Stochastic Motion Research Articles

Applications of Neuro Deep Learning Models in Predictive Data Analytics for the Movements and Trends of the Indian Stock Market: Financial Data Mining, Nonlinearity, and Quantum Finance

The financial world of today is high-frequency data-driven and characterized by the application and use of information technology for better business development and decision-making. The price movements of stock markets are mainly influenced by micro and macroeconomic variables, legal frameworks, and taxation policies of the respective economies. The crux of the issue lies in exactly forecasting the future stock price movements of individual firms, based on historical prices. Achieving accuracy for forecasting the market trend has become difficult due to the prevalence of stochastic behaviour in the stock market and volatility in the stock prices. This paper analyzes the stochastic movement pattern of the highly volatile thirty individual company stocks (in terms of market capitalization) of BSE-Sensex, using the Neuro Deep Learning method, a model of deep learning approach. The findings of the study would help the investors, to make rational and well-informed investment decisions, and to optimize the returns by investing in the most valuable stocks of listed corporate enterprises.

Complex stochastic optimal control foundation of quantum mechanics

Abstract Recent studies have extended the use of the stochastic Hamilton-Jacobi-Bellman (HJB) equation to include complex variables for deriving quantum mechanical equations. However, these studies often assume that it is valid to apply the HJB equation directly to complex numbers, an approach that overlooks the fundamental problem of comparing complex numbers when finding optimal controls. This paper explores the application of the HJB equation in the context of complex variables. It provides an in-depth investigation of the stochastic movement of quantum particles within the framework of stochastic optimal control theory. We obtain the complex diffusion coefficient in the stochastic equation of motion using the Cauchy-Riemann theorem, considering that the particle’s stochastic movement is described by two perfectly correlated real and imaginary stochastic processes. During the development of the covariant form of the HJB equation, we demonstrate that if the temporal stochastic increments of the two processes are perfectly correlated, then the spatial stochastic increments must be perfectly anti-correlated, and vice versa. The diffusion coefficient we derive has a form that enables the linearization of the HJB equation. The method for linearizing the HJB equation, along with the subsequent derivation of the Dirac equation, was developed in our previous work [V. Yordanov, Scientific Reports 14, 6507 (2024)]. These insights deepen our understanding of quantum dynamics and enhance the application of stochastic optimal control theory to quantum mechanics.

Dynamic reliability assessment for high CFRDs incorporating ground motion and material parameter variability via GPDEM

The randomness of earthquake and material parameters significantly impacts the seismic response and dynamic reliability of geotechnical engineering structures. In this study, a dynamic reliability analysis method for high concrete face rockfill dams (CFRDs) under the influence of random factors is proposed by combining random sample generation methods with the generalized probability density evolution method (GPDEM). Firstly, the spectral representation-random function method is employed to achieve dimensionality reduction expression for intensity-frequency non-stationary ground motion. Sensitivity analysis is then used to identify the random variables of the rockfill constitutive model, and the improved generalized F-discrepancy (GF-discrepancy) method is utilized to generate random material parameters. Then, the random samples of earthquake and material parameter are introduced into the finite element calculation of CFRD, conducting a series of dynamic finite element calculations. Finally, GPDEM is used to derive probability information and dynamic reliability from the deterministic time history responses. The results indicate that random factors contribute to the variability of seismic response and dynamic reliability. Stochastic ground motion significantly affects extreme values, while variability in material parameters has a more pronounced influence on the overall process of seismic response. These findings provide valuable references for the seismic design of CFRDs.

Unified framework for stochastic dynamic responses and system reliability analysis of long-span cable-stayed bridges under near-fault ground motions

Long-span cable-stayed bridges are complex systems with numerous components, and prone to failures of multiple components under near-fault ground motions with long-period velocity pulses. The evaluation of dynamic system reliability of cable-stayed bridges is an important challenging issue. In this work, a unified framework for simultaneously determining both the stochastic dynamic responses and system reliabilities of long-span cable-stayed bridges under near-fault stochastic ground motions is proposed based on direct probability integral method (DPIM) with adaptive strategy. Firstly, the 3-dimensional finite element model of typical cable-stayed bridge and the stochastic synthesis model of near-fault ground motions are established. Based on probability density integral equation, new formulas in input probability space of time-variant moments of response are derived. Then, DPIM with adaptive strategy is suggested to calculate the mean value and standard deviation of response via new formulas. Dynamic system reliability of cable-stayed bridge under near-fault stochastic ground motions is evaluated by establishing failure criteria of extreme value mappings of multiple performance functions. Finally, numerical results indicate that the long-period velocity pulse of near-fault motions imposes an important effect, resulting in large mean responses and failure of cables. Failure probability of cables is significantly increased with the occurrence of velocity pulses, which causes the decrease of system reliability of cable-stayed bridge. Thus, the randomness and velocity pulse effect of near-fault ground motions should be seriously considered for reliability-based design and safety assessment of cable-stayed bridges.

