Relevant bibliographies by topics / Forward approximation

Academic literature on the topic 'Forward approximation'

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Published: 14 March 2023

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Journal articles on the topic "Forward approximation"

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Hao, Qi, and Alexey Stovas. "Analytic calculation of phase and group velocities of P-waves in orthorhombic media." GEOPHYSICS 81, no. 3 (May 2016): C79—C97. http://dx.doi.org/10.1190/geo2015-0156.1.

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We have developed an approximate method to calculate the P-wave phase and group velocities for orthorhombic media. Two forms of analytic approximations for P-wave velocities in orthorhombic media were built by analogy with the five-parameter moveout approximation and the four-parameter velocity approximation for transversely isotropic media, respectively. They are called the generalized moveout approximation (GMA)-type approximation and the Fomel approximation, respectively. We have developed approximations for elastic and acoustic orthorhombic media. We have characterized the elastic orthorhombic media in Voigt notation, and we can describe the acoustic orthorhombic media by introducing the modified Alkhalifah’s notation. Our numerical evaluations indicate that the GMA-type and Fomel approximations are accurate for elastic and acoustic orthorhombic media with strong anisotropy, and the GMA-type approximation is comparable with the approximation recently proposed by Sripanich and Fomel. Potential applications of the proposed approximations include forward modeling and migration based on the dispersion relation and the forward traveltime calculation for seismic tomography.
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Nguyen, Thi Ngoc Minh, Sylvain Le Corff, and Eric Moulines. "On the two-filter approximations of marginal smoothing distributions in general state-space models." Advances in Applied Probability 50, no. 01 (March 2018): 154–77. http://dx.doi.org/10.1017/apr.2018.8.

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AbstractA prevalent problem in general state-space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the results available for the approximation of smoothing distributions to these two-filter approaches which combine a forward filter approximating the filtering distributions with a backward information filter approximating a quantity proportional to the posterior distribution of the state, given future observations.
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He, Chuanlin, Yi Zheng, Xu Xiang, and Yuanliang Ma. "Kirchhoff Approximations for the Forward-Scattering Target Strength of Underwater Objects." Journal of Theoretical and Computational Acoustics 28, no. 01 (October 14, 2019): 1950008. http://dx.doi.org/10.1142/s2591728519500087.

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Kirchhoff approximations for the forward-scattering target strength of underwater objects are developed by combining Babinet’s principle and the Kirchhoff integral, where theoretical formulations and a numerical implementation are given in detail. The Kirchhoff approximation is found to be a high-frequency physical acoustic approximation. The forward-scattering target strength versus frequency and the spatial angles for spherical objects, prolate spheroids and the Benchmark Target Strength Simulation Submarine (BeTSSi-Sub) model are obtained by the Kirchhoff approximation and compared with results from theory, the deformed cylinder method (DCM) and the boundary element method (BEM). The Kirchhoff approximation shows considerable agreement with the theoretical and numerical approaches in a region of [Formula: see text] from the rigorous forward-scattering direction. The forward-scattered field contour and the corresponding directivity for the BeTSSi-Sub model are also calculated as a demonstration. Mode coupling caused by the simulated target is clearly revealed. The results indicate that the Kirchhoff approximation can predict the forward-scattering target strength of complex underwater objects.
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Cheng, Yi. "Forward approximation and backward approximation in fuzzy rough sets." Neurocomputing 148 (January 2015): 340–53. http://dx.doi.org/10.1016/j.neucom.2014.06.062.

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Kratsios, Anastasis. "The Universal Approximation Property." Annals of Mathematics and Artificial Intelligence 89, no. 5-6 (January 22, 2021): 435–69. http://dx.doi.org/10.1007/s10472-020-09723-1.

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AbstractThe universal approximation property of various machine learning models is currently only understood on a case-by-case basis, limiting the rapid development of new theoretically justified neural network architectures and blurring our understanding of our current models’ potential. This paper works towards overcoming these challenges by presenting a characterization, a representation, a construction method, and an existence result, each of which applies to any universal approximator on most function spaces of practical interest. Our characterization result is used to describe which activation functions allow the feed-forward architecture to maintain its universal approximation capabilities when multiple constraints are imposed on its final layers and its remaining layers are only sparsely connected. These include a rescaled and shifted Leaky ReLU activation function but not the ReLU activation function. Our construction and representation result is used to exhibit a simple modification of the feed-forward architecture, which can approximate any continuous function with non-pathological growth, uniformly on the entire Euclidean input space. This improves the known capabilities of the feed-forward architecture.
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Paronetto, Fabio. "Elliptic approximation of forward-backward parabolic equations." Communications on Pure & Applied Analysis 19, no. 2 (2020): 1017–36. http://dx.doi.org/10.3934/cpaa.2020047.

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Momoniat, E. "Matrix Exponentiation and the Frank-Kamenetskii Equation." Mathematical Problems in Engineering 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/713798.

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Long time solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a vessel are obtained using matrix exponentiation. Spatial derivatives are approximated by high-order finite difference approximations. A forward difference approximation to the time derivative leads to a Lawson-Euler scheme. Computations performed with a BDF approximation to the time derivative and a fourth-order Runge-Kutta approximation to the time derivative are compared to results obtained with the Lawson-Euler scheme. Variation in the central temperature of the vessel corresponding to changes in the shape parameter and Frank-Kamenetskii parameter are computed and discussed.
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Jetta, Mahipal. "A highly stable explicit scheme for a fourth-order nonlinear diffusion filter." International Journal of Modeling, Simulation, and Scientific Computing 11, no. 04 (July 2, 2020): 2050030. http://dx.doi.org/10.1142/s1793962320500300.

