Bayesian Structured Prediction Using Gaussian Processes

We introduce a conceptually novel structured prediction model, GPstruct, which is kernelized, non-parametric and Bayesian, by design. We motivate the model with respect to existing approaches, among others, conditional random fields (CRFs), maximum margin Markov networks (M3N), and structured support vector machines (SVMstruct), which embody only a subset of its properties. We present an inference procedure based on Markov Chain Monte Carlo. The framework can be instantiated for a wide range of structured objects such as linear chains, trees, grids, and other general graphs. As a proof of concept, the model is benchmarked on several natural language processing tasks and a video gesture segmentation task involving a linear chain structure. We show prediction accuracies for GPstruct which are comparable to or exceeding those of CRFs and SVMstruct.

A Structured Prediction Approach for Statistical Machine Translation

We propose a new formally syntax-based method for statistical machine translation. Transductions between parsing trees are transformed into a problem of sequence tagging, which is then tackled by a search- based structured prediction method. This allows us to automatically acquire transla- tion knowledge from a parallel corpus without the need of complex linguistic parsing. This method can achieve compa- rable results with phrase-based method (like Pharaoh), however, only about ten percent number of translation table is used. Experiments show that the structured pre- diction approach for SMT is promising for its strong ability at combining words.

Structured Approaches for Exploring Interpersonal Relationships in Natural Language Text

Human relationships have long been studied by scientists from domains like sociology, psychology, literature, etc. for understanding people's desires, goals, actions and expected behaviors. In this dissertation we study inter-personal relationships as expressed in natural language text. Modeling inter-personal relationships from text finds application in general natural language understanding, as well as real-world domains such as social networks, discussion forums, intelligent virtual agents, etc. We propose that the study of relationships should incorporate not only linguistic cues in text, but also the contexts in which these cues appear. Our investigations, backed by empirical evaluation, support this thesis, and demonstrate that the task benefits from using structured models that incorporate both types of information. We present such structured models to address the task of modeling the nature of relationships between any two given characters from a narrative. To begin with, we assume that relationships are of two types: cooperative and non-cooperative. We first describe an approach to jointly infer relationships between all characters in the narrative, and demonstrate how the task of characterizing the relationship between two characters can benefit from including information about their relationships with other characters in the narrative. We next formulate the relationship-modeling problem as a sequence prediction task to acknowledge the evolving nature of human relationships, and demonstrate the need to model the history of a relationship in predicting its evolution. Thereafter, we present a data-driven method to automatically discover various types of relationships such as familial, romantic, hostile, etc. Like before, we address the task of modeling evolving relationships but don't restrict ourselves to two types of relationships. We also demonstrate the need to incorporate not only local historical but also global context while solving this problem. Lastly, we demonstrate a practical application of modeling inter-personal relationships in the domain of online educational discussion forums. Such forums offer opportunities for its users to interact and form deeper relationships. With this view, we address the task of identifying initiation of such deeper relationships between a student and the instructor. Specifically, we analyze contents of the forums to automatically suggest threads to the instructors that require their intervention. By highlighting scenarios that need direct instructor-student interactions, we alleviate the need for the instructor to manually peruse all threads of the forum and also assist students who have limited avenues for communicating with instructors. We do this by incorporating the discourse structure of the thread through latent variables that abstractly represent contents of individual posts and model the flow of information in the thread. Such latent structured models that incorporate the linguistic cues without losing their context can be helpful in other related natural language understanding tasks as well. We demonstrate this by using the model for a very different task: identifying if a stated desire has been fulfilled by the end of a story.

