Stochastic Perturbation Research Articles

Intrinsic predictability limits arising from Indian Ocean Madden–Julian oscillation (MJO) heating: effects on tropical and extratropical teleconnections

Abstract. Since the Madden–Julian oscillation (MJO) is a major source for tropical and extratropical variability on weekly to monthly timescales, the intrinsic predictability of its global teleconnections is of great interest. As the tropical diabatic heating associated with the MJO ultimately drives these teleconnections, the variability in heating among ensemble forecasts initialized from the same episode of the MJO will limit this predictability. In order to assess this limitation, a suite of 60 d ensemble reforecasts has been carried out with the ECMWF forecast model, spanning 13 starting dates from 1 November and 1 January for different years. The initial dates were chosen so that phases 2 and 3 of the MJO (with anomalous tropical heating in the Indian Ocean sector) were present in the observed initial conditions. The 51 members of an individual ensemble use identical initial conditions for the atmosphere and ocean. Stochastic perturbations to the tendencies produced by the atmospheric physics parameterizations are applied only over the Indian Ocean region (50–120∘ E). This guarantees that the spread between reforecasts within an ensemble is due to perturbations in heat sources only in the Indian Ocean sector. The point-wise spread in the intra-ensemble (or error) variance of vertically integrated tropical heating Q is larger than the average ensemble mean signal even at early forecast times; however the planetary wave (PW) component of Q (zonal waves 1–3) is predictable for 25 to 45 d, the time taken for the error variance to reach 50 % to 70 % of saturation. These scales never reach 90 % of saturation during the forecasts. The upper-level tropical PW divergence is even more predictable than Q (40 to 50 d). In contrast, the PW component of the 200 hPa Rossby wave source, which is responsible for propagating the influence of tropical heating to the extratropics, is only predictable for 20 to 30 d. A substantial ensemble spread of 300 hPa meridional wind propagates from the tropics to the Northern Hemisphere storm-track regions by days 15–16. Following the growth of upper-tropospheric spread in planetary wave heat flux, the stratosphere provides a feedback in enhancing the error via downward propagation towards the end of the reforecasts.

Robust synchronization of coupled logical networks subject to stochastic function perturbations

This article analyzes the robust synchronization of coupled logical networks (LNs) subject to stochastic function perturbations (SFPs). Firstly, by defining a synchronization states set, the robustness of synchronization with probability one (SPO) is divided into two cases. According to these two cases, the rough reachable set and refined reachable set are constructed, based on which, several criteria are derived for the robust SPO of coupled LNs with SFPs. Secondly, with the help of rough reachable set and refined reachable set, several necessary and sufficient conditions are proposed to verify the synchronization in distribution of coupled LNs with SFPs. Finally, the obtained theoretical results are applied to an idealized model of protein-nucleic acid interactions.

Homogenization of Schrödinger equations. Extended effective mass theorems for non-crystalline matter

This paper concerns the homogenization of Schrödinger equations for non-crystalline matter, that is to say the coefficients are given by the composition of stationary functions with stochastic deformations. Two rigorous results of so-called effective mass theorems in solid state physics are obtained: a general abstract result (beyond the classical stationary ergodic setting), and one for quasi-perfect materials (i.e. the disorder in the non-crystalline matter is limited). The former relies on the double-scale limits and the wave function is spanned on the Bloch basis. Therefore, we have extended the Bloch Theory which was restricted until now to crystals (periodic setting). The second result relies on the Perturbation Theory and a special case of stochastic deformations, namely stochastic perturbation of the identity.

On probabilistic entropies application in uniaxial deformation of hyper‐elastic materials

AbstractUncertainty quantification and reliability assessment for uniaxial tension of some hyper‐elastic material characterized by a few different constitutive equations is analyzed in this paper. The stretch of hyper‐elastic material is adopted as the Gaussian input with given expected value's range relevant to the experimentation and constant standard deviation. This goal is achieved with the use of the stochastic perturbation technique to calculate the first two probabilistic moments of the increasing tensile stress. Additionally, the Shannon probabilistic entropy fluctuations are determined for this test. Finally, reliability index is calculated using the stress‐based limit function and two reliability approaches–the First Order Reliability Method and the Bhattacharyya relative entropy.