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The standard finite difference scheme (forward difference approximation for time derivative and central difference approximations for spatial derivatives) for fourth-order nonlinear diffusion filter allows very small time-step size to obtain stable results. The alternating directional implicit (ADI) splitting scheme such as Douglas method is highly stable but compromises accuracy for a relatively larger time-step size. In this paper, we develop [Formula: see text] stencils for the approximation of second-order spatial derivatives based on the finite pointset method. We then make use of these stencils for approximating the fourth-order partial differential equation. We show that the proposed scheme allows relatively bigger time-step size than the standard finite difference scheme, without compromising on the quality of the filtered image. Further, we demonstrate through numerical simulations that the proposed scheme is more efficient, in obtaining quality filtered image, than an ADI splitting scheme.
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Lakshmanan, Valliappa, Robert Rabin, Jason Otkin, John S. Kain, and Scott Dembek. "Visualizing Model Data Using a Fast Approximation of a Radiative Transfer Model." Journal of Atmospheric and Oceanic Technology 29, no. 5 (May 1, 2012): 745–54. http://dx.doi.org/10.1175/jtech-d-11-00007.1.

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Abstract Visualizing model forecasts using simulated satellite imagery has proven very useful because the depiction of forecasts using cloud imagery can provide inferences about meteorological scenarios and physical processes that are not characterized well by depictions of those forecasts using radar reflectivity. A forward radiative transfer model is capable of providing such a visible-channel depiction of numerical weather prediction model output, but present-day forward models are too slow to run routinely on operational model forecasts. It is demonstrated that it is possible to approximate the radiative transfer model using a universal approximator whose parameters can be determined by fitting the output of the forward model to inputs derived from the raw output from the prediction model. The resulting approximation is very close to the result derived from the complex radiative transfer model and has the advantage that it can be computed in a small fraction of the time required by the forward model. This approximation is carried out on model forecasts to demonstrate its utility as a visualization and forecasting tool.
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Allen, K. Radway, and W. S. Hearn. "Some Procedures for use in Cohort Analysis and Other Population Simulations." Canadian Journal of Fisheries and Aquatic Sciences 46, no. 3 (March 1, 1989): 483–88. http://dx.doi.org/10.1139/f89-064.

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The catch equation [Formula: see text] must often be solved either forwards or backwards. Because Ft is an implicit function of catch, population size, and M, the solution must be either iterative or approximate. In this paper an improved approximation to Nt+1 is developed of the form[Formula: see text]for the forward solution and a corresponding equation for backward solution. Appropriate values of A are presented for a range of combinations of M and F; and A = 0.585 gives approximations to Nt+1 with an error of less than 1% provided that (Ft + M) is less than about 1.5. Much closer approximations are obtained if A is calculated for each case as a polynomial in M and either Ct/Nt for the forward solution or Ct−1/Nt for the backward solution. The appropriate coefficients for these polynomials are derived both by truncating Taylor's expansion and by statistical methods, and are presented here. One such polynomial for A gives errors of less than 0.02% where (F + M) is less than 1.1. Similarly good approximations can also be obtained by interpolating into a table of Nt+1/Nt against M and C/N.
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Dissertations / Theses on the topic "Forward approximation"

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Garcia, Andrew Michael. "Feed-Forward Air-Fuel Ratio Control during Transient Operation of an Alternative Fueled Engine." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366034780.

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Bourgey, Florian. "Stochastic approximations for financial risk computations." Thesis, Institut polytechnique de Paris, 2020. http://www.theses.fr/2020IPPAX052.

