experiments involving three specific instances, demonstrating its capability to provide accurate solutions.

Stochastic Model Updating with Uncertainty Quantification: An Overview and Tutorial

This paper presents an overview of the theoretic framework of stochastic model updating, including critical aspects of model parameterisation, sensitivity analysis, surrogate modelling, test-analysis correlation, parameter calibration, etc. Special attention is paid to uncertainty analysis, which extends model updating from the deterministic domain to the stochastic domain. This extension is significantly promoted by uncertainty quantification metrics, no longer describing the model parameters as unknown-but-fixed constants but random variables with uncertain distributions, i.e. imprecise probabilities. As a result, the stochastic model updating no longer aims at a single model prediction with maximum fidelity to a single experiment, but rather a reduced uncertainty space of the simulation enveloping the complete scatter of multiple experiment data. Quantification of such an imprecise probability requires a dedicated uncertainty propagation process to investigate how the uncertainty space of the input is propagated via the model to the uncertainty space of the output. The two key aspects, forward uncertainty propagation and inverse parameter calibration, along with key techniques such as P-box propagation, statistical distance-based metrics, Markov chain Monte Carlo sampling, and Bayesian updating, are elaborated in this tutorial. The overall technical framework is demonstrated by solving the NASA Multidisciplinary UQ Challenge 2014, with the purpose of encouraging the readers to reproduce the result following this tutorial. The second practical demonstration is performed on a newly designed benchmark testbed, where a series of lab-scale aeroplane models are manufactured with varying geometry sizes, following pre-defined probabilistic distributions, and tested in terms of their natural frequencies and model shapes. Such a measurement database contains naturally not only measurement errors but also, more importantly, controllable uncertainties from the pre-defined distributions of the structure geometry. Finally, open questions are discussed to fulfil the motivation of this tutorial in providing researchers, especially beginners, with further directions on stochastic model updating with uncertainty treatment perspectives.

Development of a software platform for bridge modal and damage identification based on ambient excitation

Modal and damage identification based on ambient excitation can greatly improve the efficiency of high-speed railway bridge vibration detection. This paper first describes the basic principles of stochastic subspace identification, peak-picking, and frequency domain decomposition method in modal analysis based on ambient excitation, and the effectiveness of these three methods is verified through finite element calculation and numerical simulation. Then the damage element is added to the finite element model to simulate the crack, and the curvature mode difference and the curvature mode area difference square ratio are calculated by using the stochastic subspace identification results to verify their ability of damage identification and location. Finally, the above modal and damage identification techniques are integrated to develop a bridge modal and damage identification software platform. The final results show that all three modal identification methods can accurately identify the vibration frequency and mode shape, both damage identification methods can accurately identify and locate the damage, and the developed software platform is simple and efficient.

Stochastic domain wall-magnetic tunnel junction artificial neurons for noise-resilient spiking neural networks

The spatiotemporal nature of neuronal behavior in spiking neural networks (SNNs) makes SNNs promising for edge applications that require high energy efficiency. To realize SNNs in hardware, spintronic neuron implementations can bring advantages of scalability and energy efficiency. Domain wall (DW)-based magnetic tunnel junction (MTJ) devices are well suited for probabilistic neural networks given their intrinsic integrate-and-fire behavior with tunable stochasticity. Here, we present a scaled DW-MTJ neuron with voltage-dependent firing probability. The measured behavior was used to simulate a SNN that attains accuracy during learning compared to an equivalent, but more complicated, multi-weight DW-MTJ device. The validation accuracy during training was also shown to be comparable to an ideal leaky integrate and fire device. However, during inference, the binary DW-MTJ neuron outperformed the other devices after Gaussian noise was introduced to the Fashion-MNIST classification task. This work shows that DW-MTJ devices can be used to construct noise-resilient networks suitable for neuromorphic computing on the edge.

Multilevel quasi-Monte Carlo for random elliptic eigenvalue problems I: regularity and error analysis

Abstract Stochastic partial differential equation (PDE) eigenvalue problems are useful models for quantifying the uncertainty in several applications from the physical sciences and engineering, e.g., structural vibration analysis, the criticality of a nuclear reactor or photonic crystal structures. In this paper we present a multilevel quasi-Monte Carlo (MLQMC) method for approximating the expectation of the minimal eigenvalue of an elliptic eigenvalue problem with coefficients that are given as a series expansion of countably-many stochastic parameters. The MLQMC algorithm is based on a hierarchy of discretizations of the spatial domain and truncations of the dimension of the stochastic parameter domain. To approximate the expectations, randomly shifted lattice rules are employed. This paper is primarily dedicated to giving a rigorous analysis of the error of this algorithm. A key step in the error analysis requires bounds on the mixed derivatives of the eigenfunction with respect to both the stochastic and spatial variables simultaneously. Under stronger smoothness assumptions on the parametric dependence, our analysis also extends to multilevel higher-order quasi-Monte Carlo rules. An accompanying paper (Gilbert, A. D. & Scheichl, R. (2023) Multilevel quasi-Monte Carlo methods for random elliptic eigenvalue problems II: efficient algorithms and numerical results. IMA J. Numer. Anal.) focusses on practical extensions of the MLQMC algorithm to improve efficiency and presents numerical results.