A Simplified Controller Design for Fixed/Preassigned-Time Synchronization of Stochastic Discontinuous Neural Networks

This paper addresses the synchronization problem of delayed stochastic neural networks with discontinuous activation functions (DSNNsDF), specifically focusing on fixed/preassigned-time synchronization. The objective is to develop a class of simplified controllers capable of effectively addressing the challenges posed by time delays, discontinuous activation functions, and stochastic perturbations during the synchronization process. In this regard, we propose several controllers with simpler structures to achieve the desired preassigned-time synchronization (PTS) result. To enhance the accuracy of time estimation, stochastic fixed-time control theory is employed. Rigorous numerical simulations are conducted to validate the effectiveness of our approach. The utilization of our proposed results significantly improves the performance of the synchronization controller for DSNNsDF, thereby enabling advancements and diverse applications in the field.

"On Stability of One Mathematical Model of the Epidemic Spread Under Stochastic Perturbations"

"On Stability of One Mathematical Model of the Epidemic Spread Under Stochastic Perturbations"

State estimation of a physical system with unknown governing equations

State estimation is concerned with reconciling noisy observations of a physical system with the mathematical model believed to predict its behaviour for the purpose of inferring unmeasurable states and denoising measurable ones1,2. Traditional state-estimation techniques rely on strong assumptions about the form of uncertainty in mathematical models, typically that it manifests as an additive stochastic perturbation or is parametric in nature3. Here we present a reparametrization trick for stochastic variational inference with Markov Gaussian processes that enables an approximate Bayesian approach for state estimation in which the equations governing how the system evolves over time are partially or completely unknown. In contrast to classical state-estimation techniques, our method learns the missing terms in the mathematical model and a state estimate simultaneously from an approximate Bayesian perspective. This development enables the application of state-estimation methods to problems that have so far proved to be beyond reach. Finally, although we focus on state estimation, the advancements to stochastic variational inference made here are applicable to a broader class of problems in machine learning.

A generalist predator–prey system with the effects of fear and refuge in deterministic and stochastic environments

In the present study, we investigate the dynamics of a generalist predator–prey system by considering that the fear of predators suppresses the birth rate and enhances the intraspecies competition of the prey species. Also, we assume that a constant proportion of the prey population is taking refuge, which results in a reduction in the predation pressure. We consider Cosner functional response to describe the interactions between prey and predator species. We rigorously analyze the proposed model analytically as well as numerically. We see that the system exhibits multi-stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including saddle–node, Hopf and transcritical bifurcations with varying degrees of fear, on the prey’s reproduction and intraspecies competition, induced by the predator species. The emergence of multistability scenarios in the system is also stimulated by the birth rate of prey species and the growth in predator species due to the additional food sources. We modify our proposed model to its stochastic counterpart by considering the impact of environmental white noises on the natural death rates of both prey and predator species. The simulation results for the stochastic system demonstrate that the fluctuations in the densities of prey and predator populations due to stochastic perturbations are highly sensitive to the intensities of the environmental noises. Additionally, we find that the stochastic system showcases noise-induced transitions whenever the deterministic system exhibits bistability.

A stochastic variant of replicator dynamics in zero-sum games and its invariant measures

We study the behavior of a stochastic variant of replicator dynamics in two-agent zero-sum games. Inspired by the well studied deterministic replicator equation, this model gives arguably a more realistic description of real world settings and, as we demonstrate here, exhibits totally distinct behavior when compared to its deterministic counterpart which is known to be recurrent. In more detail, we characterize the statistics of such systems by their invariant measures which can be shown to be entirely supported on the boundary of the space of mixed strategies. Depending on the noise strength we can furthermore characterize these invariant measures by finding accumulation of mass at specific parts of the boundary. In particular, regardless of the magnitude of noise, we show that any invariant probability measure is a convex combination of Dirac measures on pure strategy profiles, which correspond to vertices/corners of the agents’ simplices. Thus, in the presence of stochastic perturbations, even in the most classic zero-sum settings, such as Matching Pennies, we observe a stark disagreement between the axiomatic prediction of Nash equilibrium and the evolutionary emergent behavior derived by an assumption of stochastically adaptive, learning agents.

