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Добірка наукової літератури з теми "Probabilistic representation of PDEs"

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Опубліковано: 1 червня 2024

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Статті в журналах з теми "Probabilistic representation of PDEs":

1

BERNAL, FRANCISCO, GONÇALO DOS REIS, and GREIG SMITH. "Hybrid PDE solver for data-driven problems and modern branching." European Journal of Applied Mathematics 28, no. 6 (May 22, 2017): 949–72. http://dx.doi.org/10.1017/s0956792517000109.

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The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations about the parallelization and scalability of realistic problems are often critical enough to warrant acknowledgement in the modelling phase. The purpose of this paper is to spread awareness of the Probabilistic Domain Decomposition (PDD) method, a fresh approach to the parallelization of PDEs with excellent scalability properties. The idea exploits the stochastic representation of the PDE and its approximation via Monte Carlo in combination with deterministic high-performance PDE solvers. We describe the ingredients of PDD and its applicability in the scope of data science. In particular, we highlight recent advances in stochastic representations for non-linear PDEs using branching diffusions, which have significantly broadened the scope of PDD. We envision this work as a dictionary giving large-scale PDE practitioners references on the very latest algorithms and techniques of a non-standard, yet highly parallelizable, methodology at the interface of deterministic and probabilistic numerical methods. We close this work with an invitation to the fully non-linear case and open research questions.
2

BLOMKER, D., M. ROMITO, and R. TRIBE. "A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees." Annales de l'Institut Henri Poincare (B) Probability and Statistics 43, no. 2 (March 2007): 175–92. http://dx.doi.org/10.1016/j.anihpb.2006.02.001.

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3

Gevorkyan, Ashot S., Aleksander V. Bogdanov, Vladimir V. Mareev, and Koryun A. Movsesyan. "Theoretical and Numerical Study of Self-Organizing Processes in a Closed System Classical Oscillator and Random Environment." Mathematics 10, no. 20 (October 18, 2022): 3868. http://dx.doi.org/10.3390/math10203868.

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A self-organizing joint system classical oscillator–random environment is considered within the framework of a complex probabilistic process that satisfies a Langevin-type stochastic differential equation. Various types of randomness generated by the environment are considered. In the limit of statistical equilibrium (SEq), second-order partial differential equations (PDE) are derived that describe the distribution of classical environmental fields. The mathematical expectation of the oscillator trajectory is constructed in the form of a functional-integral representation, which, in the SEq limit, is compactified into a two-dimensional integral representation with an integrand: the solution of the second-order complex PDE. It is proved that the complex PDE in the general case is reduced to two independent PDEs of the second order with spatially deviating arguments. The geometric and topological features of the two-dimensional subspace on which these equations arise are studied in detail. An algorithm for parallel modeling of the problem has been developed.
4

Yan, Long, Bohang Xu, and Zhangjun Liu. "Dimension Reduction Method-Based Stochastic Wind Field Simulations for Dynamic Reliability Analysis of Communication Towers." Buildings 13, no. 10 (October 16, 2023): 2608. http://dx.doi.org/10.3390/buildings13102608.

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The communication tower is a lifeline engineering that ensures the normal operation of wireless communication systems. Extreme wind disasters are inevitable while it is in service. Two dimension-reduction (DR) probabilistic representations based on proper orthogonal decomposition (POD) and wavenumber spectral representation (WSR), say DR-POD and DR-WSR, were thus proposed in this study. In order to determine the least representative sample size that satisfies the engineering accuracy requirements, the simulation error and simulation duration of 10 simulation points distributed along the height direction of the communication tower under different representative sample numbers were compared. Furthermore, for the fluctuating wind field with different numbers of simulation points distributed along the height of the communication tower, the simulation accuracy as well as efficiency of the DR-POD and the DR-WSR were compared. Finally, a high-rise communication tower structure’s wind-induced dynamic response study and wind-resistance reliability analysis were performed utilizing an alliance of the probability density evolution method (PDEM) and two DR probabilistic models, taking 10 load points into account. The structural dynamic analysis illustrates that the reliability of the communication tower structure and the wind-induced dynamic response allying the two DR probabilistic models with the PDEM have outstanding consistency.
5

Ren, Panpan, and Feng-Yu Wang. "Space-distribution PDEs for path independent additive functionals of McKean–Vlasov SDEs." Infinite Dimensional Analysis, Quantum Probability and Related Topics 23, no. 03 (September 2020): 2050018. http://dx.doi.org/10.1142/s0219025720500186.

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Let [Formula: see text] be the space of probability measures on [Formula: see text] with finite second moment. The path independence of additive functionals of McKean–Vlasov SDEs is characterized by PDEs on the product space [Formula: see text] equipped with the usual derivative in space variable and Lions’ derivative in distribution. These PDEs are solved by using probabilistic arguments developed from Ref. 2. As a consequence, the path independence of Girsanov transformations is identified with nonlinear PDEs on [Formula: see text] whose solutions are given by probabilistic arguments as well. In particular, the corresponding results on the Girsanov transformation killing the drift term derived earlier for the classical SDEs are recovered as special situations.
6

Xiao, Lishun, Shengjun Fan, and Dejian Tian. "A probabilistic approach to quasilinear parabolic PDEs with obstacle and Neumann problems." ESAIM: Probability and Statistics 24 (2020): 207–26. http://dx.doi.org/10.1051/ps/2019023.

