Probabilistic solutions to DAEs learning from physical data

2021 ◽  
pp. 1-19
Author(s):  
Zongmin Wu ◽  
Ran Zhang
Keyword(s):  
Chaotic Behavior ◽  
Continuous System ◽  
Random Parameter ◽  
Information Criterion ◽  
Optimization Method ◽  
Reference Trajectory ◽  
Differential Algebraic Equation ◽  
Long Time ◽  
Random Switching ◽  
Discrete Analogues

The nonlinear chaotic differential/algebraic equation (DAE) has been established to simulate the nonuniform oscillations of the motion of a falling sphere in the non-Newtonian fluid. The DAE is obtained only by learning the experimental data with sparse optimization method. However, the deterministic solution will become increasingly inaccurate for long time approximation of the continuous system. In this paper, we introduce two probabilistic solutions to compute the totally DAE, the Random branch selection iteration (RBSI) and Random switching iteration (RSI). The samples are also taken as the reference trajectory to learn random parameter. The proposed probabilistic solutions can be regarded as the discrete analogues of differential inclusion and switching DAEs, respectively. They have been also compared with the deterministic method, i.e. backward differentiation formula (BDF). The deterministic methods only give limited candidates of all the probability solutions, while the RSI can include all the possible trajectories. The numerical results and statistical information criterion show that RSI can successfully reveal the sustaining instabilities of the motion itself and long time chaotic behavior.

scholarly journals Prerecruit survival and recruitment of northern Gulf of St Lawrence Atlantic cod

2008 ◽  
Vol 65 (6) ◽  
pp. 946-952 ◽  
Author(s):  
Daniel E. Duplisea ◽  
Dominique Robert
Keyword(s):  
Linear Models ◽  
Atlantic Cod ◽  
Information Criterion ◽  
Factors Affecting ◽  
Control Rules ◽  
Strategy Evaluation ◽  
Stock Biomass ◽  
Spawning Stock ◽  
Long Time ◽  
Parsimonious Model

Abstract Duplisea, D. E., and Robert, D. 2008. Prerecruit survival and recruitment of northern Gulf of St Lawrence Atlantic cod. – ICES Journal of Marine Science, 65: 946–952. Recruitment (R) of exploited marine fish populations is usually modelled exclusively as a function of spawning-stock biomass (SSB). A problem arising when modelling over long time-series is that the nature of the R–SSB relationship is unlikely to be stationary. Changes are often interpreted as productivity regime shifts and are linked to alterations in prerecruit survival rate. We examine the role of environment and predation by fish and harp seals as factors affecting the R–SSB relationship in the northern Gulf of St Lawrence cod, by fitting linear models using combinations of covariates to explain cod prerecruit survival. The most parsimonious model (based on a Bayesian Information Criterion, BIC) included cod, mackerel, and temperature, whereas redfish and seals did not appear in any of the best-fit models. Recruitment models derived from this analysis could be used in operating models for management strategy evaluation simulations for northern Gulf cod, so one could develop harvest control rules that are robust to changes in recruitment productivity regimes.

INTEGRAL TREATMENT FOR TIME EVOLUTION: THE GENERAL INTERACTIVITY

1999 ◽  
Vol 14 (20) ◽  
pp. 3239-3252
Author(s):  
E. CASUSO
Keyword(s):  
Dynamical Systems ◽  
Time Evolution ◽  
Time Distribution ◽  
Chaotic Behavior ◽  
Order Approximation ◽  
Natural Systems ◽  
Structural Discontinuity ◽  
Long Time ◽  
Integral Treatment ◽  
First Order Approximation

Assuming that the unpredictability associated with many dynamical systems is an artefact of the differential treatment of their time evolution, we propose here an integral treatment as an alternative. We make the assumption that time is two-dimensional, and that the time distribution in the past of observables characterizing the dynamical system, is some characteristic "projection" of its time distribution in the future. We show here how this method can be used to predict the time evolution of several dynamically complex systems over long time intervals. The present work can be considered as the natural next step to the assumption of nonderivability for subatomic dynamical systems to explain the connection between Quantum Mechanics and General Relativity. Here we propose that matter and space–time are not only nonderivable but also show structural discontinuity. Starting with this premise we use continuity and derivability, but only as a first order approximation to reality. Extrapolation to very large or very small scales, or to predictions over long time scales for many natural systems on intermediate scales (human scales), may lead to chaotic behavior, or to nondeterministic or probabilistic theories.