Exponentiated gradient algorithms for conditional random fields and max-margin Markov Networks

Log-linear and maximum-margin models are two commonly-used methods in supervised machine learning, and are frequently used in structured prediction problems. Efficient learning of parameters in these models is therefore an important problem, and becomes a key factor when learning from very large data sets. This paper describes exponentiated gradient (EG) algorithms for training such models, where EG updates are applied to the convex dual of either the log-linear or max-margin objective function; the dual in both the log-linear and max-margin cases corresponds to minimizing a convex function with simplex constraints. We study both batch and online variants of the algorithm, and provide rates of convergence for both cases. In the max-margin case, O(1/ε) EG updates are required to reach a given accuracy ε in the dual; in contrast, for log-linear models only O(log(1/ε)) updates are required. For both the max-margin and log-linear cases, our bounds suggest that the online EG algorithm requires a factor of n less computation to reach a desired accuracy than the batch EG algorithm, where n is the number of training examples. Our experiments confirm that the online algorithms are much faster than the batch algorithms in practice. We describe how the EG updates factor in a convenient way for structured prediction problems, allowing the algorithms to be efficiently applied to problems such as sequence learning or natural language parsing. We perform extensive evaluation of the algorithms, comparing them to L-BFGS and stochastic gradient descent for log-linear models, and to SVM-Struct for max-margin models. The algorithms are applied to a multi-class problem as well as to a more complex large-scale parsing task. In all these settings, the EG algorithms presented here outperform the other methods.

A Simple Label Switching Algorithm for Semisupervised Structural SVMs

In structured output learning, obtaining labeled data for real-world applications is usually costly, while unlabeled examples are available in abundance. Semisupervised structured classification deals with a small number of labeled examples and a large number of unlabeled structured data. In this work, we consider semisupervised structural support vector machines with domain constraints. The optimization problem, which in general is not convex, contains the loss terms associated with the labeled and unlabeled examples, along with the domain constraints. We propose a simple optimization approach that alternates between solving a supervised learning problem and a constraint matching problem. Solving the constraint matching problem is difficult for structured prediction, and we propose an efficient and effective label switching method to solve it. The alternating optimization is carried out within a deterministic annealing framework, which helps in effective constraint matching and avoiding poor local minima, which are not very useful. The algorithm is simple and easy to implement. Further, it is suitable for any structured output learning problem where exact inference is available. Experiments on benchmark sequence labeling data sets and a natural language parsing data set show that the proposed approach, though simple, achieves comparable generalization performance.

基于结构转换和序列标注的形式化句法统计翻译模型研究

随着全球化的不断深入和互联网的发展，人们在日常工作和生活中常常需要面对大量的非母语信息，如何利用计算机实现不同语言之间的自动转换以克服人类的语言障碍已成为当前人们的迫切需求。由于统计机器翻译方法具有语言依赖性弱、系统开发周期短、翻译质量较好等优点，目前已成为机器翻译研究界的热点研究方向。本文从形式化句法的角度，针对目前统计机器翻译方法中存在的非连续短语处理、训练和搜索相独立以及短语顺序的调整等问题开展了研究工作。论文的主要工作和创新点总结如下： 1. 改进的短语翻译模型 目前常用的基于短语的翻译模型没有考虑对非连续短语的处理。我们提出了一种基于非连续短语的统计翻译模型，利用该模型可以使翻译的基本单元从连续短语扩展到带有间隔的非连续短语，通过借助上下文词汇信息以达到改善翻译结果的目的。同时，由于该方法抽取的短语数量较少，也使得解码的效率得到了提高。实验表明，改进的非连续短语模型在取得与层次型短语模型相当的翻译性能的情况下，计算效率也得到了提高。 2. 基于SEARN的形式化句法模型 在目前的机器学习方法中，训练和搜索的过程相对独立，训练时采用的复杂结构信息在搜索过程中常常难于保持。我们提出了一种转换操作，将集成训练和搜索的结构化预测方法（Search-based Structured Prediction，SEARN）用于转换后的序列标注问题，以解决双语句法树之间的映射。实验表明，该方法在抽取短语数量只有短语模型十分之一的情形下，仍可取得与短语模型相当的翻译性能。 3. 基于压平的双语句法树结构的形式化句法模型 短语顺序是翻译时需要关注的关键问题之一，目前的方法通常只是以源语言端的信息作为调序的依据。我们提出了一种基于压平的双语句法树结构的形式化句法方法。其核心是抽取带有方向属性的短语对，利用这种方向属性辅助目标句子的生成，从而改善目标句子的内部结构（短语顺序）以提高翻译质量。在NIST MT08机器翻译评测数据上的实验表明，这种方法和基于短语的系统相比BLUE值获得7%的提高。 4. 基于序列标注的形式化句法模型 在翻译时句子中的某些区域通常倾向于作为一个整体来进行翻译，目前的方法对句子中的所有词都允许任意位置的词序调整，带来了很多不合理的顺序调整结果。我们提出了一种基于序列标注的形式化句法模型。首先利用压平的双语句法树结构表示双语句子，然后通过我们定义的标签对树节点进行标记，最后借助条件随机场模型对这些标签进行学习。通过这些标签可以区分出能够作为整体翻译的区域，以及句子中难于翻译的部分。同时，对不同的翻译区域可以采用不同的翻译方法，通过局部翻译质量的提高可以带来了整个句子翻译质量的改善。该模型和基于层次型短语的模型比较，BLUE值得到了5%的提高。

