scholarly journals Προσδιορισμός πεπερασμένων σεισμικών ρηγμάτων από γεωδαιτικές παρατηρήσεις με βάση την αριθμητική-στοχαστική μέθοδο της τοπολογικής αντιστροφής (αλγόριθμος TOPological INVersion, TOPINV)

2016 ◽  
Author(s):  
Βασιλική Σαλτογιάννη
Keyword(s):  
Monte Carlo ◽  
Cost Function ◽  
A Priori ◽  
Dislocation Models

Οι σημειακές θραύσεις των πετρωμάτων κατά τη διάρκεια ενός σεισμού προκαλούν μόνιμες παραμορφώσεις στη γύρω βραχόμαζα και περιγράφονται από διαφορικές εξισώσεις. Συνήθως θεωρείται ότι τα ρήγματα μπορούν να προσομοιωθούν από μία ή περισσότερες επίπεδες επιφάνειες θραύσης (πεπερασμένα ρήγματα) σε ελαστικό χώρο, και έχουν προταθεί συστήματα συνήθων εξισώσεων που συνδέουν τα χαρακτηριστικά του κάθε ρήγματος που προσδιορίζονται από 9 μεταβλητές με επιφανειακές παραμορφώσεις (elastic dislocation models). Εάν, οι μόνιμες παραμορφώσεις επεκτείνονται μέχρι και την επιφάνεια του εδάφους και έχουν μετρηθεί με γεωδαιτικές μεθόδους, συνήθως GPS, είναι δυνατόν να δημιουργηθεί σύστημα εξισώσεων παρατήρησης που συνδέει τα χαρακτηριστικά των σεισμικών ρηγμάτων με γεωδαιτικές παρατηρήσεις. Η επίλυση τω συστημάτων αυτών (αντιστροφή) μπορεί να προσδιορίσει τη γεωμετρία και την κινηματική ενός σεισμικού ρήγματος (ή περισσότερων σεισμικών ρηγμάτων). Η αντιστροφή δεν είναι συνήθως δυνατή με τυπικές αλγεβρικές μεθόδους επειδή οι εξισώσεις οδηγούν σε υπερστατικό σύστημα παρατηρήσεων, είναι γενικά εξαιρετικά μη γραμμικές, δεν υπάρχουν διαθέσιμες προσεγγιστικές εκτιμήσεις των χαρακτηριστικών των ρηγμάτων και οι σταθεροί όροι των εξισώσεων (μετρήσεις) χαρακτηρίζονται από αβεβαιότητες (σφάλματα).Για το λόγο αυτό έχουν προταθεί διάφορες αριθμητικές τεχνικές αντιστροφής, συνήθως δειγματοληπτικές (sampling search) βασισμένες στη μέθοδο Monte Carlo, οι οποίες εστιάζονται στην ελαχιστοποίηση μίας αντικειμενικής συνάρτησης (συνάρτηση κόστους, cost function) για συγκεκριμένα πεδία τιμών (χώρο αναζήτησης n διαστάσεων για σύστημα n αγνώστων). Τα βασικά μειονεκτήματα των μεθόδων αυτών είναι a priori δεσμευμένες τιμές αγνώστων, εκτιμήσεις εγκλωβισμένες σε τοπικά ακρότατα, υποτίμηση της αβεβαιότητας των παρατηρήσεων, λύσεις με υψηλό βαθμό συσχέτισης και ελλιπής προσδιορισμός των στατιστικών τους χαρακτηριστικών.Με στόχο να αντιμετωπιστούν τέτοιου είδους προβλήματα, αναπτύχθηκε μια εναλλακτική μέθοδος τοπολογικής/γεωμετρικής αντιστροφής (αλγόριθμος TOPological INVersion, TOPINV) με πηγή έμπνευσης την παραδοσιακή πλοήγηση με χρήση φάρων. Η βέλτιστη λύση δεν βασίζεται σε μία σημειακή ακρότατη λύση, αλλά στον προσδιορισμό ενός n-διάστατου χώρου που περιέχει την «αληθή» λύση. Αυτό επιτυγχάνεται αφενός με τη μετατροπή των εξισώσεων παρατήρησης σε ανισώσεις συναρτήσει των σφαλμάτων των μετρήσεων και μιας παραμέτρου βελτιστοποίησης k. Και αφετέρου με τη μετατροπή του n-διάστατου (υπερ-)χώρου των πιθανών λύσεων σε διακριτό χώρο σημείων. Για επιλεγμένη τιμή της παραμέτρου k και με λογική Boole προσδιορίζονται τα σημεία που ικανοποιούν τις ανισώσεις παρατήρησης (ομοίομορφη αναζήτηση, uniform search), και κατά πόσο ορίζουν συμπαγή χώρο (ή χώρους) n διαστάσεων, ο οποιος εξ ορισμού περιέχει την αληθή λύση του συστήματος των εξισώσεων. Από τον πληθυσμό των σημείων αυτών υπολογίζεται η βέλτιστη λύση (ή λύσεις) και ο αντίστοιχος Πίνακας Μεταβλητότητας-Συμμεταβλητότητας ως πρώτες και δεύτερες στατιστικές ροπές, αντίστοιχα.Η αποτελεσματικότητα της μεθόδου τεκμηριώνεται με την επίλυση προβλημάτων με βάση συνθετικά δεδομένα, όπου είναι γνωστή η αληθής λύση, και με ανάλυση ευαισθησίας αναφορικά με την συμπαγότητα (compactness) της λύσης, την ακρίβειά της (precision) και την απόκλισή της από την αληθή τιμή (αξιοπιστία, accuracy).Η μέθοδος εφαρμόστηκε σε αντιστροφή γεωδαιτικών παρατηρήσεων για τον προσδιορισμό δύο σεισμικών ρηγμάτων (18 συνολικά άγνωστες μεταβλητές) που ενεργοποιήθηκαν κατά το σεισμό του 2003 της Λευκάδας, μεγέθους 6.2, του πρώτου σεισμού στον Ελληνικό χώρο που καλύφθηκε από εκτενή δεδομένα GPS, προσφέροντας ακριβή λύση χωρίς δεσμεύσεις και συμβατή με ανεξάρτητα σεισμολογικά δεδομένα.