Probabilistic solution of non-linear random ship roll motion by data-driven method

In this paper, a data-driven method is employed to investigate the probability density function (PDF) of nonlinear stochastic ship roll motion. The mathematical model of ship roll motion comprises a linear term with cubic damping and a nonlinear restoring moment represented as an odd-degree polynomial up to the fifth order. The data-driven method integrates maximum entropy, the pseudo-inverse algorithm, and a backpropagation (BP) neural network to obtain the PDF. The process begins with simulating data for the nonlinear stochastic system, followed by dimensional analysis to identify dimensionless parameter clusters. Optimization algorithms are then employed to solve for the coefficients, leading to the development of a BP neural network model trained to predict the PDF across various system characteristics and excitation intensities. The method's effectiveness is validated with Monte Carlo simulations, demonstrating high accuracy and reduced sensitivity to parameter variations.

Probabilistic Performance-Pattern Decomposition (PPPD): Analysis framework and applications to stochastic mechanical systems

Numerous research efforts have been devoted to developing quantitative solutions to stochastic mechanical systems. In general, the problem is perceived as “solved” when a complete or partial probabilistic description on quantities of interest (QoIs) is determined. However, in the presence of complex system behavior, there is a critical need to go beyond computing probabilities. In fact, to gain a better understanding of the system, it is crucial to extract physical characterizations from the probabilistic structure of the QoIs, especially when the QoIs are computed in a data-driven fashion. Motivated by this perspective, the paper proposes a framework to obtain structuralized characterizations on behaviors of stochastic systems. The framework is named Probabilistic Performance-Pattern Decomposition (PPPD). PPPD analysis aims to decompose complex response behaviors, conditional to a prescribed performance state, into meaningful patterns in the space of system responses, and to investigate how the patterns are triggered in the space of basic random variables. To illustrate the application of PPPD, the paper studies three numerical examples: (1) an illustrative example with hypothetical stochastic processes input and output; (2) a stochastic Lorenz system with periodic as well as chaotic behaviors; and (3) a simplified shear-building model subjected to a stochastic ground motion excitation.

Physically adjusted ground motion prediction equations for induced seismicity at Preston New Road, UK

Predicting ground motions due to induced seismicity is a challenging task owing to the scarcity of data and heterogeneity of the uppermost crust. Dealing with this requires a thorough understanding of the underlying physics and consideration of inter-site variability. The most common ground motion model used in practice is the parametric ground motion prediction equation (GMPE), of which hundreds exist in the literature. However, relatively few are developed with a focus on induced seismicity. Developing GMPEs that are specific to an appropriate magnitude-distance range (R<30\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R < 30$$\\end{document} km; 2≤M≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2 \\le M \\le 6$$\\end{document}) is important for induced seismicity applications. This paper proposes a framework for the development of physically-based GMPEs to provide more accurate and reliable estimates of the potential induced-seismicity ground motion hazard, allowing for better risk assessment and management strategies. To demonstrate this approach, a new set of GMPEs for the 2018-2019 induced seismicity sequence at the Preston New Road (PNR) shale gas site near Blackpool, United Kingdom, is presented. The physically-based GMPE was developed based on a pseudo-finite-fault stochastic ground motion simulation, calibrated with parameters derived from the spectral analysis of weak-motion records from induced seismic events. An optimization-based calibration technique using the area metric (AM) was subsequently performed to calibrate optimal parameters for simulating ground motion at the PNR site. Finally, using a suite of forward simulations for events with 1≤M≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\le M \\le 6$$\\end{document} recorded at distances up to 30 km, combined with empirical data, a location-specific GMPE was derived through adjustment of an existing model.