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In this paper, by a probabilistic approach we prove that there exists a unique viscosity solution to obstacle problems of quasilinear parabolic PDEs combined with Neumann boundary conditions and algebra equations. The existence and uniqueness for adapted solutions of fully coupled forward-backward stochastic differential equations with reflections play a crucial role. Compared with existing works, in our result the spatial variable of solutions of PDEs lives in a region without convexity constraints, the second order coefficient of PDEs depends on the gradient of the solution, and the required conditions for the coefficients are weaker.
7

Haneche, M., K. Djaballah, and K. Khaldi. "An algorithm for probabilistic solution of parabolic PDEs." Sequential Analysis 40, no. 4 (October 2, 2021): 441–65. http://dx.doi.org/10.1080/07474946.2021.2010403.

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8

Denis, Laurent, Anis Matoussi, and Jing Zhang. "Quasilinear Stochastic PDEs with two obstacles: Probabilistic approach." Stochastic Processes and their Applications 133 (March 2021): 1–40. http://dx.doi.org/10.1016/j.spa.2020.11.002.

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9

Matoussi, Anis, Dylan Possamaï, and Wissal Sabbagh. "Probabilistic interpretation for solutions of fully nonlinear stochastic PDEs." Probability Theory and Related Fields 174, no. 1-2 (July 10, 2018): 177–233. http://dx.doi.org/10.1007/s00440-018-0859-4.

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10

Sow *, A. B., and E. Pardoux. "Probabilistic interpretation of a system of quasilinear parabolic PDEs." Stochastics and Stochastic Reports 76, no. 5 (October 2004): 429–77. http://dx.doi.org/10.1080/10451120412331303150.

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Статті в журналах Дисертації

Дисертації з теми "Probabilistic representation of PDEs":

1

Izydorczyk, Lucas. "Probabilistic backward McKean numerical methods for PDEs and one application to energy management." Electronic Thesis or Diss., Institut polytechnique de Paris, 2021. http://www.theses.fr/2021IPPAE008.

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Cette thèse s'intéresse aux équations différentielles stochastiques de type McKean(EDS) et à leur utilisation pour représenter des équations aux dérivées partielles (EDP) non linéaires. Ces équations ne dépendent pas seulement du temps et de la position d'une certaine particule mais également de sa loi. En particulier nous traitons le cas inhabituel de la représentation d'EDP de type Fokker-Planck avec condition terminale fixée. Nous discutons existence et unicité pour ces EDP et de leur représentation sous la forme d'une EDS de type McKean, dont l'unique solutioncorrespond à la dynamique du retourné dans le temps d'un processus de diffusion.Nous introduisons la notion de représentation complètement non-linéaire d'une EDP semilinéaire. Celle-ci consiste dans le couplage d'une EDS rétrograde et d'un processus solution d'une EDS évoluant de manière rétrograde dans le temps. Nous discutons également une application à la représentation d'une équation d'Hamilton-Jacobi-Bellman (HJB) en contrôle stochastique. Sur cette base, nous proposonsun algorithme de Monte-Carlo pour résoudre des problèmes de contrôle. Celui ciest avantageux en termes d'efficience calculatoire et de mémoire, en comparaisonavec les approches traditionnelles progressive rétrograde. Nous appliquons cette méthode dans le contexte de la gestion de la demande dans les réseaux électriques. Pour finir, nous faisons le point sur l'utilisation d'EDS de type McKean généralisées pour représenter des EDP non-linéaires et non-conservatives plus générales que Fokker-Planck
This thesis concerns McKean Stochastic Differential Equations (SDEs) to representpossibly non-linear Partial Differential Equations (PDEs). Those depend not onlyon the time and position of a given particle, but also on its probability law. In particular, we treat the unusual case of Fokker-Planck type PDEs with prescribed final data. We discuss existence and uniqueness for those equations and provide a probabilistic representation in the form of McKean type equation, whose unique solution corresponds to the time-reversal dynamics of a diffusion process.We introduce the notion of fully backward representation of a semilinear PDE: thatconsists in fact in the coupling of a classical Backward SDE with an underlying processevolving backwardly in time. We also discuss an application to the representationof Hamilton-Jacobi-Bellman Equation (HJB) in stochastic control. Based on this, we propose a Monte-Carlo algorithm to solve some control problems which has advantages in terms of computational efficiency and memory whencompared to traditional forward-backward approaches. We apply this method in the context of demand side management problems occurring in power systems. Finally, we survey the use of generalized McKean SDEs to represent non-linear and non-conservative extensions of Fokker-Planck type PDEs
2

Sabbagh, Wissal. "Some Contributions on Probabilistic Interpretation For Nonlinear Stochastic PDEs." Thesis, Le Mans, 2014. http://www.theses.fr/2014LEMA1019/document.

