scholarly journals Simulation of Rare Events in Stochastic Systems

2021 ◽  
Vol 2096 (1) ◽  
pp. 012151
Author(s):  
A A Kabanov ◽  
S A Dubovik
Keyword(s):  
Optimal Control ◽  
Optimal Control Theory ◽  
Stochastic Systems ◽  
Rare Events ◽  
Rare Event ◽  
Intraseasonal Oscillation ◽  
Time Instant ◽  
Action Functional ◽  
Nonlinear Stochastic Model ◽  
Linear And Nonlinear Systems

Abstract The paper presents algorithms for simulation rare events in stochastic systems based on the theory of large deviations. Here, this approach is used in conjunction with the tools of optimal control theory to estimate the probability that some observed states in a stochastic system will exceed a given threshold by some upcoming time instant. Algorithms for obtaining controlled extremal trajectory (A-profile) of the system, along which the transition to a rare event (threshold) occurs most likely under the influence of disturbances that minimize the action functional, are presented. It is also shown how this minimization can be efficiently performed using numerical-analytical methods of optimal control for linear and nonlinear systems. These results are illustrated by an example for a precipitation-measured monsoon intraseasonal oscillation (MISO) described by a low-order nonlinear stochastic model.

Numerical Methods for Monitoring Rare Events in Nonlinear Stochastic Systems

2021 ◽  
Vol 22 (6) ◽  
pp. 291-297
Author(s):  
A. A. Kabanov ◽  
S. A. Dubovik
Keyword(s):  
Optimal Control ◽  
Numerical Methods ◽  
Large Deviations ◽  
Stochastic Systems ◽  
Rare Events ◽  
Rare Event ◽  
Stable State ◽  
The State ◽  
Nonlinear Stochastic Systems ◽  
State Dependent

In this article, we consider the development of numerical methods of large deviations analysis for rare events in nonlinear stochastic systems. The large deviations of the controlled process from a certain stable state are the basis for predicting the occurrenceof a critical situation (a rare event). The rare event forecasting problem is reduced to the Lagrange-Pontryagin optimal control problem.The presented approach for solving the Lagrange-Pontryagin problem differs from the approach used earlier for linear systems in that it uses feedback control. In the nonlinear case, approximate methods based on the representation of the system model in the state-space form with state-dependent coefficients (SDC) matrixes are used: the state-dependent Riccati equation (SDRE) and the asymptotic sequence of Riccati equations (ASRE). The considered optimal control problem allow us to obtain a numerical-analytical solutionthat is convenient for real-time implementation. Based on the developed methods of large deviations analysis, algorithms for estimating the probability of occurrence of a rare event in a dynamical systemare presented. The numerical applicability of the developed methods is shown by the example of the FitzHugh-Nagumo model for the analysis of switching between excitable modes. The simulation results revealed an additional problem related to the so-called parameterization problem of the SDC matrices. Since the use of different representations for SDC matrices gives different results in terms of the system trajectory, the choice of matrices is proposed to be carried out at each algorithm iteration so as to provide conditions for the solvability of the Lagrange-Pontryagin problem.

scholarly journals Оn momentum flow density of the gravitational field

2021 ◽  
Vol 17 (2) ◽  
pp. 137-147
Author(s):  
Oleg I. Drivotin ◽  
Keyword(s):  
Optimal Control ◽  
Optimal Control Theory ◽  
Physical Theory ◽  
Momentum Density ◽  
Momentum Balance ◽  
Flow Density ◽  
Action Functional ◽  
Surface Integral ◽  
Momentum Balance Equation ◽  
Density Flow

Momentum is considered on the basis of the approach widely used in the calculus of variations and in the optimal control theory, where variation of a cost functional is investigated. In physical theory, it is the action functional. Action variation under Lie dragging can be expressed as a surface integral of some differential form. The momentum density flow is defined using this form. In this work, the momentum balance equation is obtained. This equation shows that the momentum field transforms into a momentum of a mass. Examples showing the momentum flow structure for a mass distribution representing a uniform thin layer are provided.

Framework for rare event detection using Artificial Neural Network based context free grammar

2020 ◽  
Vol 39 (6) ◽  
pp. 8463-8475
Author(s):  
Palanivel Srinivasan ◽  
Manivannan Doraipandian
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Event Detection ◽  
Performance Metrics ◽  
Rare Events ◽  
Rare Event ◽  
Video Stream ◽  
Context Free Grammar ◽  
Artificial Neural ◽  
Context Free

Rare event detections are performed using spatial domain and frequency domain-based procedures. Omnipresent surveillance camera footages are increasing exponentially due course the time. Monitoring all the events manually is an insignificant and more time-consuming process. Therefore, an automated rare event detection contrivance is required to make this process manageable. In this work, a Context-Free Grammar (CFG) is developed for detecting rare events from a video stream and Artificial Neural Network (ANN) is used to train CFG. A set of dedicated algorithms are used to perform frame split process, edge detection, background subtraction and convert the processed data into CFG. The developed CFG is converted into nodes and edges to form a graph. The graph is given to the input layer of an ANN to classify normal and rare event classes. Graph derived from CFG using input video stream is used to train ANN Further the performance of developed Artificial Neural Network Based Context-Free Grammar – Rare Event Detection (ACFG-RED) is compared with other existing techniques and performance metrics such as accuracy, precision, sensitivity, recall, average processing time and average processing power are used for performance estimation and analyzed. Better performance metrics values have been observed for the ANN-CFG model compared with other techniques. The developed model will provide a better solution in detecting rare events using video streams.

Dispersion of nanoparticles with optimal control theory based on destabilization

2014 ◽  
Vol 2 ◽  
pp. 86-86
Author(s):  
Miki U. Kobayashi ◽  
Nobuaki Aoki ◽  
Noriyoshi Manabe ◽  
Tadafumi Adschiri
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Dispersion Of Nanoparticles
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