SEQUENTIAL DECISIONS AND PREDICTIONS IN NATURAL LANGUAGE PROCESSING

Natural language processing has achieved great success in a wide range of ap- plications, producing both commercial language services and open-source language tools. However, most methods take a static or batch approach, assuming that the model has all information it needs and makes a one-time prediction. In this disser- tation, we study dynamic problems where the input comes in a sequence instead of all at once, and the output must be produced while the input is arriving. In these problems, predictions are often made based only on partial information. We see this dynamic setting in many real-time, interactive applications. These problems usually involve a trade-off between the amount of input received (cost) and the quality of the output prediction (accuracy). Therefore, the evaluation considers both objectives (e.g., plotting a Pareto curve). Our goal is to develop a formal understanding of sequential prediction and decision-making problems in natural language processing and to propose efficient solutions. Toward this end, we present meta-algorithms that take an existent batch model and produce a dynamic model to handle sequential inputs and outputs. Webuild our framework upon theories of Markov Decision Process (MDP), which allows learning to trade off competing objectives in a principled way. The main machine learning techniques we use are from imitation learning and reinforcement learning, and we advance current techniques to tackle problems arising in our settings. We evaluate our algorithm on a variety of applications, including dependency parsing, machine translation, and question answering. We show that our approach achieves a better cost-accuracy trade-off than the batch approach and heuristic-based decision- making approaches. We first propose a general framework for cost-sensitive prediction, where dif- ferent parts of the input come at different costs. We formulate a decision-making process that selects pieces of the input sequentially, and the selection is adaptive to each instance. Our approach is evaluated on both standard classification tasks and a structured prediction task (dependency parsing). We show that it achieves similar prediction quality to methods that use all input, while inducing a much smaller cost. Next, we extend the framework to problems where the input is revealed incremen- tally in a fixed order. We study two applications: simultaneous machine translation and quiz bowl (incremental text classification). We discuss challenges in this set- ting and show that adding domain knowledge eases the decision-making problem. A central theme throughout the chapters is an MDP formulation of a challenging problem with sequential input/output and trade-off decisions, accompanied by a learning algorithm that solves the MDP.

Structured professional judgement approach to risk assessment: generalisability across patient groups for the prediction of adverse outcomes in secure mental health care

This is a redacted version of the the final thesis. Copyright material has been removed to comply with UK Copyright Law.

Integration of relational and hierarchical network information for protein function prediction