Spectral Indices and Evidence of Wave–Wave Modulation in Observations of the Interplanetary Magnetic Field

We present wave and turbulence observations from the DSCOVR spacecraft during the 2017 September solar flare and coronal mass ejection (CME) events. On September 4–12, the spectral index within the magnetic field power spectral density inertial range was consistent with Kolmogorov −5/3. This is despite the 9 days being composed of a complex mix of different features, including solar flares, solar energetic particle events, and CMEs. When analyzing shorter time periods, the spectral index varies. For two days where there were consecutive CMEs, the index follows Kraichnan–Iroshinikov −3/2, while on two quiet days, it was a mixture of −1, −3/2, and −2. The inertial range spectral index taken over the entire 9 days hides or averages out spectral features that occur over shorter time periods. We use a more realistic estimate of the amount of Doppler shifting into the spacecraft frame to show that the break frequencies on most days were located close to the H+ cyclotron frequency. We present evidence of wave–wave modulation and suggest that lower-frequency waves in the solar wind can modulate the growth rates/propagation of ion cyclotron waves, providing a method to transfer energy in the solar wind to smaller scales. Furthermore, we suggest that the indices in the inertial range can be explained by combining containment due to wave generation/propagation and stochastic Brownian motion in the solar wind. When these two phenomena are equal, they combine to create a −3/2 index.

Utilization of stochastic ground motion simulations for scenario-based performance assessment of geo-structures

Probabilistic seismic performance assessments of engineered structures can be highly sensitive to the seismic input excitation and its variability. In the present study, the scenario-based performance assessment recommended by Federal Emergency Management Agency (FEMA) P-58 guidelines is adopted to estimate seismic fragility of concrete dams for various seismic hazard scenarios. Due to the scarcity of recorded ground motions and thereby their poor representation of uncertainties, stochastic ground motion simulation methods are utilized to obtain the required input excitations. Moreover, to understand the uncertainty in ground motion simulation models, two broadband stochastic simulation models are used to generate input excitations representing six seismic hazard scenarios defined by earthquake magnitude, source-to-site distance, and soil conditions.Optimal intensity measure parameters for each scenario are identified using a systematic procedure that considers criteria such as efficiency, practicality, proficiency, sufficiency, and hazard compatibility. Fragility curves and surfaces are derived using the cloud analysis technique, taking into account various damage measures and limit state functions. The study finds that the derived fragility curves are particularly sensitive to the selection of earthquake scenarios, the choice of records, and the methods used to calculate fragility curves, with less sensitivity observed to different engineering demand parameters. Given this sensitivity, particularly to ground motion selection, the study highlights the necessity of incorporating both model-to-model variability (epistemic uncertainty) and record-to-record variability (aleatory uncertainty), alongside the established material and modeling uncertainties, in the probabilistic seismic assessment.

Computational modeling of near-fault earthquake-induced landslides considering stochastic ground motions and spatially varying soil

Landslides represent a large-deformation process influenced by various factors of uncertainty, such as types of ground motion (GM), randomness of GMs, and spatial variability of soils. The behavior of landslides is profoundly affected, making their assessment and measurement challenging. This paper proposes a computational approach for simulating the large-deformation process of landslides based on three-dimensional (3D) non-ordinary state-based peridynamics (NOSBPD). The analysis results of NOSBPD indicate that the mean runout distance triggered by pulse-like ground motions (PLGMs) is 16% greater than that induced by non-pulse ground motions (NPGMs), suggesting that PLGMs exhibit higher destructiveness. Besides, this paper establishes a runout distance assessment framework by considering the stochastic nature of PLGMs. This framework allows for the evaluation of the specific risk probability of landslides caused by stochastic PLGMs that match the target spectrum specified by codes. By introducing the theory of random fields and implementing a coupled procedure in peridynamics, we conducted a detailed analysis of the impact of spatial heterogeneity on the evolution process and consequences of landslides. Additionally, compared to two-dimensional (2D) analysis, the mean runout distance obtained from 3D analysis increased by 27.5%. This suggests that 2D analysis may underestimate the consequences of landslides. The findings of this study can serve as a scientific foundation for predicting the extent and scope of landslides triggered by near-fault earthquakes.

Time-domain dimension-reduction representation for stochastic ground motion utilizing filtered white noise

A method is proposed for characterizing and simulating both stationary and fully non-stationary stochastic ground motions. This method is based on discrete filtered white noise models, including single and double filtered, with the latter is introduced to suppress low-frequency components. Specifically, the proposed method expresses seismic ground motion as a linear combination of products involving orthogonal random variables and deterministic functions. Further, by defining high-dimensional orthogonal random variables as orthogonal functions of extremely low dimensional elementary random variables, efficient dimension-reduction (DR) of primitive ground motion process can be achieved. To illustrate this concept, three distinct categories of random orthogonal functions involving only one or two elementary random variables are examined, employing filtered white noise models to simulate ground motion acceleration processes, thereby demonstrating the accuracy and efficiency of the proposed method. Simultaneously, recommendations for employing the proposed method in simulations are provided based on an analysis of the impacts of various parameters on random ground motion processes. Case studies demonstrate the accuracy and robustness of the proposed method compared to Monte Carlo (MC) methods. Furthermore, case studies on fully non-stationary ground motion highlight the practical applicability of the proposed method in engineering.