Distributed Adaptive-Neural Finite-Time Consensus Control for Stochastic Nonlinear Multiagent Systems Subject to Saturated Inputs.

In this article, the problem of distributed finite-time consensus control for a class of stochastic nonlinear multiagent systems (MASs) (with directed graph communication) in the presence of unknown dynamics of agents, stochastic perturbations, external disturbances (mismatched and matched), and input saturation nonlinearities is addressed and studied. By combining the backstepping control method, the command filter technique, a finite-time auxiliary system, and artificial neural networks, innovative control inputs are designed and proposed such that outputs of follower agents converge to the output of the leader agent within a finite time. Radial-basis function neural networks (RBFNNs) are employed to approximate unknown dynamics, stochastic perturbations, and external disturbances. To overcome the complexity explosion problem of the conventional backstepping method, a novel finite-time command filter approach is proposed. Then, to deal with the destructive effects of input saturation nonlinearities, the finite-time auxiliary system is designed and developed. By mathematical analysis, it is proven that the mentioned MAS (injected by the proposed control inputs) is semiglobally finite-time stable in probability (SGFSP) and all consensus tracking errors converge to a small neighborhood of the zero during a finite time. Finally, a numerical simulation onto a group of four single-link robot manipulators is carried out to illustrate the effectiveness of the suggested control scheme.

Switching Event-Triggered Adaptive Resilient Dynamic Surface Control for Stochastic Nonlinear CPSs With Unknown Deception Attacks.

This work concentrates on the adaptive resilient dynamic surface controller design problem for uncertain nonlinear lower triangular stochastic cyber-physical systems (CPSs) subject to unknown deception attacks based on a switching threshold event-triggered mechanism. The adverse effect of deception attacks on the stochastic CPSs is that the exact system state variables become unavailable. Furthermore, it should be emphasized that the coexistence of unknown nonlinearities, stochastic perturbations, and unknown sensor and actuator attacks makes it a very difficult and challenging event to implement the control design. To get the desired controller, radial basis function (RBF) neural networks (NNs) are introduced so that the design obstacle caused from the unknown nonlinearities can be easily solved. On this basis, in order to save resources and effectively transmit, the event-triggered control scheme based on a switching threshold strategy is further considered. In the backstepping design process, the dynamic surface control (DSC) technique is presented to deal with the issue of "explosion of complexity." By skillfully designing a new coordinate transformation and the attack compensators, the problem of unknown deception attacks is successfully handled. Under our proposed control scheme, all the closed-loop signals are bounded in probability and the stabilization errors converge to an adjustable neighborhood of the origin in probability. Finally, the simulation results on the double chemical reactor show the validity of the proposed design scheme.

Stochastic Gradient Perturbation: An Implicit Regularizer for Person Re-Identification

Generalization of the person re-identification (ReID) model plays an important role in practical application, and we discuss a simple yet effective regularizer to improve it inspired by Adversarial Training (AT). AT has been indicated as an advanced regularizer due to its adversarial mechanism, ability to mine hard samples, and nature of data augmentation. However, serving as an augmentation-based regularizer, AT shows low diversity of the perturbation, excessive computational cost, and the optimization dilemma between adversarial robustness and accuracy for ReID task, and is thus suboptimal. To tackle these limitations and get a more effective regularizer for ReID, we rethink the nature of AT and unveil that the adversarial data augmentation is essentially reflected by gradients. Based on this, a novel implicit regularizer, named Stochastic Gradient Perturbation (SGP), is proposed, which naturally brings three merits: 1) Better diversity of the perturbation due to the proposed non-directional stochastic perturbations rather than directional adversarial perturbations. 2) Lower computational cost due to the proposed implicit gradient augmentation rather than explicitly additional data. 3) The optimization dilemma of the adversarial robustness and generalization is naturally overcome since SGP contains the adversarial gradient perturbation. Further, we put forward a perspective that the generalization and adversarial robustness may have an inter unity. Experiments on the baseline and SOTA models demonstrate powerful performances of the plugged-played SGP, and both generalization and adversarial robustness can be guaranteed.