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L'objectif de cette thèse est l'étude de la représentation probabiliste des différentes classes d'EDPSs non-linéaires(semi-linéaires, complètement non-linéaires, réfléchies dans un domaine) en utilisant les équations différentielles doublement stochastiques rétrogrades (EDDSRs). Cette thèse contient quatre parties différentes. Nous traitons dans la première partie les EDDSRs du second ordre (2EDDSRs). Nous montrons l'existence et l'unicité des solutions des EDDSRs en utilisant des techniques de contrôle stochastique quasi- sure. La motivation principale de cette étude est la représentation probabiliste des EDPSs complètement non-linéaires. Dans la deuxième partie, nous étudions les solutions faibles de type Sobolev du problème d'obstacle pour les équations à dérivées partielles inteégro-différentielles (EDPIDs). Plus précisément, nous montrons la formule de Feynman-Kac pour l'EDPIDs par l'intermédiaire des équations différentielles stochastiques rétrogrades réfléchies avec sauts (EDSRRs). Plus précisément, nous établissons l'existence et l'unicité de la solution du problème d'obstacle, qui est considérée comme un couple constitué de la solution et de la mesure de réflexion. L'approche utilisée est basée sur les techniques de flots stochastiques développées dans Bally et Matoussi (2001) mais les preuves sont beaucoup plus techniques. Dans la troisième partie, nous traitons l'existence et l'unicité pour les EDDSRRs dans un domaine convexe D sans aucune condition de régularité sur la frontière. De plus, en utilisant l'approche basée sur les techniques du flot stochastiques nous démontrons l'interprétation probabiliste de la solution faible de type Sobolev d'une classe d'EDPSs réfléchies dans un domaine convexe via les EDDSRRs. Enfin, nous nous intéressons à la résolution numérique des EDDSRs à temps terminal aléatoire. La motivation principale est de donner une représentation probabiliste des solutions de Sobolev d'EDPSs semi-linéaires avec condition de Dirichlet nul au bord. Dans cette partie, nous étudions l'approximation forte de cette classe d'EDDSRs quand le temps terminal aléatoire est le premier temps de sortie d'une EDS d'un domaine cylindrique. Ainsi, nous donnons les bornes pour l'erreur d'approximation en temps discret. Cette partie se conclut par des tests numériques qui démontrent que cette approche est effective
The objective of this thesis is to study the probabilistic representation (Feynman-Kac for- mula) of different classes ofStochastic Nonlinear PDEs (semilinear, fully nonlinear, reflected in a domain) by means of backward doubly stochastic differential equations (BDSDEs). This thesis contains four different parts. We deal in the first part with the second order BDS- DEs (2BDSDEs). We show the existence and uniqueness of solutions of 2BDSDEs using quasi sure stochastic control technics. The main motivation of this study is the probabilistic representation for solution of fully nonlinear SPDEs. First, under regularity assumptions on the coefficients, we give a Feynman-Kac formula for classical solution of fully nonlinear SPDEs and we generalize the work of Soner, Touzi and Zhang (2010-2012) for deterministic fully nonlinear PDE. Then, under weaker assumptions on the coefficients, we prove the probabilistic representation for stochastic viscosity solution of fully nonlinear SPDEs. In the second part, we study the Sobolev solution of obstacle problem for partial integro-differentialequations (PIDEs). Specifically, we show the Feynman-Kac formula for PIDEs via reflected backward stochastic differentialequations with jumps (BSDEs). Specifically, we establish the existence and uniqueness of the solution of the obstacle problem, which is regarded as a pair consisting of the solution and the measure of reflection. The approach is based on stochastic flow technics developed in Bally and Matoussi (2001) but the proofs are more technical. In the third part, we discuss the existence and uniqueness for RBDSDEs in a convex domain D without any regularity condition on the boundary. In addition, using the approach based on the technics of stochastic flow we provide the probabilistic interpretation of Sobolev solution of a class of reflected SPDEs in a convex domain via RBDSDEs. Finally, we are interested in the numerical solution of BDSDEs with random terminal time. The main motivation is to give a probabilistic representation of Sobolev solution of semilinear SPDEs with Dirichlet null condition. In this part, we study the strong approximation of this class of BDSDEs when the random terminal time is the first exit time of an SDE from a cylindrical domain. Thus, we give bounds for the discrete-time approximation error.. We conclude this part with numerical tests showing that this approach is effective
3

Tan, Xiaolu. "Stochastic control methods for optimal transportation and probabilistic numerical schemes for PDEs." Palaiseau, Ecole polytechnique, 2011. https://theses.hal.science/docs/00/66/10/86/PDF/These_TanXiaolu.pdf.