Dimensionality-reduced antenna modeling with stochastically established constrained domain

Over the recent years, surrogate modeling methods have become increasingly widespread in the design of contemporary antenna systems. On the one hand, it is associated with a growing awareness of numerical optimization, instrumental in achieving high-performance structures. On the other hand, considerable computational expenses incurred by massive full-wave electromagnetic (EM) analyses, routinely employed as a major design tool, foster the development of novel design techniques that exhibit practically acceptable costs while ensuring reliability. In this context, substituting EM simulations by fast surrogates is a profitable solution. Data-driven modeling is arguably the most popular approach owing to its versatility and the abundance of specific methods. Yet, a construction of approximation surrogates is severely encumbered by the curse of dimensionality, and even more so by the broad ranges of material and geometry parameters the model should cover to be applicable for solving practical design tasks. The recently reported performance-driven modeling paradigm offers workaround these obstacles by restricting the surrogate rendition to a small section of the parameter space, containing designs of sufficiently high quality according to performance requirements imposed on the system under study. Nevertheless, identification of this region is based on database designs that have to be pre-optimized, which is associated with significant CPU expenses. The usage of the reference designs can be replaced by stochastic domain identification, leading to considerable computational savings. This paper introduces a further advancement, where the metamodel domain is outlined based on the spectral analysis of the random observables pre-selected using an automated decision-making process. Our procedure retains the benefits of the prior techniques but also reduces the domain dimensionality, which translates into additional cost reduction of training data acquisition. These have been conclusively demonstrated through numerical validation involving three microstrip antennas and comprehensive comparisons with six state-of-the-art benchmark techniques.

FerroCoin: Ferroelectric Tunnel Junction-Based True Random Number Generator

In this paper, we propose a Ferroelectric Tunnel Junction (FTJ)-based true random number generator (TRNG) that utilizes the stochastic domain switching phenomenon in ferroelectric materials. Ferroelectrics are promising for extracting randomness owing to their innate switching entropy in the multi-domain state. The random numbers generated by the proposed TRNG are shown to pass all the NIST SP 800-22 tests. The robustness of the proposed TRNG is also validated at various temperature and process corners. Important metrics such as power, bit rate, and energy/bit are calculated. This is the first comprehensive work demonstrating a ferroelectric-based TRNG with all these metrics. Compared to state-of-the-art TRNGs using other emerging technologies, we can achieve a higher bit rate with lower power consumption. We also perform material-level optimization with different ferroelectric materials, and showcase the trade-off between the bit rate and the power consumption. The proposed TRNG shows high robustness and reliability, and thus has the potential for implementing a low power on-chip solution.

Spintronic Heterostructures for Artificial Intelligence: A Materials Perspective

With the advent of the Big Data era, neuromorphic computing (NC) (also known as brain‐inspired computing) has gained a lot of research interest. Spintronic devices are the emerging candidates for implementing the NC due to their intrinsic nonvolatility, extremely high endurance, low‐power consumption, and complementary metal‐oxide compatibility. Many research groups have proposed various NC architectures based on spintronic devices. Herein, a collective survey of different spintronic‐based approaches is given for NC. The reviewed approaches include the progress of stochastic magnetic tunnel junction (MTJ) devices, spin‐torque nano‐oscillator, spin‐Hall nano‐oscillator, domain walls, and skyrmion devices. In all of these approaches, spin–orbit torque (SOT)‐based magnetization control, which is achieved via spintronics heterostructures, plays a significant role. Various heterostructures of heavy metal and ferromagnetic layers that have been proposed are reviewed for generating SOT. In addition, the phenomena and materials involved in the generation of orbital torque are summarized due to the orbital Hall effect (OHE), which has recently gained researchers’ attention. Finally, an outlook on the opportunities and challenges for spintronic‐based NC hardware is provided, shedding light on its great potential for artificial intelligence (AI) applications.

