ShipHullGAN : a generic parametric modeller for ship hull design using deep convolutional generative model

In this work, we introduce ShipHullGAN, a generic parametric modeller built using deep convolutional generative adversarial networks (GANs) for the versatile representation and generation of ship hulls. At a high level, the new model intends to address the current conservatism in the parametric ship design paradigm, where parametric modellers can only handle a particular ship type. We trained ShipHullGAN on a large dataset of 52,591 physically validated designs from a wide range of existing ship types, including container ships, tankers, bulk carriers, tugboats, and crew supply vessels. We developed a new shape extraction and representation strategy to convert all training designs into a common geometric representation of the same resolution, as typically GANs can only accept vectors of fixed dimension as input. A space-filling layer is placed right after the generator component to ensure that the trained generator can cover all design classes. During training, designs are provided in the form of a shape-signature tensor (SST) which harnesses the compact geometric representation using geometric moments that further enable the inexpensive incorporation of physics-informed elements in ship design. We have shown through extensive comparative studies and optimisation cases that ShipHullGAN can generate designs with augmented features resulting in versatile design spaces that produce traditional and novel designs with geometrically valid and practically feasible shapes

Efficient tools for the design and simulation of microelectromechanical and microfluidic systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 131-136).In air-packaged surface micromachined devices and microfluidic devices the surface to volume ratio is such that drag forces play a very important role in device behavior and performance. Especially for surface micromachined devices, the amount of drag is greatly influenced by the presence of the nearby substrate. In this thesis a precorrected FFT accelerated boundary element method specialized for calculating the drag force on structures above a substrate is presented. The method uses the Green's function for Stokes flow bounded by an infinite plane to implicitly represent the device substrate, requiring a number of modifications to the precorrected FFT algorithm. To calculate the velocity due to force distribution on a panel near a substrate an analytical panel integration algorithm was also developed. Computational results demonstrate that the use of the implicit representation of the substrate reduces computation time and memory while increasing the solution accuracy. The results also demonstrate that surprisingly, and unfortunately, even though representing the substrate implicitly has many benefits it does not completely decouple discretization fineness from distance to the substrate. To simulate the time dependent behavior of micromechanical and microfluidic systems, a stable velocity implicit time stepping scheme coupling the precorrected FFT solver with rigid body dynamics was introduced and demonstrated. The ODE library was integrated with the solver to enable the simulation of systems with collisions, contacts and friction. Several techniques for speeding up the calculation of each time step were presented and tested. The time integration algorithm was successfully used to simulate the behavior of several real-world microfluidic devices.by Carlos Pinto Coelho.Ph.D

2D and 3D Shape Descriptors

The field of computer vision studies the computational tools and methods required for computers to be able to process visual information, for example images and video. Shape descriptors are one of the tools commonly used in image processing applications. Shape descriptors are mathematical functions which are applied to an image and produce numerical values which are representative of a particular characteristic of the image. These numerical values can then be processed in order to provide some information about the image. For example, these values can be fed to a classifier in order to assign a class label to the image. There are a number of shape descriptors already existing in the literature for 2D and 3D images. The aim of this thesis is to develop additional shape descriptors which provide an improvement over (or an alternative to) those already existing in the literature. A large majority of the existing 2D shape descriptors use surface information to produce a measure. However, in some applications surface information is not present and only partially extracted contours are available. In such cases, boundary based shape descriptors must be used. A new boundary based shape descriptor called Linearity is introduced. This measure can be applied to open or closed curve segments. In general the availability of 3D images is comparatively smaller than that of 2D images. As a consequence, the number of existing 3D shape descriptors is also relatively smaller. However, there is an increasing interest in the development of 3D descriptors. In this thesis we present two basic 3D measures which afterwards are modified to produce a range of new shape descriptors. All of these descriptors are similar in their behaviour, however they can be combined and applied in different image processing applications such as image retrieval and classification. This simple fact is demonstrated through several examples.Mexican Science Council (Consejo Nacional de Ciencia y Tecnologia, CONACyT

A moment matrix approach to computing symmetric cubatures

A quadrature is an approximation of the definite integral of a function by a weighted sum of function values at specified points, or nodes, within the domain of integration. Gaussian quadratures are constructed to yield exact results for any polynomial of degree 2r − 1 or less by a suitable choice of r nodes and weights. Cubature is a generalization of quadrature in higher dimension. Constructing a cubature amounts to find a linear form Λ : R[x] → R, p → r j=1 a j p(ξ j) from the knowledge of its restriction to R[x] ≤d. The unknowns are the number of nodes r, the weights a j and the nodes ξ j. An approach based on moment matrices was proposed in [25]. We give a basis-free version in terms of the Hankel operator H associated to Λ. The existence of a cubature of degree d with r nodes boils down to conditions of ranks and positive semidefiniteness on H. We then recognize the nodes as the solutions of a generalized eigenvalue problem. Standard domains of integration are symmetric under the action of a finite group. It is natural to look for cubatures that respect this symmetry [13, 27, 28]. Introducing adapted bases obtained from representation theory, the symmetry constraint allows to block diago-nalize the Hankel operator H. We then deal with smaller-sized matrices both for securing the existence of the cubature and computing the nodes. The sizes of the blocks are furthermore explicitly related to the orbit types of the nodes with the new concept of the matrix of multiplicities of a finite group. It provides preliminary criteria of existence of a cubature with a given organisation of the nodes in orbit types. The Maple implementation of the presented algorithms allows to determine, with moderate computational efforts, all the symmetric cubatures of a given degree. We present new relevant cubatures