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Dans cette thèse, nous examinons plusieurs méthodes d'approximations stochastiques à la fois pour le calcul de mesures de risques financiers et pour le pricing de produits dérivés.Comme les formules explicites sont rarement disponibles pour de telles quantités, le besoin d'approximations analytiques rapides,efficaces et fiables est d'une importance capitale pour les institutions financières.Nous visons ainsi à donner un large aperçu de ces méthodes d'approximation et nous nous concentrons sur trois approches distinctes.Dans la première partie, nous étudions plusieurs méthodes d'approximation Monte Carlo multi-niveaux et les appliquons à deux problèmes pratiques :l'estimation de quantités impliquant des espérances imbriquées (comme la marge initiale) ainsi que la discrétisation des intégrales apparaissant dans les modèles rough pour la variance forward pour le pricing d'options sur le VIX.Dans les deux cas, nous analysons les propriétés d'optimalité asymptotique des estimateurs multi-niveaux correspondants et démontrons numériquement leur supériorité par rapport à une méthode de Monte Carlo classique.Dans la deuxième partie, motivés par les nombreux exemples issus de la modélisation en risque de crédit, nous proposons un cadre général de métamodélisation pour de grandes sommes de variables aléatoires de Bernoulli pondérées, qui sont conditionnellement indépendantes par rapport à un facteur commun X. Notre approche générique est basée sur la décomposition en polynômes du chaos du facteur commun et sur une approximation gaussienne. Les estimations d'erreur L2 sont données lorsque le facteur X est associé à des polynômes orthogonaux classiques.Enfin, dans la dernière partie de cette thèse, nous nous intéressons aux asymptotiques en temps court de la volatilité implicite américaine et les prix d'options américaines dans les modèles à volatilité locale. Nous proposons également une approximation en loi de l'indice VIX dans des modèles rough pour la variance forward, exprimée en termes de proxys log-normaux et dérivons des résultats d'expansion pour les options sur le VIX dont les coefficients sont explicites
In this thesis, we investigate several stochastic approximation methods for both the computation of financial risk measures and the pricing of derivatives.As closed-form expressions are scarcely available for such quantities, %and because they have to be evaluated daily, the need for fast, efficient, and reliable analytic approximation formulas is of primal importance to financial institutions.We aim at giving a broad overview of such approximation methods and we focus on three distinct approaches.In the first part, we study some Multilevel Monte Carlo approximation methods and apply them for two practical problems: the estimation of quantities involving nested expectations (such as the initial margin) along with the discretization of integrals arising in rough forward variance models for the pricing of VIX derivatives.For both cases, we analyze the properties of the corresponding asymptotically-optimal multilevel estimatorsand numerically demonstrate the superiority of multilevel methods compare to a standard Monte Carlo.In the second part, motivated by the numerous examples arising in credit risk modeling, we propose a general framework for meta-modeling large sums of weighted Bernoullirandom variables which are conditional independent of a common factor X.Our generic approach is based on a Polynomial Chaos Expansion on the common factor together withsome Gaussian approximation. L2 error estimates are given when the factor X is associated withclassical orthogonal polynomials.Finally, in the last part of this dissertation, we deal withsmall-time asymptotics and provide asymptoticexpansions for both American implied volatility and American option prices in local volatility models.We also investigate aweak approximations for the VIX index inrough forward variance models expressed in termsof lognormal proxiesand derive expansions results for VIX derivatives with explicit coefficients
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Carcuz, Jerez Juan Ramon de Jesus. "An AVO method toward direct detection of lithologies combining P-P and P-S reflection data." Texas A&M University, 2003. http://hdl.handle.net/1969/38.

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Brideson, Michael. "Electromagnetic induction tomography : a feasibility study." Thesis, Queensland University of Technology, 2000.

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Manai, Arij. "Some contributions to backward stochastic differential equations and applications." Thesis, Le Mans, 2019. http://www.theses.fr/2019LEMA1022.

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Cette thèse est consacrée à l'étude des équations différentielles stochastiques rétrogrades (EDSR) et leurs applications. Dans le chapitre 1, on étudie le problème de maximisation de l'utilité de la richesse terminale où le prix de l'actif peut être discontinue sous des contraintes sur les stratégies de l'agent. Nous nous concentrons sur l'EDSR dont la solution représente l'utilité maximale, ce qui permet de transférer des résultats sur les EDSR quadratiques, en particulier les résultats de stabilité, au problème de maximisation d'utilité. Dans le chapitre 2, nous considèrons le problème de valorisation d'options Américaines des points de vue théorique et numérique en s'appuyant sur la représentation du prix de l'option comme solution de viscosité d'une équation parabolique non linéaire. Nous étendons le résultat prouvé dans [Benth, Karlsen and Reikvam 2003] pour un put ou call Américain à un cas plus général dans un cadre multidimensionnel. Nous proposons deux schémas numériques inspirés par les processus de branchement. Nos expériences numériques montrent que l'approximation du générateur discontinu, associé à l'EDP, par des polynômes locaux n'est pas efficace tandis qu'une simple procédure de randomisation donne de très bon résultats. Dans le chapitre 3, nous prouvons des résultats d'existence et d'unicité pour une classe générale d'équations progressives-rétrogrades à champs moyen sous une condition de monotonicité faible et une hypothèse non-dégénérescence sur l'équation progressive et nous donnons une application dans le domaine de stockage d'énergie dans le cas où la production d'électricité est imprévisible
This thesis is dedicated to the study of backward stochastic differential equations (BSDEs) and their applications. In chapter 1, we study the problem of maximizing the utility from terminal wealth where the stock price may jump and there are investment constraints on the agent 's strategies. We focus on the BSDE whose solution represents the maximal utility, which allows transferring results on quadratic BSDEs, in particular the stability results, to the problem of utility maximisation. In chapter 2, we consider the problem of pricing American options from theoretical and numerical sides based upon an alternative representation of the value of the option in the form of a viscosity solution of a parabolic equation with a nonlinear reaction term. We extend the viscosity solution characterization proved in [Benth, Karlsen and Reikvam 2003] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting. We address two new numerical schemes inspired by the branching processes. Our numerical experiments show that approximating the discontinuous driver of the associated reaction/diffusion PDE by local polynomials is not efficient, while a simple randomization procedure provides very good results. In chapter 3, we prove existence and uniqueness results for a general class of coupled mean-field forward-backward SDEs with jumps under weak monotonicity conditions and without the non-degeneracy assumption on the forward equation and we give an application in the field of storage in smart grids in the case where the production of electricity is unpredictable
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Ould, Aly Sidi Mohamed. "Modélisation de la courbe de variance et modèles à volatilité stochastique." Phd thesis, Université Paris-Est, 2011. http://tel.archives-ouvertes.fr/tel-00604530.