Cardinal temperatures and thermal time required foremergence of lenti (Lens culinaris Medik)

2017 ◽  
Author(s):  
Ali reza Safahani ◽  
Behnam Kamakar ◽  
Amir Nabizadeh
Keyword(s):  
Lens Culinaris ◽  
Seedling Emergence ◽  
Information Criterion ◽  
Optimization Method ◽  
Thermal Time ◽  
Coefficient Of Determination ◽  
Nonlinear Regression Models ◽  
Maximum Temperatures ◽  
Time Required ◽  
Cardinal Temperatures

The present study was performed to compare four nonlinear regression models (segmented, beta, beta modified, and dent-like) to describe the emergence rate–temperature relationships of six lentil (Lens culinaris Medik) cultivars at field experiment with a range of sowing dates, with the aim of identifying the cardinal temperatures and physiological days (i.e., number of days under optimum temperatures) required for seedling emergence. Models and statistical indices were calibrated using an iterative optimization method and their performance was compared by root mean square error (RMSD), coefficient of determination (R2) and corrected Akaike information criterion correction (AIC). The beta model was found to be the best model for predicting the response of lentil emergence to temperature, (R2= 0.99; RMSD= 0.005; AICc= -232.97). Based on the model outputs, the base, optimum, and maximum temperatures of seedling emergence were 4.5, 22.9, and 40 °C, respectively. The Six physiological days (equivalent to a thermal time of 94 °C days) were required from sowing to emergence

scholarly journals An Accurate Predictor-Corrector-Type Nonstandard Finite Difference Scheme for an SEIR Epidemic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Asma Farooqi ◽  
Riaz Ahmad ◽  
Rashada Farooqi ◽  
Sayer O. Alharbi ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Continuous System ◽  
Euler Method ◽  
State Variables ◽  
Nonstandard Finite Difference Scheme ◽  
Long Time ◽  
Predictor Corrector ◽  
Nonstandard Finite Difference

The present work deals with the construction, development, and analysis of a viable normalized predictor-corrector-type nonstandard finite difference scheme for the SEIR model concerning the transmission dynamics of measles. The proposed numerical scheme double refines the solution and gives realistic results even for large step sizes, thus making it economical when integrating over long time periods. Moreover, it is dynamically consistent with a continuous system and unconditionally convergent and preserves the positive behavior of the state variables involved in the system. Simulations are performed to guarantee the results, and its effectiveness is compared with well-known numerical methods such as Runge–Kutta (RK) and Euler method of a predictor-corrector type.

scholarly journals QUANTIFYING EMERGENCE IN TERMS OF PERSISTENT MUTUAL INFORMATION

2010 ◽  
Vol 13 (03) ◽  
pp. 327-338 ◽  
Author(s):  
ROBIN C. BALL ◽  
MARINA DIAKONOVA ◽  
ROBERT S. MACKAY
Keyword(s):  
Mutual Information ◽  
Chaotic Behavior ◽  
Past History ◽  
Logistic Map ◽  
Period Doubling ◽  
Emergent Behavior ◽  
Complexity Measures ◽  
Spatially Extended ◽  
Long Time ◽  
Definition Of

We define Persistent Mutual Information (PMI) as the Mutual (Shannon) Information between the past history of a system and its evolution significantly later in the future. This quantifies how much past observations enable long-term prediction, which we propose as the primary signature of (Strong) Emergent Behavior. The key feature of our definition of PMI is the omission of an interval of "present" time, so that the mutual information between close times is excluded: this renders PMI robust to superposed noise or chaotic behavior or graininess of data, distinguishing it from a range of established Complexity Measures. For the logistic map, we compare predicted with measured long-time PMI data. We show that measured PMI data captures not just the period doubling cascade but also the associated cascade of banded chaos, without confusion by the overlayer of chaotic decoration. We find that the standard map has apparently infinite PMI, but with well-defined fractal scaling which we can interpret in terms of the relative information codimension. Whilst our main focus is in terms of PMI over time, we can also apply the idea to PMI across space in spatially-extended systems as a generalization of the notion of ordered phases.