UAV-assisted dependency-aware computation offloading in device–edge–cloud collaborative computing based on improved actor–critic DRL

Unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) has become a popular research topic, addressing challenges posed by the pressure of cloud computing and the limited service scope of MEC. However, the limited computing resources of UAVs and the data dependency of specific tasks hinder the practical implementation of efficient computational offloading (CO). Accordingly, a device–edge–cloud collaborative computing model is proposed in this study to provide complementary offloading services. This model considers stochastic movement and channel obstacles, representing the dependency relationships as a directed acyclic graph. An optimization problem is formulated to simultaneously optimize system costs (i.e., delay and energy consumption) and UAV endurance, taking into account resource and task-dependent constraints. Additionally, a saturated training SAC-based UAV-assisted dependency-aware computation offloading algorithm (STS-UDCO) is developed. STS-UDCO learns the entropy and value of the CO policy to efficiently approximate the optimal solution. The adaptive saturation training rule proposed in STS-UDCO dynamically controls the update frequency of the critic based on the current fitted state to enhance training stability. Finally, extensive experiments demonstrate that STS-UDCO achieves superior convergence and stability, while also reducing the system total cost and convergence speed by at least 11.83% and 39.10%, respectively, compared with other advanced algorithms.

Assessing seismic hazard and uncertainty in Büyükçekmece using ground motion simulations

This study presents a comprehensive seismic hazard assessment for Büyükçekmece, a district in Istanbul, Turkey, situated near the seismically active North Anatolian Fault (NAF). The study utilizes stochastic ground motion simulations with the validated EXSIM algorithm to understand the potential impact of medium to large-magnitude earthquakes (ranging from MW 6.3 to 7.42) on this vulnerable community. The research employs a site-specific approach, considering unique amplification factors for each location. By conducting 50 scenario-based simulations, the study assesses the seismic hazard, highlighting the importance of comprehending variations in ground motion, even when they are small, for a more precise hazard assessment. Furthermore, this study addresses the critical issue of uncertainty, particularly concerning stress parameters and hypocenter locations. The researchers demonstrate that variability in these factors can introduce substantial uncertainty in ground motion predictions. The study provides insights into the range of potential ground motion outcomes through probabilistic assessments involving multiple scenarios and stress drop values. Notably, the results indicate that ground motion levels vary with earthquake magnitudes and underscore the significance of accounting for this variability. This research emphasizes the seismic vulnerability of Büyükçekmece and the importance of accurate ground motion simulations, offering valuable insights for earthquake preparedness and mitigation efforts in the region.

Bridging multi-level vehicle behavioural patterns with long-term pavement condition: a bidirectional modelling approach for progressively mixed autonomous traffic flow

The increasing of AVs’ market penetration rate (MPR) changes the traffic behavioural pattern and ultimately influences pavement. Pavement condition, in turn, influences microscopic behaviours. The above bidirection influencing mechanism has not been investigated fully yet. This research fill this gap by modelling the linkage between multi-level microscopic behaviour and pavement sustainability. Three levels of behaviour are considered: travel behaviour, microscopic traffic behaviour, and driving behaviour. The latter two are modelled using stochastic lateral movement model, while the former one is captured by a mixed autonomous traffic assignment model. Microscopic behaviours’ influence on pavement is described by a data-driven model, while the reverse counterpart is described by connecting pavement condition with link wandering and disutility. Our analysis results reveal that at link level, AVs can cause extra 50% drop in free flow speed due to pavement deterioration. Neglecting pavement evolution in strategic assignments leads to a 0.2% increase in network cost.

Energy fluctuations of a Brownian particle freely moving in a liquid

We study the statistical properties of the variation of the kinetic energy of a spherical Brownian particle that freely moves in an incompressible fluid at constant temperature. Based on the underdamped version of the generalized Langevin equation that includes the inertia of both the particle and the displaced fluid, we derive an analytical expression for the probability density function of such a kinetic energy variation during an arbitrary time interval, which exactly amounts to the energy exchanged with the fluid in absence of external forces. We also determine all the moments of this probability distribution, which can be fully expressed in terms of a function that is proportional to the velocity autocorrelation function of the particle. The derived expressions are verified by means of numerical simulations of the stochastic motion of a particle in a viscous liquid with hydrodynamic backflow for representative values of the time-scales of the system. Furthermore, we also investigate the effect of viscoelasticity on the statistics of the kinetic energy variation of the particle, which reveals the existence of three distinct regimes of the energy exchange process depending on the values of the viscoelastic parameters of the fluid.