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La première partie de cette thèse est consacrée aux problématiques liées à la modélisation markovienne de la courbe de variance forward. Elle est divisée en 3 chapitres. Dans le premier chapitre, nous présentons le cadre général de la modélisation de type HJM-Markov pour la courbe de variance forward. Nous revisitons le cadre affine-markovien modélisation et nous l'illustrons par l'exemple du modèle de Bühler. Dans le deuxième chapitre, nous proposons un nouveau modèle pour la courbe de variance forward qui combine les caractéristiques des deux versions (continue et discrète) du modèle de Bergomi 2008, sans se réduire ni à l'une ni à l'autre. Un des avantages de ce modèle est que les prix des futures et options sur VIX peuvent être exprimés comme des espérances de fonctions déterministes d'une variable aléatoire gaussienne, ce qui réduit le problème de la calibration à l'inversion de certaines fonctions monotones. Dans le troisième chapitre, on propose une méthode d'approximation pour les prix d'options européennes dans des modèles à volatilité stochastique de type multi-factoriels lognormal (comprenant le modèle présenté dans le deuxième chapitre, les modèles de Bergomi et le modèle de Scot 1987). Nous obtenons un développement d'ordre 3 de la densité du sous-jacent par rapport au paramètre de la volatilité de la volatilité. Nous présentons aussi une méthode de réduction de variance de type "variable de contrôle" pour la simulation par la méthode de Monte-Carlo qui utilise l'approximation explicite que nous obtenons de la fonction de répartition de la loi du sous-jacent. La deuxième partie de cette thèse est consacrée à l'étude des propriétés de monotonie des prix d'options européennes par rapport aux paramètres du CIR dans le modèle de Heston. Elle est divisée en deux chapitres. Dans le premier chapitre (cf. chapitre 4), nous donnons quelques résultats généraux sur le processus CIR. Nous montrons d'abord que les queues de distribution d'une combinaison du CIR et de sa moyenne arithmétique se comportent comme des exponentielles. Nous étudions ensuite les dérivées de la solution de ce processus par rapport aux paramètres de sa dynamique. Ces dérivées sont données comme solutions d'équations différentielles stochastiques, qu'on résout pour obtenir des représentations de ces dérivées en fonction des trajectoires du CIR. Le chapitre 5 est consacré à l'étude de la monotonie du prix d'un Put européen par rapport aux paramètres du CIR et à la corrélation dans le modèle de Heston. Nous montrons que, sous certaines conditions, les prix d'options européennes sont monotones par rapport aux paramètres du drift du CIR. Nous montrons ensuite que le paramètre de la volatilité de la volatilité joue le rôle de la volatilité si on prend la variance réalisée comme sous-jacent. En particulier, les prix d'options convexes sur la variance réalisée sont strictement croissants par rapport à la volatilité de la volatilité. Enfin, nous étudions la monotonie du prix du Put européen par rapport à la corrélation. Nous montrons que le prix du put du Put est croissant par rapport à la corrélation pour les petites valeurs du Spot et décroissant pour les grandes valeurs. Nous étudions ensuite les points de changement de monotonie pour les courtes et longues maturités
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Ren, Huiying. "Experimental Studies of Turbulent Boundary Layers Over a Rough Forward-facing Step and its Coarse Scale Resolution Approximations." Wright State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=wright1292449621.

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Iben, Taarit Marouan. "Valorisation des ajustements Xva : de l’exposition espérée aux risques adverses de corrélation." Thesis, Paris Est, 2018. http://www.theses.fr/2018PESC1059/document.

