Reusable components for knowledge modelling

In this work I illustrate an approach to the development of a library of problem solving components for knowledge modelling. This approach is based on an epistemological modelling framework, the Task/Method/Domain/Application (TMDA) model, and on a principled methodology, which provide an integrated view of both library construction and application development by reuse. The starting point of the proposed approach is given by a task ontology. This formalizes a conceptual viewpoint over a class of problems, thus providing a task-specific framework, which can be used to drive the construction of a task model through a process of model-based knowledge acquisition. The definitions in the task ontology provide the initial elements of a task-specific library of problem solving components. In order to move from problem specification to problem solving, a generic, i.e. taskindependent, model of problem solving as search is introduced, and instantiated in terms of the concepts in the relevant task ontology, say T. The result is a task-specific, but method-independent, problem solving model. This generic problem solving model provides the foundation from which alternative problem solving methods for a class of tasks can be defined. Specifically, the generic problem solving model provides i) a highly generic method ontology, say M; ii) a set of generic building blocks (generic tasks), which can be used to construct task-specific problem solving methods; and iii) an initial problem solving method, which can be characterized as the most generic problem solving method, which subscribes to M and is applicable to T. More specific problem solving methods can then be (re-)constructed from the generic problem solving model through a process of method/ontology specialization and method-to-task application. The resulting library of reusable components enjoys a clear theoretical basis and provides robust support for reuse. In the thesis I illustrate the approach in the area of parametric design

Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple boundary, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including B\'ezier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition, the optimal placement of interior B\'ezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C1=G1-continuity constraints on the interface of neighboring B\'ezier patches with respect to each quad in the quadrangulation, the high-quality B\'ezier patch parameterization is obtained by a C1-constrained local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe

Progressive construction of a parametric reduced-order model for PDE-constrained optimization

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by a given Reduced-Order Model (ROM) is defined with the goal of converging to the solution of a given PDE-constrained optimization problem. For each reduced optimization problem, the constraining ROM is trained from sampling the High-Dimensional Model (HDM) at the solution of some of the previous problems in the sequence. The reduced optimization problems are equipped with a nonlinear trust-region based on a residual error indicator to keep the optimization trajectory in a region of the parameter space where the ROM is accurate. A technique for incorporating sensitivities into a Reduced-Order Basis (ROB) is also presented, along with a methodology for computing sensitivities of the reduced-order model that minimizes the distance to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced optimization framework is applied to subsonic aerodynamic shape optimization and shown to reduce the number of queries to the HDM by a factor of 4-5, compared to the optimization problem solved using only the HDM, with errors in the optimal solution far less than 0.1%