Correction to: Formalism for stochastic perturbations and analysis in relativistic stars

Correction to: Formalism for stochastic perturbations and analysis in relativistic stars

Impacts of the stochastically perturbed parameterization on the precipitation ensemble forecasts of the Betts–Miller–Janjić (BMJ) scheme in Eastern China

This study investigated the impact of stochastic perturbations on precipitation forecasts generated by the Betts-Miller-Janjic (BMJ) cumulus parameterization scheme. Two types of stochastic perturbation approaches were compared. The first approach involved perturbing the temperature and humidity tendencies derived from the BMJ scheme. The second approach focused on perturbing the reference profiles of temperature and humidity estimated within the BMJ scheme. These profile perturbations led to reference profiles becoming either warmer and wetter or colder and drier. Ten precipitation cases occurring in eastern China during the summer of 2019 were selected to evaluate the different perturbation methods. The default BMJ scheme exhibited a significant wet bias at the light rain threshold due to overestimating entropy change and a dry bias at the heavier rain threshold. The tendency perturbation approach, which perturbed the temperature and humidity, did not affect the entropy change and produced precipitation placement similar to its unperturbed counterpart. These attributes resulted in a small ensemble spread and relatively low forecast skill scores. Perturbing the reference profiles, conversely, influenced the entropy change in the BMJ scheme, leading to a larger ensemble spread and higher forecast skill scores regarding the spatial distribution of precipitation. Asymmetrically perturbing the reference profiles considered the wet bias, which increased the grid points with negative entropy change and outperformed the symmetric perturbation. The asymmetric perturbation also increased the chance of heavier rain because more water was retained in the air, alleviating the corresponding dry bias.

Improved artificial potential field route planning method based on stochastic perturbation

As a typical route planning algorithm, the APF method has been widely used in robotics, autopilot and other fields. However, it also has weakness in local optimal point. In computer science and mathematics, stochastic perturbation is an accepted approach that can assist optimization algorithms leave the local optimal solution and achieve the global optimal solution as well as improve robustness and adaptability in specific application situations. therefore, the problem can be successfully solved by using stochastic perturbation. In this article, the traditional APF improved through stochastic perturbation. When the robot is running in an APF, the distance between the robot and the target point is calculated at all times. If the distance between the robot and the target point remains unchanged for a period of time or if the stop point oscillates, it is determined whether the robot has reached the target point at this time. If not, it is determined that the robot has fallen into a local optimal point at this time. After completing the judgment, stochastic perturbation is applied to the robot, causing it to jump out of the local optimal point and continue to navigate to the target point. The results of the comparison between the paths generated by the traditional method and the improved method validate the effectiveness of this method.

A forecast-model-based extreme weather event attribution system developed for Aotearoa New Zealand

A largely automated extreme weather event (EWE) attribution system has been developed that uses the Weather Research and Forecast numerical weather prediction model to simulate EWEs under current and pre-industrial climate conditions. The system has been applied to two extreme precipitation events in Aotearoa New Zealand with the goal of quantifying the effect of anthropogenic climate change on the severity of these events. The forecast simulation of the target event under current climate conditions constitutes the first scenario (ALL). We then apply a climate change signal in the form of delta fields in sea-surface temperature, atmospheric temperature and specific humidity, creating a second ‘naturalised’ scenario (NAT) which is designed to represent the weather system in the absence of human interference with the climate system. A third scenario, designed to test for coherence, is generated by applying deltas of opposite sign compared to the naturalised scenario (ALL+). Each scenario comprises a 22-member ensemble which includes one simulation that was not subject to stochastic perturbation. Comparison of the three ensembles shows that: (1) the NAT ensemble develops an extreme event which resembles the observed event, (2) the severity, i.e. maximum intensity and/or the size of area affected by heavy precipitation, changes when naturalising the boundary conditions, (3) the change in severity is consistently represented within the three scenarios and the signal is robust across the different ensemble members, i.e. it is typically shown in most of the 22 ensemble members. Thus, the attribution system presented here can be used to provide information about the influence of anthropogenic climate change on the severity of specific extreme events.