scholarly journals COSMIC COVARIANCE AND THE LOW QUADRUPOLE ANISOTROPY IN THE WMAP DATA

2008 ◽  
Vol 23 (17n20) ◽  
pp. 1489-1497 ◽  
Author(s):  
LUNG-YIH CHIANG ◽  
PAVEL D. NASELSKY ◽  
PETER COLES
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
A Priori ◽  
Gaussian Random Field ◽  
Minimum Variance ◽  
Microwave Background ◽  
Data Release ◽  
Intrinsic Correlation ◽  
Wmap Data ◽  
Cmb Temperature

Low quadrupole power in the cosmic microwave background (CMB) temperature anisotropies has been a puzzle since WMAP data release. In this talk I will demonstrate that the minimum variance optimization (MVO), a methodology used by many authors including the WMAP science team to separate the CMB from foreground contamination, serves not only to extract the CMB, but to subtract the “cosmic covariance”, an intrinsic correlation between the CMB and the foregrounds. Such subtraction induces low variance in the signal via MVO, which in turn propagates into the multipoles, causing a quadrupole deficit with more than 90% CL. As we do not know the CMB and the foregrounds a priori, and their correlation is subtracted by the MVO in any case, there is therefore an unknown error in the quadrupole power even before the cosmic variance interpretation. We combine the MVO and Monte Carlo simulations, assuming CMB is a Gaussian random field, and the estimated quadrupole power falls in [308.13, 401.97] μ K 2 (at 1 − σ level).

