Object detection and object classification using machine learning Algorithms

Urban objects are characterized by a very variable representation in terms of shape, texture and color. In addition, they are present multiple times on the images to be analyzed and can be stuck to each other. To carry out the automatic localization and recognition of the different objects we propose to use supervised learning approaches. Due to their characteristics, urban objects are difficult to detect and conventional detection approaches do not offer satisfactory performance. We proposed the use of a wide margin separator network (SVM) in order to better merge the information from the different resolutions and therefore to improve the representativeness of the urban object. The use of an SVM network makes it possible to improve performance but at a significant computational cost. We then proposed to use an activation path making it possible to reduce complexity without losing efficiency. This path will activate the network sequentially and stop the exploration when the probability of detecting an object is high. In the case of a location based on the extraction of characteristics then the classification, the computational reduction is a factor of five. Subsequently, we have shown that we can combine the SVM network with feature maps from convolutional neural networks.

Efficient Symbolic Integration for Probabilistic Inference

Weighted model integration (WMI) extends weighted model counting (WMC) to the integration of functions over mixed discrete-continuous probability spaces. It has shown tremendous promise for solving inference problems in graphical models and probabilistic programs. Yet, state-of-the-art tools for WMI are generally limited either by the range of amenable theories, or in terms of performance. To address both limitations, we propose the use of extended algebraic decision diagrams (XADDs) as a compilation language for WMI. Aside from tackling typical WMI problems, XADDs also enable partial WMI yielding parametrized solutions. To overcome the main roadblock of XADDs -- the computational cost of integration -- we formulate a novel and powerful exact symbolic dynamic programming (SDP) algorithm that seamlessly handles Boolean, integer-valued and real variables, and is able to effectively cache partial computations, unlike its predecessor. Our empirical results demonstrate that these contributions can lead to a significant computational reduction over existing probabilistic inference algorithms.

Advances in Hierarchical Model Reduction and combination with other computational reduction methods

In this work we present address the combination of the Hierarchical Model (Hi-Mod) reduction approach with projection-based reduced order methods, exploiting either on Greedy Reduced Basis (RB) or Proper Orthogonal Decomposition (POD), in a parametrized setting. The Hi-Mod approach, introduced in, is suited to reduce problems in pipe-like domains featuring a dominant axial dynamics, such as those arising for instance in haemodynamics. The Hi-Mod approach aims at reducing the computational cost by properly combining a finite element discretization of the dominant dynamics with a modal expansion in the transverse direction. In a parametrized context, the Hi-Mod approach has been employed as the high-fidelity method during the offline stage of model order reduction techniques based on RB or POD. The resulting combined reduction methods, which have been named Hi-RB and Hi-POD, respectively, will be presented with applications in diffusion-advection problems, fluid dynamics and optimal control problems, focusing on the approximation stability of the proposed methods and their computational performance.

Computational reduction strategies for bifurcation and stability analysis in fluid-dynamics

We focus on reduced order modelling for nonlinear parametrized Partial Differential Equations, frequently used in the mathematical modelling of physical systems. A common issue in this kind of problems is the possible loss of uniqueness of the solution as the parameters are varied and a singular point is encountered. In the present work, the numerical detection of singular points is performed online through a Reduced Basis Method, coupled with a Spectral Element Method for the numerically intensive offline computations. Numerical results for laminar fluid mechanics problems will be presented, where pitchfork, hysteresis, and Hopf bifurcation points are detected by an inexpensive reduced model. Some of the presented 2D and 3D flow results deal with the study of instabilities in a simplified model of a mitral regurgitant flow in order to understand the onset of the Coanda effect. The first results are in good agreement with the reference.