BACKGROUND:In the current climate of high-throughput computational biology, the inference of a protein's function from related measurements, such as protein-protein interaction relations, has become a canonical task. Most existing technologies pursue this task as a classification problem, on a term-by-term basis, for each term in a database, such as the Gene Ontology (GO) database, a popular rigorous vocabulary for biological functions. However, ontology structures are essentially hierarchies, with certain top to bottom annotation rules which protein function predictions should in principle follow. Currently, the most common approach to imposing these hierarchical constraints on network-based classifiers is through the use of transitive closure to predictions.RESULTS:We propose a probabilistic framework to integrate information in relational data, in the form of a protein-protein interaction network, and a hierarchically structured database of terms, in the form of the GO database, for the purpose of protein function prediction. At the heart of our framework is a factorization of local neighborhood information in the protein-protein interaction network across successive ancestral terms in the GO hierarchy. We introduce a classifier within this framework, with computationally efficient implementation, that produces GO-term predictions that naturally obey a hierarchical 'true-path' consistency from root to leaves, without the need for further post-processing.CONCLUSION:A cross-validation study, using data from the yeast Saccharomyces cerevisiae, shows our method offers substantial improvements over both standard 'guilt-by-association' (i.e., Nearest-Neighbor) and more refined Markov random field methods, whether in their original form or when post-processed to artificially impose 'true-path' consistency. Further analysis of the results indicates that these improvements are associated with increased predictive capabilities (i.e., increased positive predictive value), and that this increase is consistent uniformly with GO-term depth. Additional in silico validation on a collection of new annotations recently added to GO confirms the advantages suggested by the cross-validation study. Taken as a whole, our results show that a hierarchical approach to network-based protein function prediction, that exploits the ontological structure of protein annotation databases in a principled manner, can offer substantial advantages over the successive application of 'flat' network-based methods.

THE PREVALENCE AND PREDICTION OF PULMONARY FIBROSIS IN AN

This thesis describes an ancillary project to the Early Diagnosis of Mesothelioma and Lung Cancer in Prior Asbestos Workers study and was conducted to determine the effects of asbestos exposure, pulmonary function and cigarette smoking in the prediction of pulmonary fibrosis. 613 workers who were occupationally exposed to asbestos for an average of 25.9 (SD=14.69) years were sampled from Sarnia, Ontario. A structured questionnaire was administered during a face-to-face interview along with a low-dose computed tomography (LDCT) of the thorax. Of them, 65 workers (10.7%, 95%CI 8.12—12.24) had LDCT-detected pulmonary fibrosis. The model predicting fibrosis included the variables age, smoking (dichotomized), post FVC % splines and post- FEV1% splines. This model had a receiver operator characteristic area under the curve of 0.738. The calibration of the model was evaluated with R statistical program and the bootstrap optimism-corrected calibration slope was 0.692. Thus, our model demonstrated moderate predictive performance.

Controlling the computational modes of the arbitrarily structured C-grid

The arbitrarily structured C-grid, TRiSK (Thuburn, Ringler, Skamarock and Klemp, 2009, 2010) is being used in the ``Model for Prediction Across Scales'' (MPAS) and is being considered by the UK Met Office for their next dynamical core. However the hexagonal C-grid supports a branch of spurious Rossby modes which lead to erroneous grid-scale oscillations of potential vorticity (PV). It is shown how these modes can be harmlessly controlled by using upwind-biased interpolation schemes for PV. A number of existing advection schemes for PV are tested, including that used in MPAS, and none are found to give adequate results for all grids and all cases. Therefore a new scheme is proposed; continuous, linear-upwind stabilised transport (CLUST), a blend between centred and linear-upwind with the blend dependent on the flow direction with respect to the cell edge. A diagnostic of grid-scale oscillations is proposed which gives further discrimination between schemes than using potential enstrophy alone and indeed some schemes are found to destroy potential enstrophy while grid-scale oscillations grow. CLUST performs well on hexagonal-icosahedral grids and unrotated skipped latitude-longitude grids of the sphere for various shallow water test cases. Despite the computational modes, the hexagonal icosahedral grid performs well since these modes are easy and harmless to filter. As a result TRiSK appears to perform better than a spectral shallow water model.

Analytic prediction of structural stress-strain relations of microstructured metal

Nanostructured and ultra-fine grained metals have higher strength but extremely limited ductility compared to coarse grained metals. However, their ductility can be greatly improved by introducing a specific range of grain sizes in the microstructures. In the paper, multiscale unit cell approach (UCA) is developed and applied to predict the averaged stress-strain relations of the multiscale microstructure metals. The unit cell models are three-phase structured at different scale lengths of 100 nm, 1 μm and 10 μm with different volume fractions and periodic boundary conditions. The contributions of multi-scale microstructures to the macroscopic structural properties of metals are also studied using a analytic approach—two-step mean-field method (TSMF), where three microstructural parameters are introduced and thus mechanical properties such as strength and ductility are presented as a function of these parameters. For verification of these proposed numerical and theoretical algorithms, the structural properties of the pure nickel with three-grain microstructures are studied and the results from FEA and the proposed theory have good agreement.