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Nous entamons ce rapport de thèse par l’évaluation de l’espérance espérée qui représente une des composantes majeures des ajustements XVA. Sous l’hypothèse d’indépendance entre l’exposition et les coûts de financement et de crédit, nous dérivons dans le chapitre 3 une représentation nouvelle de l’exposition espérée comme la solution d’une équation différentielle ordinaire par rapport au temps d’observation du défaut. Nous nous basons, pour le cas unidimensionnel, sur des arguments similaires à ceux de la volatilité locale de Dupire. Et pour le cas multidimensionnel, nous nous référons à la formule de la Co-aire. Cette représentation permet d’expliciter l’impact de la volatilité sur l’exposition espérée : Cette valeur temps fait intervenir la volatilité des sous-jacents ainsi que la sensibilité au premier ordre du prix, évalués sur un ensemble fini de points. Malgré des limitations numériques, cette méthode est une approche précise et rapide pour la valorisation de la XVA unitaire en dimension 1 et 2.Les chapitres suivants sont dédiés aux aspects du risque de corrélations entre les enveloppes d’expositions et les coûts XVA. Nous présentons une modélisation du risque général de corrélation à travers une diffusion stochastique multivariée, comprenant à la fois les sous-jacents des dérivés et les intensités de défaut. Dans ce cadre, nous exposons une nouvelle approche de valorisation par développements asymptotiques, telle que le prix d’un ajustement XVA correspond au prix de l’ajustement à corrélation nulle, auquel s’ajoute une somme explicite de termes correctifs. Le chapitre 4 est consacré à la dérivation technique et à l’étude de l’erreur numérique dans le cadre de la valorisation de dérivés contingents au défaut. La qualité des approximations numériques dépend uniquement de la régularité du processus de diffusion de l’intensité de crédit, et elle est indépendante de la régularité de la fonction payoff. Les formules de valorisation pour CVA et FVA sont présentées dans le chapitre 5. Une généralisation des développements asymptotiques pour le cadre bilatéral de défaut est adressée dans le chapitre 6.Nous terminons ce mémoire en abordant un cas du risque spécifique de corrélation lié aux contrats de migration de rating. Au-delà des formules de valorisation, notre contribution consiste à présenter une approche robuste pour la construction et la calibration d’un modèle de transition de ratings consistant avec les probabilités de défaut implicites de marché
The point of departure of this thesis is the valuation of the expected exposure which represents one of the major components of XVA adjustments. Under independence assumptions with credit and funding costs, we derive in Chapter 3 a new representation of the expected exposure as the solution of an ordinary differential equation w.r.t the default time variable. We rely on PDE arguments in the spirit of Dupire’s local volatility equation for the one dimensional problem. The multidimensional extension is addressed using the co-area formula. This forward representation gives an explicit expression of the exposure’s time value, involving the local volatility of the underlying diffusion process and the first order Greek delta, both evaluated only on finite set of points. From a numerical perspective, dimensionality is the main limitation of this approach. Though, we highlight high accuracy and time efficiency for standalone calculations in dimensions 1 and 2.The remaining chapters are dedicated to aspects of the correlation risk between the exposure and XVA costs. We start with the general correlation risk which is classically modeled in a joint diffusion process for market variables and the credit/funding spreads. We present a novel approach based on asymptotic expansions in a way that the price of an XVA adjustment with correlation risk is given by the classical correlation-free adjustment to which is added a sum of explicit correction terms depending on the exposure Greeks. Chapter 4 is consecrated to the technical derivation and error analysis of the expansion formulas in the context of pricing credit contingent derivatives. The accuracy of the valuation approach is independent of the smoothness of the payoff function, but it is related to the regularity of the credit intensity model. This finding is of special interest for pricing in a real financial context. Pricing formulas for CVA and FVA adjustments are derived in Chapter 5, along with numerical experiments. A generalization of the asymptotic expansions to a bilateral default risk setting is addressed in Chapter 6.Our thesis ends by tackling the problem of modeling the specific Right-Way Risk induced by rating trigger events within the collateral agreements. Our major contribution is the calibration of a rating transition model to market implied default probabilities
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Romero, Merino Enrique. "Learning with Feed-forward Neural Networks: Three Schemes to Deal with the Bias/Variance Trade-off." Doctoral thesis, Universitat Politècnica de Catalunya, 2004. http://hdl.handle.net/10803/6644.

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In terms of the Bias/Variance decomposition, very flexible (i.e., complex) Supervised Machine Learning systems may lead to unbiased estimators but with high variance. A rigid model, in contrast, may lead to small variance but high bias. There is a trade-off between the bias and variance contributions to the error, where the optimal performance is achieved.

In this work we present three schemes related to the control of the Bias/Variance decomposition for Feed-forward Neural Networks (FNNs) with the (sometimes modified) quadratic loss function:

1. An algorithm for sequential approximation with FNNs, named Sequential Approximation with Optimal Coefficients and Interacting Frequencies (SAOCIF). Most of the sequential approximations proposed in the literature select the new frequencies (the non-linear weights) guided by the approximation of the residue of the partial approximation. We propose a sequential algorithm where the new frequency is selected taking into account its interactions with the previously selected ones. The interactions are discovered by means of their optimal coefficients (the linear weights). A number of heuristics can be used to select the new frequencies. The aim is that the same level of approximation may be achieved with less hidden units than if we only try to match the residue as best as possible. In terms of the Bias/Variance decomposition, it will be possible to obtain simpler models with the same bias. The idea behind SAOCIF can be extended to approximation in Hilbert spaces, maintaining orthogonal-like properties. In this case, the importance of the interacting frequencies lies in the expectation of increasing the rate of approximation. Experimental results show that the idea of interacting frequencies allows to construct better approximations than matching the residue.

2. A study and comparison of different criteria to perform Feature Selection (FS) with Multi-Layer Perceptrons (MLPs) and the Sequential Backward Selection (SBS) procedure within the wrapper approach. FS procedures control the Bias/Variance decomposition by means of the input dimension, establishing a clear connection with the curse of dimensionality. Several critical decision points are studied and compared. First, the stopping criterion. Second, the data set where the value of the loss function is measured. Finally, we also compare two ways of computing the saliency (i.e., the relative importance) of a feature: either first train a network and then remove temporarily every feature or train a different network with every feature temporarily removed. The experiments are performed for linear and non-linear models. Experimental results suggest that the increase in the computational cost associated with retraining a different network with every feature temporarily removed previous to computing the saliency can be rewarded with a significant performance improvement, specially if non-linear models are used. Although this idea could be thought as very intuitive, it has been hardly used in practice. Regarding the data set where the value of the loss function is measured, it seems clear that the SBS procedure for MLPs takes profit from measuring the loss function in a validation set. A somewhat non-intuitive conclusion is drawn looking at the stopping criterion, where it can be seen that forcing overtraining may be as useful as early stopping.