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Cette thèse porte sur les méthodes numériques pour les équations aux dérivées partielles (EDP) non-linéaires dégénérées, ainsi que pour des problèmes de contrôle d'EDP non-linéaires résultants d'un nouveau problème de transport optimal. Toutes ces questions sont motivées par des applications en mathématiques financières. La thèse est divisée en quatre parties. Dans une première partie, nous nous intéressons à la condition nécessaire et suffisante de la monotonie du thêta-schéma de différences finies pour l'équation de diffusion en dimension un. Nous donnons la formule explicite dans le cas de l'équation de la chaleur, qui est plus faible que la condition classique de Courant-Friedrichs-Lewy (CFL). Dans une seconde partie, nous considérons une EDP parabolique non-linéaire dégénérée et proposons un schéma de type ''splitting'' pour la résoudre. Ce schéma réunit un schéma probabiliste et un schéma semi-lagrangien. Au final, il peut être considéré comme un schéma Monte-Carlo. Nous donnons un résultat de convergence et également un taux de convergence du schéma. Dans une troisième partie, nous étudions un problème de transport optimal, où la masse est transportée par un processus d'état type ''drift-diffusion'' controllé. Le coût associé est dépendant des trajectoires de processus d'état, de son drift et de son coefficient de diffusion. Le problème de transport consiste à minimiser le coût parmi toutes les dynamiques vérifiant les contraintes initiales et terminales sur les distributions marginales. Nous prouvons une formule de dualité pour ce problème de transport, étendant ainsi la dualité de Kantorovich à notre contexte. La formulation duale maximise une fonction valeur sur l'espace des fonctions continues bornées, et la fonction valeur correspondante à chaque fonction continue bornée est la solution d'un problème de contrôle stochastique optimal. Dans le cas markovien, nous prouvons un principe de programmation dynamique pour ces problèmes de contrôle optimal, proposons un algorithme de gradient projeté pour la résolution numérique du problème dual, et en démontrons la convergence. Enfin dans une quatrième partie, nous continuons à développer l'approche duale pour le problème de transport optimal avec une application à la recherche de bornes de prix sans arbitrage des options sur variance étant donnés les prix des options européennes. Après une première approximation analytique, nous proposons un algorithme de gradient projeté pour approcher la borne et la stratégie statique correspondante en options vanilles
This thesis deals with the numerical methods for a fully nonlinear degenerate parabolic partial differential equations (PDEs), and for a controlled nonlinear PDEs problem which results from a mass transportation problem. The manuscript is divided into four parts. In a first part of the thesis, we are interested in the necessary and sufficient condition of the monotonicity of finite difference thêta-scheme for a one-dimensional diffusion equations. An explicit formula is given in case of the heat equation, which is weaker than the classical Courant-Friedrichs-Lewy (CFL) condition. In a second part, we consider a fully nonlinear degenerate parabolic PDE and propose a splitting scheme for its numerical resolution. The splitting scheme combines a probabilistic scheme and the semi-Lagrangian scheme, and in total, it can be viewed as a Monte-Carlo scheme for PDEs. We provide a convergence result as well as a rate of convergence. In the third part of the thesis, we study an optimal mass transportation problem. The mass is transported by the controlled drift-diffusion dynamics, and the associated cost depends on the trajectories, the drift as well as the diffusion coefficient of the dynamics. We prove a strong duality result for the transportation problem, thus extending the Kantorovich duality to our context. The dual formulation maximizes a value function on the space of all bounded continuous functions, and every value function corresponding to a bounded continuous function is the solution to a stochastic control problem. In the Markovian cases, we prove the dynamic programming principle of the optimal control problems, and we propose a gradient-projection algorithm for the numerical resolution of the dual problem, and provide a convergence result. Finally, in a fourth part, we continue to develop the dual approach of mass transportation problem with its applications in the computation of the model-independent no-arbitrage price bound of the variance option in a vanilla-liquid market. After a first analytic approximation, we propose a gradient-projection algorithm to approximate the bound as well as the corresponding static strategy in vanilla options
4

Helmkay, Owen. "Information representation, problem format, and mental algorithms in probabilistic reasoning." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ66153.pdf.

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5

Tarrago, Pierre. "Non-commutative generalization of some probabilistic results from representation theory." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1123/document.