A Backward Monte Carlo method for fast-ion-loss simulations

2021 ◽  
Author(s):  
Filippo Zonta ◽  
Lucia Sanchis ◽  
Eero Hirvijoki
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
A Priori ◽  
Target Surface ◽  
A Priori Information ◽  
Ion Distributions ◽  
Plasma Facing Components ◽  
Priori Information ◽  
Fast Ion

Abstract This paper presents a novel scheme to improve the statistics of simulated fast-ion loss signals and power loads to plasma-facing components in fusion devices. With the so-called Backward Monte Carlo method, the probabilities of marker particles reaching a chosen target surface can be approximately traced from the target back into the plasma. Utilizing the probabilities as {\it a priori} information for the well-established Forward Monte Carlo method, statistics in fast-ion simulations are significantly improved. For testing purposes, the scheme has been implemented to the ASCOT suite of codes and applied to a realistic ASDEX Upgrade configuration of beam-ion distributions.

Triple-Defect B2 Binary Intermetallics: Bragg-Williams Solution and Monte Carlo Simulations

2009 ◽  
Vol 289-292 ◽  
pp. 361-368 ◽  
Author(s):  
Andrzej Biborski ◽  
L. Zosiak ◽  
Rafal Abdank-Kozubski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Vacancy Concentration ◽  
A Priori ◽  
Equilibrium Concentration ◽  
Pair Interaction ◽  
Type Model ◽  
Interaction Energies ◽  
Atomic Pair ◽  
Antisite Defects

Surprisingly low rate of “order-order” kinetics in stoichiometric NiAl intermetallic known of very high vacancy concentration suggested a specific triple-defect mechanism of ordering/disordering in this system [1]. This mechanism implies a correlation between the concentrations of antisite defects and vacancies; the latters being trapped in triple defects and thus, inactive as atomic migration agents. The process was modelled by means of Monte Carlo (MC) simulations recognised as a powerful tool for such tasks [2], but requiring now the implementation of thermal vacancy thermodynamics. Temperature dependence of vacancy concentration in an AB B2 binary system was determined within an Ising-type model solved first in Bragg-Williams approximation [3] and then by means of MC simulation of a Grandcanonical Ensemble. Without any a priori assumptions concerning the formation of particular types of point defects the model yielded temperature domains where the concentrations of antisite defects and vacancies were proportional. The effect associated with the formation of triple defects appeared for specific values of atomic pair-interaction energies. Moreover, non-stoichiometric A-B systems with the same atomic pair-interaction energies showed the existence of constitutional vacancies at low temperatures. Monte Carlo simulations of “order-order” (disordering) kinetics in B2 AB systems modelled with triple-defect-promoting atomic pair-interaction energies were run with temperature-dependent concentra-tion (i.e. number) of vacancies given by the above model. The simulated relaxations showed two stages: (i) rapid formation of triple defects engaging almost all vacancies present in the system, (ii) very slow process of further generation of antisite defects until the equilibrium concentration was reached. The result reproduced very well the experimental observations [1].

scholarly journals Step-Wise Group Screening Designs with Unequal A-Priori Probabilities and Errors in Observations

2003 ◽  
Vol 8 (2) ◽  
pp. 153
Author(s):  
M.M. Manene
Keyword(s):  
Cost Function ◽  
Group Size ◽  
A Priori ◽  
Expected Number ◽  
Total Cost ◽  
Screening Designs ◽  
Expected Total Cost

The performance of step-wise group screening with unequal a-priori probabilities in terms of the expected number of runs and the expected maximum number of incorrect decisions is considered. A method of obtaining optimal step-wise designs with unequal a-priori probabilities is presented for the case in which the direction of each defective factor is assumed to be known a -priori and observations are subject to error. An appropriate cost function is introduced and the value of the group size which minimizes the expected total cost is obtained.  

scholarly journals On Time-Frequency Synchronization in LoRa System: From Analysis to Near-Optimal Algorithm

2021 ◽  
Author(s):  
Vincent Savaux ◽  
Christophe Delacourt ◽  
Patrick Savelli
Keyword(s):  
Cost Function ◽  
Optimal Algorithm ◽  
A Priori ◽  
Low Complexity ◽  
Frequency Offset ◽  
Maximization Problem ◽  
Frequency Synchronization ◽  
Time Frequency ◽  
Time Offset ◽  
Ml Estimator