3. A modification of the quadratic loss function for classification problems, inspired in Support Vector Machines (SVMs) and the AdaBoost algorithm, named Weighted Quadratic Loss (WQL) function. The modification consists in weighting the contribution of every example to the total error. In the linearly separable case, the solution of the hard margin SVM also minimizes the proposed loss function. The hardness of the resulting solution can be controlled, as in SVMs, so that this scheme may also be used for the non-linearly separable case. The error weighting proposed in WQL forces the training procedure to pay more attention to the points with a smaller margin. Therefore, variance tries to be controlled by not attempting to overfit the points that are already well classified. The model shares several properties with the SVMs framework, with some additional advantages. On the one hand, the final solution is neither restricted to have an architecture with so many hidden units as points (or support vectors) in the data set nor to use kernel functions. The frequencies are not restricted to be a subset of the data set. On the other hand, it allows to deal with multiclass and multilabel problems in a natural way. Experimental results are shown confirming these claims.

A wide experimental work has been done with the proposed schemes, including artificial data sets, well-known benchmark data sets and two real-world problems from the Natural Language Processing domain. In addition to widely used activation functions, such as the hyperbolic tangent or the Gaussian function, other activation functions have been tested. In particular, sinusoidal MLPs showed a very good behavior. The experimental results can be considered as very satisfactory. The schemes presented in this work have been found to be very competitive when compared to other existing schemes described in the literature. In addition, they can be combined among them, since they deal with complementary aspects of the whole learning process.
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Duan, Junbo. "Restauration et séparation de signaux polynômiaux par morceaux. Application à la microscopie de force atomique." Thesis, Nancy 1, 2010. http://www.theses.fr/2010NAN10082/document.

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Cette thèse s'inscrit dans le domaine des problèmes inverses en traitement du signal. Elle est consacrée à la conception d'algorithmes de restauration et de séparation de signaux parcimonieux et à leur application à l'approximation de courbes de forces en microscopie de force atomique (AFM), où la notion de parcimonie est liée au nombre de points de discontinuité dans le signal (sauts, changements de pente, changements de courbure). Du point de vue méthodologique, des algorithmes sous-optimaux sont proposés pour le problème de l'approximation parcimonieuse basée sur la pseudo-norme l0 : l'algorithme Single Best Replacement (SBR) est un algorithme itératif de type « ajout-retrait » inspiré d'algorithmes existants pour la restauration de signaux Bernoulli-Gaussiens. L'algorithme Continuation Single Best Replacement (CSBR) est un algorithme permettant de fournir des approximations à des degrés de parcimonie variables. Nous proposons aussi un algorithme de séparation de sources parcimonieuses à partir de mélanges avec retards, basé sur l'application préalable de l'algorithme CSBR sur chacun des mélanges, puis sur une procédure d'appariement des pics présents dans les différents mélanges. La microscopie de force atomique est une technologie récente permettant de mesurer des forces d'interaction entre nano-objets. L'analyse de courbes de forces repose sur des modèles paramétriques par morceaux. Nous proposons un algorithme permettant de détecter les régions d'intérêt (les morceaux) où chaque modèle s'applique puis d'estimer par moindres carrés les paramètres physiques (élasticité, force d'adhésion, topographie, etc.) dans chaque région. Nous proposons finalement une autre approche qui modélise une courbe de force comme un mélange de signaux sources parcimonieux retardées. La recherche des signaux sources dans une image force-volume s'effectue à partir d'un grand nombre de mélanges car il y autant de mélanges que de pixels dans l'image
This thesis handles several inverse problems occurring in sparse signal processing. The main contributions include the conception of algorithms dedicated to the restoration and the separation of sparse signals, and their application to force curve approximation in Atomic Force Microscopy (AFM), where the notion of sparsity is related to the number of discontinuity points in the signal (jumps, change of slope, change of curvature).In the signal processing viewpoint, we propose sub-optimal algorithms dedicated to the sparse signal approximation problem based on the l0 pseudo-norm : the Single Best Replacement algorithm (SBR) is an iterative "forward-backward" algorithm inspired from existing Bernoulli-Gaussian signal restoration algorithms. The Continuation Single Best Replacement algorithm (CSBR) is an extension providing approximations at various sparsity levels. We also address the problem of sparse source separation from delayed mixtures. The proposed algorithm is based on the prior application of CSBR on every mixture followed by a matching procedure which attributes a label for each peak occurring in each mixture.Atomic Force Microscopy (AFM) is a recent technology enabling to measure interaction forces between nano-objects. The force-curve analysis relies on piecewise parametric models. We address the detection of the regions of interest (the pieces) where each model holds and the subsequent estimation of physical parameters (elasticity, adhesion forces, topography, etc.) in each region by least-squares optimization. We finally propose an alternative approach in which a force curve is modeled as a mixture of delayed sparse sources. The research of the source signals and the delays from a force-volume image is done based on a large number of mixtures since there are as many mixtures as the number of image pixels
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Books on the topic "Forward approximation"

1

Biolley, Serge de. Approximation of substantive criminal law in the EU: The way forward. Bruxelles: Editions de l'Université de Bruxelles, 2013.