Traffic flow breakdown prediction using feature reduction through Rough-Neuro fuzzy Networks

The prediction of the traffic behavior could help to make decision about the routing process, as well as enables gains on effectiveness and productivity on the physical distribution. This need motivated the search for technological improvements in the Routing performance in metropolitan areas. The purpose of this paper is to present computational evidences that Artificial Neural Network ANN could be use to predict the traffic behavior in a metropolitan area such So Paulo (around 16 million inhabitants). The proposed methodology involves the application of Rough-Fuzzy Sets to define inference morphology for insertion of the behavior of Dynamic Routing into a structured rule basis, without human expert aid. The dynamics of the traffic parameters are described through membership functions. Rough Sets Theory identifies the attributes that are important, and suggest Fuzzy relations to be inserted on a Rough Neuro Fuzzy Network (RNFN) type Multilayer Perceptron (MLP) and type Radial Basis Function (RBF), in order to get an optimal surface response. To measure the performance of the proposed RNFN, the responses of the unreduced rule basis are compared with the reduced rule one. The results show that by making use of the Feature Reduction through RNFN, it is possible to reduce the need for human expert in the construction of the Fuzzy inference mechanism in such flow process like traffic breakdown. © 2011 IEEE.

Learning with Kernels on Graphs: DAG-based kernels, data streams and RNA function prediction.

In many application domains data can be naturally represented as graphs. When the application of analytical solutions for a given problem is unfeasible, machine learning techniques could be a viable way to solve the problem. Classical machine learning techniques are defined for data represented in a vectorial form. Recently some of them have been extended to deal directly with structured data. Among those techniques, kernel methods have shown promising results both from the computational complexity and the predictive performance point of view. Kernel methods allow to avoid an explicit mapping in a vectorial form relying on kernel functions, which informally are functions calculating a similarity measure between two entities. However, the definition of good kernels for graphs is a challenging problem because of the difficulty to find a good tradeoff between computational complexity and expressiveness. Another problem we face is learning on data streams, where a potentially unbounded sequence of data is generated by some sources. There are three main contributions in this thesis. The first contribution is the definition of a new family of kernels for graphs based on Directed Acyclic Graphs (DAGs). We analyzed two kernels from this family, achieving state-of-the-art results from both the computational and the classification point of view on real-world datasets. The second contribution consists in making the application of learning algorithms for streams of graphs feasible. Moreover,we defined a principled way for the memory management. The third contribution is the application of machine learning techniques for structured data to non-coding RNA function prediction. In this setting, the secondary structure is thought to carry relevant information. However, existing methods considering the secondary structure have prohibitively high computational complexity. We propose to apply kernel methods on this domain, obtaining state-of-the-art results.