Physically based stochastic perturbations improve a high‐resolution forecast of convection

AbstractA physically based stochastic perturbation (PSP) scheme has been implemented in the convection‐permitting ICON‐D2 ensemble prediction system at Deutscher Wetterdienst (DWD) and run for a three‐month trial experiment in summer 2021. The scheme mimics the impact of boundary‐layer turbulence on the smallest resolved scales and impacts convective precipitation in particular. A weather‐regime‐dependent systematic evaluation shows that PSP efficiently increases ensemble spread of precipitation in weak synoptic forcing, while producing realistic convective structures. During strong forcing, the effect of the scheme is negligible, as expected by design. A probabilistic verification shows improvements in the forecast skill of other variables as well, especially the spread‐to‐skill ratio, but identifies starting points for further improvements of the method.

Novel stability conditions for some generalization of Nicholson's blowflies model with stochastic perturbations

We consider a generalization of the well-known nonlinear Nicholson blowflies model with stochastic perturbations. Stability in probability of the positive equilibrium of the considered equation is studied. Two types of stability conditions: delay-dependent and delay-independent conditions are obtained, using the method of Lyapunov functionals and the method of linear matrix inequalities. The obtained results are illustrated by numerical simulations by means of some examples. The results are new, and complement the existing ones. doi: 10.1017/S1446181123000147

Fixed-Time Synchronization of Complex-Valued Coupled Networks with Hybrid Perturbations via Quantized Control

This paper considers the fixed-time synchronization of complex-valued coupled networks (CVCNs) with hybrid perturbations (nonlinear bounded external perturbations and stochastic perturbations). To accomplish the target of fixed-time synchronization, the CVCNs can be separated into their real and imaginary parts and establish real-valued subsystems, a novel quantized controller is designed to overcome the difficulties induced by complex parameters, variables, and disturbances. By means of the Lyapunov stability theorem and the properties of the Wiener process, some sufficient conditions are presented for the selection of control parameters to guarantee the fixed-time synchronization, and an upper bound of the setting time is also obtained, which is only related to parameters of both systems and the controller, not to the initial conditions of the systems. Finally, a numerical simulation is given to show the correctness of theoretical results and the effectiveness of the control strategy.

Assessing geometrical uncertainties in geological interface models using Markov chain Monte Carlo sampling via abstract graph

Uncertainty assessment is a common requirement in 3D modeling applications. The Markov chain Monte-Carlo (MCMC) method is a practical way to generate multiple realizations of 3D models to evaluate model uncertainty. However, when probing high-dimensional target distributions related to the detailed geometry of 3D geological interfaces, the generating 3D models by existing MCMC methods always suffer from the presence of artifacts in large geometrical deformation that modeling deformed geometries in stochastic perturbation, which limits their effectiveness and efficiency. This paper presents an abstract graph-based MCMC method for the uncertainty assessment of 3D geological interfaces. An abstract graph is used to represent the reasonable shape of the geological interface. In proposing new candidate 3D models via the MCMC iterations, the 3D models are perturbed such that the energy function measuring the distortion of the abstract graph is minimized in a least-squares sense. This can preserve the plausible geometry of the 3D models against high perturbations and provide artifact-free 3D models as candidates for MCMC sampling. The resulting MCMC iterations enable the drawing of probable realizations of 3D models while maintaining a high acceptance rate in probing the complicated target distributions of 3D geological interface models. The proposed method was applied to the assessment of uncertainties in three regional faults in the Jiaodong Peninsula, eastern China. The uncertainty assessment was carried out based on a complex probability distribution with consideration of geological-geophysical observations and prior knowledge of fault geometry. The results show that the proposed MCMC method could reasonably locate the uncertainties in free-form fault models defined by thousands of constraints. And the abstract graph-based MCMC method can sample highly-perturbed and geometrically plausible 3D models in high-resolution, which is crucial to the effectiveness and efficiency of the geometrical uncertainty assessment.