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Le sujet de cette thèse est la généralisation non-commutative de résultats probabilistes venant de la théorie des représentations. Les résultats obtenus se divisent en trois parties distinctes. Dans la première partie de la thèse, le concept de groupe quantique easy est étendu au cas unitaire. Tout d'abord, nous donnons une classification de l'ensemble des groupes quantiques easy unitaires dans le cas libre et classique. Nous étendons ensuite les résultats probabilistes de au cas unitaire. La deuxième partie de la thèse est consacrée à une étude du produit en couronne libre. Dans un premier temps, nous décrivons les entrelaceurs des représentations dans le cas particulier d'un produit en couronne libre avec le groupe symétrique libre: cette description permet également d'obtenir plusieurs résultats probabilistes. Dans un deuxième temps, nous établissons un lien entre le produit en couronne libre et les algèbres planaires: ce lien mène à une preuve d'une conjecture de Banica et Bichon. Dans la troisième partie de la thèse, nous étudions un analoque du graphe de Young qui encode la structure multiplicative des fonctions fondamentales quasi-symétriques. La frontière minimale de ce graphe a déjà été décrite par Gnedin et Olshanski. Nous prouvons que la frontière minimale coïncide avec la frontière de Martin. Au cours de cette preuve, nous montrons plusieurs résultats combinatoires asymptotiques concernant les diagrammes de Young en ruban
The subject of this thesis is the non-commutative generalization of some probabilistic results that occur in representation theory. The results of the thesis are divided into three different parts. In the first part of the thesis, we classify all unitary easy quantum groups whose intertwiner spaces are described by non-crossing partitions, and develop the Weingarten calculus on these quantum groups. As an application of the previous work, we recover the results of Diaconis and Shahshahani on the unitary group and extend those results to the free unitary group. In the second part of the thesis, we study the free wreath product. First, we study the free wreath product with the free symmetric group by giving a description of the intertwiner spaces: several probabilistic results are deduced from this description. Then, we relate the intertwiner spaces of a free wreath product with the free product of planar algebras, an object which has been defined by Bisch and Jones. This relation allows us to prove the conjecture of Banica and Bichon. In the last part of the thesis, we prove that the minimal and the Martin boundaries of a graph introduced by Gnedin and Olshanski are the same. In order to prove this, we give some precise estimates on the uniform standard filling of a large ribbon Young diagram. This yields several asymptotic results on the filling of large ribbon Young diagrams
6

Ugail, Hassan, and Eyad Elyan. "Efficient 3D data representation for biometric applications." IOS Press, 2007. http://hdl.handle.net/10454/2683.

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Yes
An important issue in many of today's biometric applications is the development of efficient and accurate techniques for representing related 3D data. Such data is often available through the process of digitization of complex geometric objects which are of importance to biometric applications. For example, in the area of 3D face recognition a digital point cloud of data corresponding to a given face is usually provided by a 3D digital scanner. For efficient data storage and for identification/authentication in a timely fashion such data requires to be represented using a few parameters or variables which are meaningful. Here we show how mathematical techniques based on Partial Differential Equations (PDEs) can be utilized to represent complex 3D data where the data can be parameterized in an efficient way. For example, in the case of a 3D face we show how it can be represented using PDEs whereby a handful of key facial parameters can be identified for efficient storage and verification.
7

Shen, Amelia H. (Amelia Huimin). "Probabilistic representation and manipulation of Boolean functions using free Boolean diagrams." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/34087.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.
Includes bibliographical references (p. 145-149).
by Amelia Huimin Shen.
Ph.D.
8

Ugail, Hassan, and S. Kirmani. "Shape reconstruction using partial differential equations." World Scientific and Engineering Academy and Society (WSEAS), 2006. http://hdl.handle.net/10454/2645.

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We present an efficient method for reconstructing complex geometry using an elliptic Partial Differential Equation (PDE) formulation. The integral part of this work is the use of three-dimensional curves within the physical space which act as boundary conditions to solve the PDE. The chosen PDE is solved explicitly for a given general set of curves representing the original shape and thus making the method very efficient. In order to improve the quality of results for shape representation we utilize an automatic parameterization scheme on the chosen curves. With this formulation we discuss our methodology for shape representation using a series of practical examples.
9

Vasudevan, Shrihari. "Spatial cognition for mobile robots : a hierarchical probabilistic concept-oriented representation of space." Zürich : ETH, 2008. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=17612.

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10

Lloyd, James Robert. "Representation, learning, description and criticism of probabilistic models with applications to networks, functions and relational data." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709264.

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Книги з теми "Probabilistic representation of PDEs":

1

Aven, Terje. Uncertainty in risk assessment: The representation and treatment of uncertainties by probabilistic and non-probabilistic methods. Chichester, West Sussex, United Kingdom: Wiley, 2014.

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2

Fisseler, Jens. Learning and modeling with probabilistic conditional logic. Heidelberg: Ios Press, 2010.

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3

Aven, Terje, Enrico Zio, Piero Baraldi, and Roger Flage. Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods. Wiley & Sons, Limited, John, 2014.

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4

Aven, Terje, Enrico Zio, Piero Baraldi, and Roger Flage. Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods. Wiley & Sons, Incorporated, John, 2013.

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5

Aven, Terje, Enrico Zio, Piero Baraldi, and Roger Flage. Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods. Wiley & Sons, Incorporated, John, 2013.

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6

Aven, Terje, Enrico Zio, Piero Baraldi, and Roger Flage. Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods. Wiley & Sons, Incorporated, John, 2013.

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7

Mselati, Benoit. Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation. American Mathematical Society (AMS), 2004.

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8

Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. Functional Integrals and Probabilistic Amplitudes. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0008.