Numerical Modeling of Energetic Charged-particle Transport with SPECTRUM Software: General Approach and Artificial Effects due to Field Discretization

Test-particle simulations are an important tool for magnetospheric and heliophysics research. In this paper, we present the Space Plasma and Energetic Charged particle TRansport on Unstructured Meshes (SPECTRUM) software as a novel tool for performing these types of simulations in arbitrary astrophysical environments, specified either analytically or numerically (i.e., on a grid). We discuss and benchmark SPECTRUM’s interface with meshed magnetohydrodynamic backgrounds, including output from the Block Adaptive Tree Solar-wind Roe-type Upwind Scheme (BATS-R-US) code. We also investigate the effects of field discretization on both deterministic and stochastic particle motion, with emphasis on space science applications, concluding that the discretization error typically enhances the diffusive behavior of the ensemble.

Sensitivity Analysis of Finite Fault Model in Stochastic Ground Motion Simulations

Sensitivity Analysis of Finite Fault Model in Stochastic Ground Motion Simulations

Using Brownian model to study the effect of temperature on diffusion coefficient

This study employs molecular simulation techniques, particularly the Brownian motion model, to investigate the influence of temperature on diffusion coefficients. Leveraging Einsteins relationship for calculating diffusion coefficients and a one-dimensional random walk model, we systematically explore the impact of simulation direction, particle quantity, and simulation duration on diffusion behavior. The research extends its scope to three-dimensional Brownian motion simulations, offering insights into the stochastic motion of particles in a fluid. The primary objective is to analyze the relationship between temperature and diffusion coefficients. Through rigorous linear regression analysis, a significant and strong linear association is identified, demonstrating that an increase in temperature correlates with an increase in the diffusion coefficient. The research not only contributes to the fundamental understanding of molecular motion but also provides practical recommendations for simulation parameters, especially in resource-constrained computational environments. The study acknowledges certain limitations in the current Brownian motion algorithm and proposes avenues for future research to enhance computational efficiency and precision. This abstract encapsulates the key methodologies, findings, and implications of the research, laying the foundation for a comprehensive exploration of temperature-dependent diffusion coefficients in molecular systems.

The importance of corner frequency in site‐based stochastic ground motion models

AbstractSynthetic ground motions (GMs) play a fundamental role in both deterministic and probabilistic seismic engineering assessments. This paper shows that the family of filtered and modulated white noise stochastic GM models overlooks a key parameter—the high‐pass filter's corner frequency, . In the simulated motions, this causes significant distortions in the long‐period range of the linear‐response spectra and in the linear‐response spectral correlations. To address this, we incorporate as an explicitly fitted parameter in a site‐based stochastic model. We optimize by individually matching the long‐period linear‐response spectrum (i.e., for ) of synthetic GMs with that of each recorded GM. We show that by fitting the resulting stochastically simulated GMs can precisely capture the spectral amplitudes, variability (i.e., variances of ), and the correlation structure (i.e., correlation of between distinct periods and ) of recorded GMs. To quantify the impact of , a sensitivity analysis is conducted through linear regression. This regression relates the logarithmic linear‐response spectrum () to 7 GM parameters, including the optimized . The results indicate that the variance of observed in natural GMs, along with its correlation with the other GM parameters, accounts for 26% of the spectral variability in long periods. Neglecting either the variance or correlation typically results in an important overestimation of the linear‐response spectral correlation.

Dimension-Reduction Representation of Multivariate Mainshock-Aftershock Ground Motions Based on Measured Records

ABSTRACT This study proposes an integrated dimension-reduction representation strategy for simulating multivariate mainshock-aftershock stochastic ground motions based on measured motion records. The strategy includes a parameter identification method for modeling evolutionary power spectrum density (EPSD) of mainshock-aftershocks, a coherence function describing the spectrum correlation between mainshock and aftershock, and the EPSD function matrix establishment for mainshock-aftershock field combining with complex spatial coherence function. Furthermore, the dimension-reduction representation for simulating the ground motions considering the sequence and spatial variability simultaneously is presented with merely two elementary random variables. Numerical results effectively demonstrate the accuracy, efficiency, and engineering applicability of the proposed method.