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1. Out-of-time-ordered correlator in the one-dimensional Kuramoto-Sivashinsky and Kardar-Parisi-Zhang equations

   https://doi.org/10.1103/PhysRevE.108.054112  

   Roy, Dipankar; Huse, David A.; Kulkarni, Manas (November 2023, Physical Review E)

   The out-of-time-ordered correlator (OTOC) has emerged as an interesting object in both classical and quantum systems for probing the spatial spread and temporal growth of initially local perturbations in spatially extended chaotic systems. Here, we study the (classical) OTOC and its “light cone” in the nonlinear Kuramoto-Sivashinsky (KS) equation, using extensive numerical simulations. We also show that the linearized KS equation exhibits a qualitatively similar OTOC and light cone, which can be understood via a saddle-point analysis of the linearly unstable modes. Given the deep connection between the KS (deterministic) and the Kardar-Parisi-Zhang (KPZ, which is stochastic) equations, we also explore the OTOC in the KPZ equation. While our numerical results in the KS case are expected to hold in the continuum limit, for the KPZ case it is valid in a discretized version of the KPZ equation. More broadly, our work unravels the intrinsic interplay between noise/instability, nonlinearity, and dissipation in partial differential equations (deterministic or stochastic) through the lens of OTOC. 

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2. Design of a Stochastic Traffic Regulator for End-to-End Network Delay Guarantees

   https://doi.org/10.1109/TNET.2022.3181858  

   Boroujeny, Massieh Kordi; Mark, Brian L. (June 2022, IEEE/ACM Transactions on Networking)

   Providing end-to-end network delay guarantees in packet-switched networks such as the Internet is highly desirable for mission-critical and delay-sensitive data transmission, yet it remains a challenging open problem. Since deterministic bounds are based on the worst-case traffic behavior, various frameworks for stochastic network calculus have been proposed to provide less conservative, probabilistic bounds on network delay, at least in theory. However, little attention has been devoted to the problem of regulating traffic according to stochastic burstiness bounds, which is necessary in order to guarantee the delay bounds in practice. We design and analyze a stochastic traffic regulator that can be used in conjunction with results from stochastic network calculus to provide probabilistic guarantees on end-to-end network delay. Two alternative implementations of the stochastic regulator are developed and compared. Numerical results are provided to demonstrate the performance of the proposed stochastic traffic regulator. 

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3. Stochastic dynamics of mechanical systems with impacts via the Step Matrix multiplication based Path Integration method

   https://doi.org/10.1007/s11071-024-09513-y  

   Sykora, Henrik T.; Kuske, Rachel; Yurchenko, Daniil (April 2024, Nonlinear Dynamics)

   Abstract In this work we propose the Step Matrix Multiplication based Path Integration method (SMM-PI) for nonlinear vibro-impact oscillator systems. This method allows the efficient and accurate deterministic computation of the time-dependent response probability density function by transforming the corresponding Chapman–Kolmogorov equation to a matrix–vector multiplication using high-order numerical time-stepping and interpolation methods. Additionally, the SMM-PI approach yields the computation of the joint probability distribution for response and impact velocity, as well as the time between impacts and other important characteristics. The method is applied to a nonlinear oscillator with a pair of impact barriers, and to a linear oscillator with a single barrier, providing relevant densities and analysing energy accumulation and absorption properties. We validate the results with the help of stochastic Monte-Carlo simulations and show the superior ability of the introduced formulation to compute accurate response statistics. 

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4. Robust Topology Design Optimization Based on Dimensional Decomposition Method

   Ren, Xuchun; Zhang, Xiaodong (January 2019, Mechanics and Engineering – Numerical Calculation and Data analysis , 2019 in Beijing)

   Abstract This paper presents an efficient approach for robust topology design optimization (RTO) which is based on polynomial dimensional decomposition (PDD) method. The level-set functions are adopted to facilitate the topology changes and shape variations. The topological derivatives of the functionals of robustness root in the concept of deterministic topological derivatives and dimensional decomposition of stochastic responses of multiple random inputs. The PDD for calculating robust topological derivatives consists of only a number of evaluations of the deterministic topological derivatives at the specified points in the stochastic space and provides effective and efficient design sensitivity analyses for RTO. The numerical examples demonstrate the effectiveness of the present method. 

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5. State-space modeling for degrading systems with stochastic neural networks and dynamic Bayesian layers

   https://doi.org/10.1080/24725854.2023.2185323  

   Farhat, Md Tanzin; Moghaddass, Ramin (February 2023, IISE Transactions)

   To monitor the dynamic behavior of degrading systems over time, a flexible hierarchical discrete-time state-space model (SSM) is introduced that can mathematically characterize the stochastic evolution of the latent states (discrete, continuous, or hybrid) of degrading systems, dynamic measurements collected from condition monitoring sources (e.g., sensors with mixed-type out-puts), and the failure process. This flexible SSM is inspired by Bayesian hierarchical modeling and recurrent neural networks without imposing prior knowledge regarding the stochastic structure of the system dynamics and its variables. The temporal behavior of degrading systems and the relationship between variables of the corresponding system dynamics are fully characterized by stochastic neural networks without having to define parametric relationships/distributions between deterministic and stochastic variables. A Bayesian filtering-based learning method is introduced to train the structure of the proposed framework with historical data. Also, the steps to utilize the proposed framework for inference and prediction of the latent states and sensor outputs are dis-cussed. Numerical experiments are provided to demonstrate the application of the proposed framework for degradation system modeling and monitoring. 

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