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Functional integrals and probabilistic amplitudes. Brief historical notes. The reconstruction of quantum mechanics from path integrals. The Feynman formulation. Definition and properties of the coherent states and the Bargmann representation.
9

Hancox, J., and J. Boardman. The Impact of an Alternative Representation of the Atmosphere on the Predictions of the Probabilistic Consequence Code CONDOR (Reports). AEA Technology Plc, 1992.

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10

Grenander, Ulf, and Michael I. Miller. Pattern Theory. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198505709.001.0001.

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Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

Частини книг з теми "Probabilistic representation of PDEs":

1

Bhattacharya, Rabi, and Edward Waymire. "Probabilistic Representation of Solutions to Certain PDEs." In Continuous Parameter Markov Processes and Stochastic Differential Equations, 273–86. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-33296-8_15.

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2

Cerf, Raphaël, and Joseba Dalmau. "Probabilistic Representation." In Probability Theory and Stochastic Modelling, 187–94. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-08663-2_23.

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3

Goertzel, Ben, Matthew Iklé, Izabela Freire Goertzel, and Ari Heljakka. "Knowledge Representation." In Probabilistic Logic Networks, 1–17. Boston, MA: Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-76872-4_2.

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4

Touzi, Nizar. "Probabilistic Numerical Methods for Nonlinear PDEs." In Fields Institute Monographs, 189–99. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4286-8_12.

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5

Sucar, Luis Enrique. "Bayesian Networks: Representation and Inference." In Probabilistic Graphical Models, 101–36. London: Springer London, 2015. http://dx.doi.org/10.1007/978-1-4471-6699-3_7.

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6

Sucar, Luis Enrique. "Bayesian Networks: Representation and Inference." In Probabilistic Graphical Models, 111–51. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61943-5_7.

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7

Baudrit, Cédric, Didier Dubois, and Hélène Fargier. "Representation of Incomplete Probabilistic Information." In Soft Methodology and Random Information Systems, 149–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-44465-7_17.

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8

Hommersom, Arjen. "Toward Probabilistic Analysis of Guidelines." In Knowledge Representation for Health-Care, 139–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18050-7_11.

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9

Bényi, Árpád, Tadahiro Oh, and Oana Pocovnicu. "On the Probabilistic Cauchy Theory for Nonlinear Dispersive PDEs." In Landscapes of Time-Frequency Analysis, 1–32. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-05210-2_1.

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10

Rosinger, Elemér E. "Parametric Representation of Functions." In Parametric Lie Group Actions on Global Generalised Solutions of Nonlinear PDEs, 17–24. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-015-9076-1_3.

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Тези доповідей конференцій з теми "Probabilistic representation of PDEs":

1

Cortés, Vicente. "A holomorphic representation formula for parabolic hyperspheres." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-1.

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2

Gollek, Hubert. "Natural algebraic representation formulas for curves in C3." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2002. http://dx.doi.org/10.4064/bc57-0-8.

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3

Gollek, Hubert. "Algebraic representation formulas for null curves in Sl(2,C)." In PDEs, Submanifolds and Affine Differential Geometry. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc69-0-18.

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4

"Probabilistic Models for Semantic Representation." In The 1st International Workshop on Ontology for e-Technologies. SciTePress - Science and and Technology Publications, 2009. http://dx.doi.org/10.5220/0002222100130022.

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5

Shivakumar, Sachin, Amritam Das, and Matthew M. Peet. "Representation of linear PDEs with spatial integral terms as Partial Integral Equations." In 2023 American Control Conference (ACC). IEEE, 2023. http://dx.doi.org/10.23919/acc55779.2023.10156465.

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6

Wu, Haoyi, and Kewei Tu. "Probabilistic Transformer: A Probabilistic Dependency Model for Contextual Word Representation." In Findings of the Association for Computational Linguistics: ACL 2023. Stroudsburg, PA, USA: Association for Computational Linguistics, 2023. http://dx.doi.org/10.18653/v1/2023.findings-acl.482.

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7

Da Silva, José L., Mohamed Erraoui, and Habib Ouerdiane. "Convolution Equation: Solution and Probabilistic Representation." In Proceedings of the 29th Conference. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814295437_0016.

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8

Jagt, Declan S., and Matthew M. Peet. "A PIE Representation of Coupled Linear 2D PDEs and Stability Analysis using LPIs." In 2022 American Control Conference (ACC). IEEE, 2022. http://dx.doi.org/10.23919/acc53348.2022.9867684.

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9

Jagt, Declan, Peter Seiler, and Matthew Peet. "A PIE Representation of Scalar Quadratic PDEs and Global Stability Analysis Using SDP." In 2023 62nd IEEE Conference on Decision and Control (CDC). IEEE, 2023. http://dx.doi.org/10.1109/cdc49753.2023.10384073.

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10

Ganzha, V. G., and E. V. Vorozhtsov. "A probabilistic symbolic-numerical method for the stability analyses of difference schemes for PDEs." In the 1993 international symposium. New York, New York, USA: ACM Press, 1993. http://dx.doi.org/10.1145/164081.164084.