Numerical Error Prediction and its applications in CFD using tau-estimation

Nowadays, Computational Fluid Dynamics (CFD) solvers are widely used within the industry to model fluid flow phenomenons. Several fluid flow model equations have been employed in the last decades to simulate and predict forces acting, for example, on different aircraft configurations. Computational time and accuracy are strongly dependent on the fluid flow model equation and the spatial dimension of the problem considered. While simple models based on perfect flows, like panel methods or potential flow models can be very fast to solve, they usually suffer from a poor accuracy in order to simulate real flows (transonic, viscous). On the other hand, more complex models such as the full Navier- Stokes equations provide high fidelity predictions but at a much higher computational cost. Thus, a good compromise between accuracy and computational time has to be fixed for engineering applications. A discretisation technique widely used within the industry is the so-called Finite Volume approach on unstructured meshes. This technique spatially discretises the flow motion equations onto a set of elements which form a mesh, a discrete representation of the continuous domain. Using this approach, for a given flow model equation, the accuracy and computational time mainly depend on the distribution of nodes forming the mesh. Therefore, a good compromise between accuracy and computational time might be obtained by carefully defining the mesh. However, defining an optimal mesh for complex flows and geometries requires a very high level expertize in fluid mechanics and numerical analysis, and in most cases a simple guess of regions of the computational domain which might affect the most the accuracy is impossible. Thus, it is desirable to have an automatized remeshing tool, which is more flexible with unstructured meshes than its structured counterpart. However, adaptive methods currently in use still have an opened question: how to efficiently drive the adaptation ? Pioneering sensors based on flow features generally suffer from a lack of reliability, so in the last decade more effort has been made in developing numerical error-based sensors, like for instance the adjoint-based adaptation sensors. While very efficient at adapting meshes for a given functional output, the latter method is very expensive as it requires to solve a dual set of equations and computes the sensor on an embedded mesh. Therefore, it would be desirable to develop a more affordable numerical error estimation method. The current work aims at estimating the truncation error, which arises when discretising a partial differential equation. These are the higher order terms neglected in the construction of the numerical scheme. The truncation error provides very useful information as it is strongly related to the flow model equation and its discretisation. On one hand, it is a very reliable measure of the quality of the mesh, therefore very useful in order to drive a mesh adaptation procedure. On the other hand, it is strongly linked to the flow model equation, so that a careful estimation actually gives information on how well a given equation is solved, which may be useful in the context of _ -extrapolation or zonal modelling. The following work is organized as follows: Chap. 1 contains a short review of mesh adaptation techniques as well as numerical error prediction. In the first section, Sec. 1.1, the basic refinement strategies are reviewed and the main contribution to structured and unstructured mesh adaptation are presented. Sec. 1.2 introduces the definitions of errors encountered when solving Computational Fluid Dynamics problems and reviews the most common approaches to predict them. Chap. 2 is devoted to the mathematical formulation of truncation error estimation in the context of finite volume methodology, as well as a complete verification procedure. Several features are studied, such as the influence of grid non-uniformities, non-linearity, boundary conditions and non-converged numerical solutions. This verification part has been submitted and accepted for publication in the Journal of Computational Physics. Chap. 3 presents a mesh adaptation algorithm based on truncation error estimates and compares the results to a feature-based and an adjoint-based sensor (in collaboration with Jorge Ponsín, INTA). Two- and three-dimensional cases relevant for validation in the aeronautical industry are considered. This part has been submitted and accepted in the AIAA Journal. An extension to Reynolds Averaged Navier- Stokes equations is also included, where _ -estimation-based mesh adaptation and _ -extrapolation are applied to viscous wing profiles. The latter has been submitted in the Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. Keywords: mesh adaptation, numerical error prediction, finite volume Hoy en día, la Dinámica de Fluidos Computacional (CFD) es ampliamente utilizada dentro de la industria para obtener información sobre fenómenos fluidos. La Dinámica de Fluidos Computacional considera distintas modelizaciones de las ecuaciones fluidas (Potencial, Euler, Navier-Stokes, etc) para simular y predecir las fuerzas que actúan, por ejemplo, sobre una configuración de aeronave. El tiempo de cálculo y la precisión en la solución depende en gran