GROWTH RATES OF TOTAL VARIATIONS OF SNAPSHOTS OF THE 1D LINEAR WAVE EQUATION WITH COMPOSITE NONLINEAR BOUNDARY REFLECTION RELATIONS

2003 ◽  
Vol 13 (05) ◽  
pp. 1183-1195 ◽  
Author(s):  
YU HUANG
Keyword(s):  
Wave Equation ◽  
Nonlinear Boundary ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Distributed Parameter ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Energy Pumping ◽  
Long Time

The linear wave equation on an interval with a van der Pol nonlinear boundary condition at one end and an energy-pumping condition at the other end is a useful model for studying chaotic behavior in distributed parameter system. In this paper, we study the dynamics of the Riemann invariants (u, v) of the wave equation by means of the total variations of the snapshots on the spatial interval. Our main contributions here are the classification of the growth of total variations of the snapshots of u and v in long-time horizon, namely, there are three cases when a certain parameter enters a different regime: the growth (i) remains bounded; (ii) is unbounded (but nonexponential); (iii) is exponential, for a large class of initial conditions with finite total variations. In particular, case (iii) corresponds to the onset of chaos. The results here sharpen those in an earlier work [Chen et al., 2001].

scholarly journals Comparison of sound velocity estimation and classification methods for ultrasonic testing of cheese

2016 ◽  
Vol 12 (1) ◽  
pp. 51-62
Author(s):  
I. Kertész ◽  
J. Felföldi
Keyword(s):  
Wavelet Decomposition ◽  
Information Criterion ◽  
Velocity Estimation ◽  
Classification Methods ◽  
New Approach ◽  
Linear Discriminant ◽  
Ultrasonic Measurements ◽  
Long Time ◽  
Time Average ◽  
Short Time

Testing of two methods novel to ultrasonic measurements was carried out on cheese samples to estimate the Time-of-Flight (TOF) parameter. The Short Time Average/Long Time Average (STA/LTA) method and the Autoregressive Akaike Information Criterion Picker (AR-AIC picker) method are used mainly in seismology for earthquake event detection. The STA/LTA method proved to be ineffective with such noise level that is present during ultrasonic measurements, but the AIC picker algorithm yielded reliable results. A new approach for classification was tested on two types of samples, those were matching in composition, but different in treatment and texture. The method used is based on the results of wavelet decomposition, and after retrieving sufficient spectral data, a linear discriminant analysis (DA) resulted in 100% correct classification, which was compared to the DA classification results based on other methods.

Control Design Applied to a Micro Electro Mechanical System: MEMS Comb Drive

2011 ◽  
Vol 217-218 ◽  
pp. 33-38 ◽  
Author(s):  
Alessandra Bonato Altran ◽  
Fábio Roverto Chavarette ◽  
Carlos Roberto Minussi ◽  
Nelson José Peruzzi ◽  
Mara Lúcia Marthins Lopes ◽  
...  
Keyword(s):  
Optimal Control ◽  
Periodic Orbit ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Micro Electro Mechanical System ◽  
Control Technique ◽  
Reference Trajectory ◽  
Comb Drive ◽  
Linear Optimal Control ◽  
Small Periodic

This paper presents the linear optimal control technique for reducing the chaotic movement of the micro-electro-mechanical Comb Drive system to a small periodic orbit. We analyze the non-linear dynamics in a micro-electro-mechanical Comb Drive and demonstrated that this model has a chaotic behavior. Chaos control problems consist of attempts to stabilize a chaotic system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. This technique is applied in analyzes the nonlinear dynamics in an MEMS Comb drive. The simulation results show the identification by linear optimal control is very effective.

scholarly journals APPLICATION OF EMERGENCY ON BUILDING FIRE USING ANT COLONY OPTIMIZATION METHOD BASED ON ANDROID

2021 ◽  
Vol 4 (2) ◽  
pp. 195-204
Author(s):  
Khusaeri Andesa ◽  
Herwin Herwin
Keyword(s):  
Ant Colony Optimization ◽  
Optimization Method ◽  
Ant Colony ◽  
Easy Access ◽  
Incident Report ◽  
Building Fires ◽  
Rescue Service ◽  
The Public ◽  
Fire Incident ◽  
Long Time

Fire and Rescue Service is an agency to handles fire problems, i.e building fires. Fire and Rescue Service of Pekanbaru is an agency to handles fire problems in Pekanbaru where the service receives information about a fire incident quickly and responsively. Fire incidents can occur anywhere, in any location, both easy or difficult access, but the Firfighter Team must be prepared in every conditions. The problem is that not all fire incidents occur in easy access places by firefighters. The incidents sometimes occur in difficult places to reach and unknown location, firefighter have to use maps to find the location. It will be wasting time to find unknown location and took a long time to arrive. The solution of this problem is to build an android-based application that can be used as a fire incident report, which is connected in one application, so residents can report through an application automatically provides the coordinates of incident. The application of Ant Colony Optimization method in finding fire locations makes it easier to hasten in searching fire locations and can be used by the public in reporting fires to Fire and Rescue Service of Pekanbaru to be processed quickly.

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