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Звіти організацій з теми "Probabilistic representation of PDEs":

1

Sakhanenko, Nikita A., and George F. Luger. Using Structured Knowledge Representation for Context-Sensitive Probabilistic Modeling. Fort Belvoir, VA: Defense Technical Information Center, January 2008. http://dx.doi.org/10.21236/ada491876.

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2

Zio, Enrico, and Nicola Pedroni. Uncertainty characterization in risk analysis for decision-making practice. Fondation pour une culture de sécurité industrielle, May 2012. http://dx.doi.org/10.57071/155chr.

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Анотація:
This document provides an overview of sources of uncertainty in probabilistic risk analysis. For each phase of the risk analysis process (system modeling, hazard identification, estimation of the probability and consequences of accident sequences, risk evaluation), the authors describe and classify the types of uncertainty that can arise. The document provides: a description of the risk assessment process, as used in hazardous industries such as nuclear power and offshore oil and gas extraction; a classification of sources of uncertainty (both epistemic and aleatory) and a description of techniques for uncertainty representation; a description of the different steps involved in a Probabilistic Risk Assessment (PRA) or Quantitative Risk Assessment (QRA), and an analysis of the types of uncertainty that can affect each of these steps; annexes giving an overview of a number of tools used during probabilistic risk assessment, including the HAZID technique, fault trees and event tree analysis.
3

Zio, Enrico, and Nicola Pedroni. Literature review of methods for representing uncertainty. Fondation pour une culture de sécurité industrielle, December 2013. http://dx.doi.org/10.57071/124ure.

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This document provides a critical review of different frameworks for uncertainty analysis, in a risk analysis context: classical probabilistic analysis, imprecise probability (interval analysis), probability bound analysis, evidence theory, and possibility theory. The driver of the critical analysis is the decision-making process and the need to feed it with representative information derived from the risk assessment, to robustly support the decision. Technical details of the different frameworks are exposed only to the extent necessary to analyze and judge how these contribute to the communication of risk and the representation of the associated uncertainties to decision-makers, in the typical settings of high-consequence risk analysis of complex systems with limited knowledge on their behaviour.
4

Zanoni, Wladimir, Jimena Romero, Nicolás Chuquimarca, and Emmanuel Abuelafia. Dealing with Hard-to-Reach Populations in Panel Data: Respondent-Driven Survey (RDS) and Attrition. Inter-American Development Bank, October 2023. http://dx.doi.org/10.18235/0005194.

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Hidden populations, such as irregular migrants, often elude traditional probabilistic sampling methods. In situations like these, chain-referral sampling techniques like Respondent-Driven Surveys (RDS) offer an effective solution. RDS, a variant of network sampling sometimes referred to as “snowball” sampling, estimates weights based on the network structures of friends and acquaintances formed during the sampling process. This ensures the samples are representative of the larger population. However, one significant limitation of these methods is the rigidity of the weights. When faced with participant attrition, recalibrating these weights to ensure continued representation poses a challenge. This technical note introduces a straightforward methodology to account for such attrition. Its applicability is demonstrated through a survey targeting Venezuelan migrants in Ecuador and Peru.
5

Wilson, D., Daniel Breton, Lauren Waldrop, Danney Glaser, Ross Alter, Carl Hart, Wesley Barnes, et al. Signal propagation modeling in complex, three-dimensional environments. Engineer Research and Development Center (U.S.), April 2021. http://dx.doi.org/10.21079/11681/40321.

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The Signal Physics Representation in Uncertain and Complex Environments (SPRUCE) work unit, part of the U.S. Army Engineer Research and Development Center (ERDC) Army Terrestrial-Environmental Modeling and Intelligence System (ARTEMIS) work package, focused on the creation of a suite of three-dimensional (3D) signal and sensor performance modeling capabilities that realistically capture propagation physics in urban, mountainous, forested, and other complex terrain environments. This report describes many of the developed technical capabilities. Particular highlights are (1) creation of a Java environmental data abstraction layer for 3D representation of the atmosphere and inhomogeneous terrain that ingests data from many common weather forecast models and terrain data formats, (2) extensions to the Environmental Awareness for Sensor and Emitter Employment (EASEE) software to enable 3D signal propagation modeling, (3) modeling of transmitter and receiver directivity functions in 3D including rotations of the transmitter and receiver platforms, (4) an Extensible Markup Language/JavaScript Object Notation (XML/JSON) interface to facilitate deployment of web services, (5) signal feature definitions and other support for infrasound modeling and for radio-frequency (RF) modeling in the very high frequency (VHF), ultra-high frequency (UHF), and super-high frequency (SHF) frequency ranges, and (6) probabilistic calculations for line-of-sight in complex terrain and vegetation.
6

Mazzoni, Silvia, Nicholas Gregor, Linda Al Atik, Yousef Bozorgnia, David Welch, and Gregory Deierlein. Probabilistic Seismic Hazard Analysis and Selecting and Scaling of Ground-Motion Records (PEER-CEA Project). Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA, November 2020. http://dx.doi.org/10.55461/zjdn7385.