medida de los modelos utilizados, así como de la dimensión espacial del problema considerado. Mientras que modelos simples basados en flujos perfectos, como modelos de flujos potenciales, se pueden resolver rápidamente, por lo general aducen de una baja precisión a la hora de simular flujos reales (viscosos, transónicos, etc). Por otro lado, modelos más complejos tales como el conjunto de ecuaciones de Navier-Stokes proporcionan predicciones de alta fidelidad, a expensas de un coste computacional mucho más elevado. Por lo tanto, en términos de aplicaciones de ingeniería se debe fijar un buen compromiso entre precisión y tiempo de cálculo. Una técnica de discretización ampliamente utilizada en la industria es el método de los Volúmenes Finitos en mallas no estructuradas. Esta técnica discretiza espacialmente las ecuaciones del movimiento del flujo sobre un conjunto de elementos que forman una malla, una representación discreta del dominio continuo. Utilizando este enfoque, para una ecuación de flujo dado, la precisión y el tiempo computacional dependen principalmente de la distribución de los nodos que forman la malla. Por consiguiente, un buen compromiso entre precisión y tiempo de cálculo se podría obtener definiendo cuidadosamente la malla, concentrando sus elementos en aquellas zonas donde sea estrictamente necesario. Sin embargo, la definición de una malla óptima para corrientes y geometrías complejas requiere un nivel muy alto de experiencia en la mecánica de fluidos y el análisis numérico, así como un conocimiento previo de la solución. Aspecto que en la mayoría de los casos no está disponible. Por tanto, es deseable tener una herramienta que permita adaptar los elementos de malla de forma automática, acorde a la solución fluida (remallado). Esta herramienta es generalmente más flexible en mallas no estructuradas que con su homóloga estructurada. No obstante, los métodos de adaptación actualmente en uso todavía dejan una pregunta abierta: cómo conducir de manera eficiente la adaptación. Sensores pioneros basados en las características del flujo en general, adolecen de una falta de fiabilidad, por lo que en la última década se han realizado grandes esfuerzos en el desarrollo numérico de sensores basados en el error, como por ejemplo los sensores basados en el adjunto. A pesar de ser muy eficientes en la adaptación de mallas para un determinado funcional, este último método resulta muy costoso, pues requiere resolver un doble conjunto de ecuaciones: la solución y su adjunta. Por tanto, es deseable desarrollar un método numérico de estimación de error más asequible. El presente trabajo tiene como objetivo estimar el error local de truncación, que aparece cuando se discretiza una ecuación en derivadas parciales. Estos son los términos de orden superior olvidados en la construcción del esquema numérico. El error de truncación proporciona una información muy útil sobre la solución: es una medida muy fiable de la calidad de la malla, obteniendo información que permite llevar a cabo un procedimiento de adaptación de malla. Está fuertemente relacionado al modelo matemático fluido, de modo que una estimación precisa garantiza la idoneidad de dicho modelo en un campo fluido, lo que puede ser útil en el contexto de modelado zonal. Por último, permite mejorar la precisión de la solución resolviendo un nuevo sistema donde el error local actúa como término fuente (_ -extrapolación). El presenta trabajo se organiza de la siguiente manera: Cap. 1 contiene una breve reseña de las técnicas de adaptación de malla, así como de los métodos de predicción de los errores numéricos. En la primera sección, Sec. 1.1, se examinan las estrategias básicas de refinamiento y se presenta la principal contribución a la adaptación de malla estructurada y no estructurada. Sec 1.2 introduce las definiciones de los errores encontrados en la resolución de problemas de Dinámica Computacional de Fluidos y se examinan los enfoques más comunes para predecirlos. Cap. 2 está dedicado a la formulación matemática de la estimación del error de truncación en el contexto de la metodología de Volúmenes Finitos, así como a un procedimiento de verificación completo. Se estudian varias características que influyen en su estimación: la influencia de la falta de uniformidad de la malla, el efecto de las no linealidades del modelo matemático, diferentes condiciones de contorno y soluciones numéricas no convergidas. Esta parte de verificación ha sido presentada y aceptada para su publicación en el Journal of Computational Physics. Cap. 3 presenta un algoritmo de adaptación de malla basado en la estimación del error de truncación y compara los resultados con sensores de featured-based y adjointbased (en colaboración con Jorge Ponsín del INTA). Se consideran casos en dos y tres dimensiones, relevantes para la validación en la industria aeronáutica. Este trabajo ha sido presentado y aceptado en el AIAA Journal. También se incluye una extensión de estos métodos a las ecuaciones RANS (Reynolds Average Navier- Stokes), en donde adaptación de malla basada en _ y _ -extrapolación son aplicados a perfiles con viscosidad de alas. Este último trabajo se ha presentado en los Actas de la Institución de Ingenieros Mecánicos, Parte G: Journal of Aerospace Engineering. Palabras clave: adaptación de malla, predicción del error numérico, volúmenes finitos