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S, Subramanian, Chunduru Srinivas, and United States. National Aeronautics and Space Administration., eds. Sensitivity of lag-damping correlations to structural and aerodynamic approximations of isolated experimental rotors in forward flight: Interim technical report under NASA-Ames Research grant no. NAG-2-797 (August 1, 1992 - December 21, 1993). Boca Raton, FL: Florida Atlantic University, Dept. of Mechanical Engineering, College of Engineering, 1994.

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GALLI/WEYEMBERG. Approximation of substantive criminal law in the EU the way forward. UNIV BRUXELLES, 2013.

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Epstein, Richard A. The Basic Structure of Intellectual Property Law. Edited by Rochelle Dreyfuss and Justine Pila. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198758457.013.7.

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This chapter puts forward a comprehensive framework for evaluating property regimes for both physical and intellectual property resources. It starts with an account of the trade-off between common and private property regimes, noting that the former is appropriate, as a first approximation for resources that facilitate communication and transportation, where holdout problems dominate externality constraints. But where high levels of investment are needed, and coordination problems are low, private property, as bounded by laws of trespass, nuisance and infringement now tend to dominate. There are no rules of acquisition for an open-access regime. But for private property in all its forms, the common and civil law rules of occupation avoid virtually all the complications that stem from Locke’s erroneous labor theory of acquisition. The chapter then explores the rules governing duration, exclusion, remedies, and alienation in multiple private property interests, including the major forms of intellectual property.
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National Aeronautics and Space Administration (NASA) Staff. Sensitivity of Lag-Damping Correlations to Structural and Aerodynamic Approximations of Isolated Experimental Rotors in Forward Flight. Independently Published, 2018.

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Book chapters on the topic "Forward approximation"

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Furutsu, Koichi. "Forward Scattering Approximation." In Springer Series on Wave Phenomena, 185–262. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-84807-0_7.

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Chassagneux, Jean-François, Hinesh Chotai, and Mirabelle Muûls. "Numerical Approximation of FBSDEs." In A Forward-Backward SDEs Approach to Pricing in Carbon Markets, 59–74. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-63115-8_4.

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Anastassiou, George A., and Razvan A. Mezei. "Reverse and Forward Fractional Integral Inequalities." In Advances in Applied Mathematics and Approximation Theory, 441–78. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6393-1_29.

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Chung, In-Hwan, Tim Dun, and Erik Schlögl. "Lognormal Forward Market Model (LFM) Volatility Function Approximation." In Contemporary Quantitative Finance, 369–405. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-03479-4_19.

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Wen, Yunqing, Guoqiang Li, and Shoji Yuen. "An Over-Approximation Forward Analysis for Nested Timed Automata." In Structured Object-Oriented Formal Language and Method, 62–80. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-17404-4_5.

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Gaya, Muhammad Sani, Norhaliza Abdul Wahab, Yahya Md Sam, and Sharatul Izah Samsuddin. "Feed-Forward Neural Network Approximation Applied to Activated Sludge System." In Communications in Computer and Information Science, 587–98. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-45037-2_63.

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Zhou, Zhenghua, and Jianwei Zhao. "Approximation of Curves Contained on the Surface by Freed-Forward Neural Networks." In Artificial Intelligence and Computational Intelligence, 286–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23896-3_34.

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Zhang, Weixiong. "Forward Pruning for Approximation and Flexible Computation, Part II: Multiagent Game Playing." In State-Space Search, 172–81. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1538-7_9.

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Lima, P. M., M. F. Teodoro, N. J. Ford, and P. M. Lumb. "Analysis and Computational Approximation of a Forward–Backward Equation Arising in Nerve Conduction." In Differential and Difference Equations with Applications, 475–83. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7333-6_42.

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Zhang, Weixiong. "Forward Pruning for Approximation and Flexible Computation, Part I: Single-Agent Combinatorial Optimization." In State-Space Search, 144–71. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1538-7_8.

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Conference papers on the topic "Forward approximation"

1

Dockhorn, Alexander, Tim Tippelt, and Rudolf Kruse. "Model Decomposition for Forward Model Approximation." In 2018 IEEE Symposium Series on Computational Intelligence (SSCI). IEEE, 2018. http://dx.doi.org/10.1109/ssci.2018.8628624.

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Barton, Russell R., Martin Meckesheimer, and Timothy W. Simpson. "Experimental Design Issues for Simultaneous Fitting of Forward and Inverse Metamodels." In ASME 2000 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/detc2000/dac-14282.

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Abstract In engineering design, approximations to engineering simulation or analysis models can provide quick, approximate predictions of system or part performance as a function of system/part design parameters. There are often preliminary requirements for performance, which can be mapped to specific values of design parameters via an inverse model. Typically, only forward models exist explicitly, but an inverse approximation can be fitted. The quality of an approximation depends on the set of runs (the experiment design) used to fit the approximation. This paper examines experiment design construction strategies for simultaneously fitting forward and inverse approximation models, using the commonly applied measure of D-optimality.
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Virmont, Jean, and Guy Ledanois. "Near-Infrared Medical Imaging: Improved Approximations for the Forward and Inverse Problems." In Advances in Optical Imaging and Photon Migration. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/aoipm.1996.ria307.