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This report is one of a series of reports documenting the methods and findings of a multi-year, multi-disciplinary project coordinated by the Pacific Earthquake Engineering Research Center (PEER) and funded by the California Earthquake Authority (CEA). The overall project is titled “Quantifying the Performance of Retrofit of Cripple Walls and Sill Anchorage in Single-Family Wood-Frame Buildings,” henceforth referred to as the “PEER–CEA Project.” The overall objective of the PEER–CEA Project is to provide scientifically based information (e.g., testing, analysis, and resulting loss models) that measure and assess the effectiveness of seismic retrofit to reduce the risk of damage and associated losses (repair costs) of wood-frame houses with cripple wall and sill anchorage deficiencies as well as retrofitted conditions that address those deficiencies. Tasks that support and inform the loss-modeling effort are: (1) collecting and summarizing existing information and results of previous research on the performance of wood-frame houses; (2) identifying construction features to characterize alternative variants of wood-frame houses; (3) characterizing earthquake hazard and ground motions at representative sites in California; (4) developing cyclic loading protocols and conducting laboratory tests of cripple wall panels, wood-frame wall subassemblies, and sill anchorages to measure and document their response (strength and stiffness) under cyclic loading; and (5) the computer modeling, simulations, and the development of loss models as informed by a workshop with claims adjustors. This report is a product of Working Group 3 (WG3), Task 3.1: Selecting and Scaling Ground-motion records. The objective of Task 3.1 is to provide suites of ground motions to be used by other working groups (WGs), especially Working Group 5: Analytical Modeling (WG5) for Simulation Studies. The ground motions used in the numerical simulations are intended to represent seismic hazard at the building site. The seismic hazard is dependent on the location of the site relative to seismic sources, the characteristics of the seismic sources in the region and the local soil conditions at the site. To achieve a proper representation of hazard across the State of California, ten sites were selected, and a site-specific probabilistic seismic hazard analysis (PSHA) was performed at each of these sites for both a soft soil (Vs30 = 270 m/sec) and a stiff soil (Vs30=760 m/sec). The PSHA used the UCERF3 seismic source model, which represents the latest seismic source model adopted by the USGS [2013] and NGA-West2 ground-motion models. The PSHA was carried out for structural periods ranging from 0.01 to 10 sec. At each site and soil class, the results from the PSHA—hazard curves, hazard deaggregation, and uniform-hazard spectra (UHS)—were extracted for a series of ten return periods, prescribed by WG5 and WG6, ranging from 15.5–2500 years. For each case (site, soil class, and return period), the UHS was used as the target spectrum for selection and modification of a suite of ground motions. Additionally, another set of target spectra based on “Conditional Spectra” (CS), which are more realistic than UHS, was developed [Baker and Lee 2018]. The Conditional Spectra are defined by the median (Conditional Mean Spectrum) and a period-dependent variance. A suite of at least 40 record pairs (horizontal) were selected and modified for each return period and target-spectrum type. Thus, for each ground-motion suite, 40 or more record pairs were selected using the deaggregation of the hazard, resulting in more than 200 record pairs per target-spectrum type at each site. The suites contained more than 40 records in case some were rejected by the modelers due to secondary characteristics; however, none were rejected, and the complete set was used. For the case of UHS as the target spectrum, the selected motions were modified (scaled) such that the average of the median spectrum (RotD50) [Boore 2010] of the ground-motion pairs follow the target spectrum closely within the period range of interest to the analysts. In communications with WG5 researchers, for ground-motion (time histories, or time series) selection and modification, a period range between 0.01–2.0 sec was selected for this specific application for the project. The duration metrics and pulse characteristics of the records were also used in the final selection of ground motions. The damping ratio for the PSHA and ground-motion target spectra was set to 5%, which is standard practice in engineering applications. For the cases where the CS was used as the target spectrum, the ground-motion suites were selected and scaled using a modified version of the conditional spectrum ground-motion selection tool (CS-GMS tool) developed by Baker and Lee [2018]. This tool selects and scales a suite of ground motions to meet both the median and the user-defined variability. This variability is defined by the relationship developed by Baker and Jayaram [2008]. The computation of CS requires a structural period for the conditional model. In collaboration with WG5 researchers, a conditioning period of 0.25 sec was selected as a representative of the fundamental mode of vibration of the buildings of interest in this study. Working Group 5 carried out a sensitivity analysis of using other conditioning periods, and the results and discussion of selection of conditioning period are reported in Section 4 of the WG5 PEER report entitled Technical Background Report for Structural Analysis and Performance Assessment. The WG3.1 report presents a summary of the selected sites, the seismic-source characterization model, and the ground-motion characterization model used in the PSHA, followed by selection and modification of suites of ground motions. The Record Sequence Number (RSN) and the associated scale factors are tabulated in the Appendices of this report, and the actual time-series files can be downloaded from the PEER Ground-motion database Portal (https://ngawest2.berkeley.edu/)(link is external).

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