This paper deals with time and frequency synchronization in LoRa system based on the preamble symbols. A thorough analysis of the maximum likelihood (ML) estimator of the delay (time offset) and the frequency offset shows that the resulting cost function is not concave. As a consequence the a priori solution to the maximization problem consists in exhaustively searching over all the possible values of both the delay and the frequency offset. Furthermore, it is shown that these parameters are intertwined and therefore they must be jointly estimated, leading to an extremely complex solution. Alternatively, we show that it is possible to recover the concavity of the cost function, from which we suggest a low-complexity synchronization algorithm, whose steps are described in detail. Simulations results show that the suggested method reaches the same performance as the ML exhaustive search, while the complexity is drastically reduced, allowing for a real-time implementation of a LoRa receiver. <br>

L1 Regularization-Based Model Reduction of Complex Chemistry Molecular Dynamics for Statistical Learning of Kinetic Monte Carlo Models

MRS Advances ◽  
2016 ◽  
Vol 1 (24) ◽  
pp. 1767-1772 ◽  
Author(s):  
Qian Yang ◽  
Carlos A. Sing-Long ◽  
Evan J. Reed
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Kinetic Monte Carlo ◽  
A Priori ◽  
Reaction Network ◽  
Md Simulations ◽  
Rate Coefficients ◽  
Elementary Reactions ◽  
L1 Regularization ◽  
Complex Chemistry

ABSTRACTKinetic Monte Carlo (KMC) methods have been a successful technique for accelerating time scales and increasing system sizes beyond those achievable with fully atomistic simulations. However, a requirement for its success is a priori knowledge of all relevant reaction pathways and their rate coefficients. This can be difficult for systems with complex chemistry, such as shock-compressed materials at high temperatures and pressures or phenolic spacecraft heat shields undergoing pyrolysis, which can consist of hundreds of molecular species and thousands of distinct reactions. In this work, we develop a method for first estimating a KMC model composed of elementary reactions and rate coefficients by using large datasets derived from a few molecular dynamics (MD) simulations of shock compressed liquid methane, and then using L1 regularization to reduce the estimated chemical reaction network. We find that the full network of 2613 reactions can be reduced by 89% while incurring approximately 9% error in the dominant species (CH4) population. We find that the degree of sparsity achievable decreases when similar accuracy is required for additional populations of species.

AN MLP TRAINING ALGORITHM TAKING INTO ACCOUNT KNOWN ERRORS ON INPUTS AND OUTPUTS

2002 ◽  
Vol 12 (05) ◽  
pp. 369-379
Author(s):  
J. SVENSSON
Keyword(s):  
Cost Function ◽  
A Priori ◽  
Hessian Matrix ◽  
Predictive Distribution ◽  
Training Algorithm ◽  
Posterior Predictive Distribution ◽  
Network Function ◽  
Error Bars ◽  
Mlp Network ◽  
Inputs And Outputs

A training algorithm is introduced that takes into account a priori known errors on both inputs and outputs in an MLP network. The new cost function introduced for this case is based on a linear approximation of the network function over the input distribution for a given input pattern. Update formulas, in the form of the gradient of the new cost function, is given for a MLP network, together with expressions for the Hessian matrix. This is later used to calculate error bars in a Bayesian framework. The error bars thus derived are discussed in relation to the more commonly used width of the target posterior predictive distribution. It will also be shown that the taking into account of known input uncertainties in the way suggested in this article will have a strong regularizing effect on the solution.

scholarly journals Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

2020 ◽  
Vol 30 (6) ◽  
pp. 1645-1663
Author(s):  
Ömer Deniz Akyildiz ◽  
Dan Crisan ◽  
Joaquín Míguez
Keyword(s):  
Monte Carlo ◽  
Cost Function ◽  
Global Minimum ◽  
Sequential Monte Carlo ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Gradient Based ◽  
Multiple Minima ◽  
The Cost

Abstract We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad “flat” regions which are hard to minimize using gradient-based techniques.

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