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We consider imaging of objects hidden in a scattering and absorbing medium, thick enough for the diffusion approximation to be valid, e.g. mammography or brain activity studies. We propose approximate models improving over Born to calculate the image: the electrostatic approximation if the object is small, plus a renormalization transform if it is larger. Using an exact solution of the ‘sphere in slab’ problem for comparison, and a Bayesian simplified inverse code, we demonstrate that these approximations improve the reconstruction.
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Dockhorn, Alexander, and Daan Apeldoorn. "Forward Model Approximation for General Video Game Learning." In 2018 IEEE Conference on Computational Intelligence and Games (CIG). IEEE, 2018. http://dx.doi.org/10.1109/cig.2018.8490411.

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Kim and Adali. "Universal approximation of fully complex feed-forward neural networks." In IEEE International Conference on Acoustics Speech and Signal Processing ICASSP-02. IEEE, 2002. http://dx.doi.org/10.1109/icassp.2002.1005904.

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Kim, Taehwan, and Tulay Adali. "Universal approximation of fully complex feed-forward neural networks." In Proceedings of ICASSP '02. IEEE, 2002. http://dx.doi.org/10.1109/icassp.2002.5743956.

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Gryazin, Yury A. "High-order approximation compact schemes for forward subsurface scattering problems." In SPIE Defense + Security, edited by Kenneth I. Ranney and Armin Doerry. SPIE, 2014. http://dx.doi.org/10.1117/12.2050189.

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Bandyk, Piotr J., and George S. Hazen. "A Forward-Speed Body-Exact Strip Theory." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-41656.

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This paper develops an extension to the body-exact strip theory of Bandyk, Beck, and Zhang [1–8], focused on improved prediction of forward-speed effects. One of the known limitations of standard strip theory is the treatment of forward speed terms. The free surface boundary conditions completely neglect the forward speed, which is usually justified by the argument of high-frequency oscillations. The pressure equation on the body includes a speed-dependent term that must computed, most commonly using the Ogilvie-Tuck theorem or numerical approximations. The strip theory variation described here circumvents these deficiencies by applying the 2D+T approach. The model assumes that each two-dimensional frame, in which a boundary value problem (BVP) is solved, remains fixed relative to an earth-fixed frame. The numerical model is based on a time-domain Rankine source method, using the same body-exact approximation as described in earlier work [1]. A suitable acceleration potential BVP is derived. Added mass and damping coefficients are calculated for two Wigley hulls, using the the standard body-exact approach and forward-speed 2D + T variant, and compared to existing model test and numerical data.
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Zhao, Jian-wei, and Fei-long Cao. "Lp Error Estimate of Approximation by a Feed-Forward Neural Network." In 2009 International Conference on Artificial Intelligence and Computational Intelligence. IEEE, 2009. http://dx.doi.org/10.1109/aici.2009.46.

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Wang, Liping, and Kristy Gau. "Automatic Step-Size Procedure in Forward-Difference for Reliability and Design Optimization." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/dac-8603.

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Abstract In this paper, an improved automatic step-size procedure in forward-difference approximation for reliability analysis and optimization design is proposed. Traditionally, the step-size is pre-selected and does not change during optimization / reliability design process. This fixed step-size procedure may provide “poor” derivative approximations for highly nonlinear problems or the problems having insufficient digits of the outputs. The proposed method computes the optimum step size for each design variable by minimizing the truncation and condition errors. The condition error is focused on the error caused by insufficient digits of the outputs in this paper. Several numerical problems are tested to demonstrate the proposed procedure. The results comparison shows that the proposed procedure provides more accurate gradients for optimization and reliability design.
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Reports on the topic "Forward approximation"

1

Arhin, Stephen, Babin Manandhar, Hamdiat Baba Adam, and Adam Gatiba. Predicting Bus Travel Times in Washington, DC Using Artificial Neural Networks (ANNs). Mineta Transportation Institute, April 2021. http://dx.doi.org/10.31979/mti.2021.1943.

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Washington, DC is ranked second among cities in terms of highest public transit commuters in the United States, with approximately 9% of the working population using the Washington Metropolitan Area Transit Authority (WMATA) Metrobuses to commute. Deducing accurate travel times of these metrobuses is an important task for transit authorities to provide reliable service to its patrons. This study, using Artificial Neural Networks (ANN), developed prediction models for transit buses to assist decision-makers to improve service quality and patronage. For this study, we used six months of Automatic Vehicle Location (AVL) and Automatic Passenger Counting (APC) data for six Washington Metropolitan Area Transit Authority (WMATA) bus routes operating in Washington, DC. We developed regression models and Artificial Neural Network (ANN) models for predicting travel times of buses for different peak periods (AM, Mid-Day and PM). Our analysis included variables such as number of served bus stops, length of route between bus stops, average number of passengers in the bus, average dwell time of buses, and number of intersections between bus stops. We obtained ANN models for travel times by using approximation technique incorporating two separate algorithms: Quasi-Newton and Levenberg-Marquardt. The training strategy for neural network models involved feed forward and errorback processes that minimized the generated errors. We also evaluated the models with a Comparison of the Normalized Squared Errors (NSE). From the results, we observed that the travel times of buses and the dwell times at bus stops generally increased over time of the day. We gathered travel time equations for buses for the AM, Mid-Day and PM Peaks. The lowest NSE for the AM, Mid-Day and PM Peak periods corresponded to training processes using Quasi-Newton algorithm, which had 3, 2 and 5 perceptron layers, respectively. These prediction models could be adapted by transit agencies to provide the patrons with accurate travel time information at bus stops or online.
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