Stochastic Computing Design and Implementation of a Sound Source Localization System

Stochastic computing (SC) is an alternative computing paradigm that processes data in the form of uniform bit-streams. SC is fault-tolerant and can compute on small, efficient circuits. However, SC is primarily used in scientific research, and its practical implementations for end-users are rare. Digital sound source localization (SSL) is a useful signal processing technique that locates speakers using multiple microphones. SC has not been integrated into SSL in practice or theory. In this work, for the first time to the best of our knowledge, we implement an SSL algorithm in the stochastic domain and develop a functional SC-based sound source localizer. The practical part of this work shows that the proposed stochastic circuit does not depend on conventional analog-to-digital conversion and can process data in the form of pulse-width-modulated (PWM) signals. The proposed SC design consumes up to 39% less area than the conventional binary design. It can also consume less power depending on the computational accuracy, for example, 6% less power consumption for 3-bit inputs. We propose a new cross-correlation (CC) design based on the state-of-the-art Sobol bit-streams for further area and power saving. The proposed design utilizes a <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MUX</monospace> unit for bit-stream generation. It saves the area footprint up to 64% and the power consumption up to 82% compared to the counter-based SC design of CC, which relies on a comparator for bit-stream generation. The presented stochastic circuits, are not limited to SSL and are readily applicable to other practical applications such as radar ranging, wireless location, sonar direction finding, beamforming, and sensor calibration. The project’s source code is made available for public access.

Stochastic discontinuous Galerkin methods for robust deterministic control of convection-diffusion equations with uncertain coefficients

We investigate a numerical behavior of robust deterministic optimal control problem subject to a convection-diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing uncertainties into a large system of deterministic problems, is applied to discretize the stochastic domain, while a discontinuous Galerkin method is preferred for the spatial discretization due to its better convergence behavior for optimization problems governed by convection dominated PDEs. Error analysis is done for the state and adjoint variables in the energy norm, while the estimate of deterministic control is obtained in the L2-norm. Large matrix system emerging from the stochastic Galerkin method is addressed by the low-rank version of GMRES method, which reduces both the computational complexity and the memory requirements by employing Kronecker-product structure of the obtained linear system. Benchmark examples with and without control constraints are presented to illustrate the efficiency of the proposed methodology.

Analysis of Controllability of Fractional Functional Random Integroevolution Equations with Delay

Various scholars have lately employed a wide range of strategies to resolve two specific types of symmetrical fractional differential equations. The evolution of a number of real-world systems in the physical and biological sciences exhibits impulsive dynamical features that can be represented via impulsive differential equations. In this paper, we explore some existence and controllability theories for the Caputo order q∈(1,2) of delay- and random-effect-affected fractional functional integroevolution equations (FFIEEs). In order to prove that random solutions exist, we must prove a random fixed point theorem using a stochastic domain and the mild solution. Then we demonstrate that our solutions are controllable. At the end, applications and example is illustrated which indicates the applicability of this manuscript.

A STOCHASTIC DOMAIN DECOMPOSITION AND POST-PROCESSING ALGORITHM FOR EPISTEMIC UNCERTAINTY QUANTIFICATION

Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires computational modeling of the PDE in bounded/unbounded regions. Uncertainty in the computational model manifests through lack of precise knowledge of the input field or configuration. Uncertainty quantification (UQ) in the output physical process is typically carried out by modeling the uncertainty using a random field, governed by an appropriate covariance function. This leads to solving high-dimensional stochastic counterparts of the PDE computational models. Such UQ-PDE models require a large number of simulations of the PDE in conjunction with samples in the high-dimensional probability space, with probability distribution associated with the covariance function. Those UQ computational models having explicit knowledge of the covariance function are known as aleatoric UQ (AUQ) models. The lack of such explicit knowledge leads to epistemic UQ (EUQ) models, which typically require solution of a large number of AUQ models. In this article, using a surrogate, post-processing, and domain decomposition framework with coarse stochastic solution adaptation, we develop an offline/online algorithm for efficiently simulating a class of EUQ-PDE models. We demonstrate the algorithm for celebrated bounded and unbounded spatial region models, with high-dimensional uncertainties.

Magnetic anisotropy of Nanostructured Fe-Ni-C Coating Produced by Electroless Deposition

The structural and magnetic properties of nanostructured Fe100-xNix-C (0&amp;lt;x&amp;lt;100) coatings produced by electroless plating with different carbohydrates as reducing agents have been investigated. The phase-structural state of the films was studied by diffraction and electron microscopy. The Ni concentration ranges of FCC and BCC phases existence in electroless deposited films were determined. The surface morphology, saturation magnetization, local magnetic anisotropy field and coercivities of films are dependent on the iron content and type of reducing agent. The correlation between coercivity Hc and the anisotropy field of the magnetic stochastic domain which were established by correlation magnetometry suggests that the magnitude of Hc is mainly determined by this anisotropy. Keywords: 3d-metal alloys, the approach to saturation magnetization law, coercivity.

Some new existence results for fractional partial random nonlocal differential equations with delay

Abstract The present paper deals with some existence results for the Darboux problem of partial fractional random differential equations with finite delay. The arguments are based on a random fixed point theorem with stochastic domain combined with the measure of noncompactness. An illustration is given to show the applicability of our results.