An efficient construction of reduced deformable objects
01 Nov 2013-Vol. 32, Iss: 6, pp 1-10
TL;DR: New model reduction techniques for the approximation of reduced forces and for the construction of reduced shape spaces of deformable objects that accelerate theConstruction of a reduced dynamical system, increase the accuracy of the approximation, and simplify the implementation of model reduction are proposed.
Abstract: Many efficient computational methods for physical simulation are based on model reduction. We propose new model reduction techniques for the approximation of reduced forces and for the construction of reduced shape spaces of deformable objects that accelerate the construction of a reduced dynamical system, increase the accuracy of the approximation, and simplify the implementation of model reduction. Based on the techniques, we introduce schemes for real-time simulation of deformable objects and interactive deformation-based editing of triangle or tet meshes. We demonstrate the effectiveness of the new techniques in different experiments with elastic solids and shells and compare them to alternative approaches.
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TL;DR: Future directions such as the "print-it-all" paradigm, that have the potential to re-imagine current research and spawn completely new avenues for exploration are pointed out.
Abstract: Additive manufacturing (AM) is poised to bring about a revolution in the way products are designed, manufactured, and distributed to end users. This technology has gained significant academic as well as industry interest due to its ability to create complex geometries with customizable material properties. AM has also inspired the development of the maker movement by democratizing design and manufacturing. Due to the rapid proliferation of a wide variety of technologies associated with AM, there is a lack of a comprehensive set of design principles, manufacturing guidelines, and standardization of best practices. These challenges are compounded by the fact that advancements in multiple technologies (for example materials processing, topology optimization) generate a "positive feedback loop" effect in advancing AM. In order to advance research interest and investment in AM technologies, some fundamental questions and trends about the dependencies existing in these avenues need highlighting. The goal of our review paper is to organize this body of knowledge surrounding AM, and present current barriers, findings, and future trends significantly to the researchers. We also discuss fundamental attributes of AM processes, evolution of the AM industry, and the affordances enabled by the emergence of AM in a variety of areas such as geometry processing, material design, and education. We conclude our paper by pointing out future directions such as the "print-it-all" paradigm, that have the potential to re-imagine current research and spawn completely new avenues for exploration. The fundamental attributes and challenges/barriers of Additive Manufacturing (AM).The evolution of research on AM with a focus on engineering capabilities.The affordances enabled by AM such as geometry, material and tools design.The developments in industry, intellectual property, and education-related aspects.The important future trends of AM technologies.
1,792 citations
08 Oct 2016
TL;DR: A new aerial video dataset and benchmark for low altitude UAV target tracking, as well as, a photo-realistic UAV simulator that can be coupled with tracking methods to easily extend existing real-world datasets.
Abstract: In this paper, we propose a new aerial video dataset and benchmark for low altitude UAV target tracking, as well as, a photo-realistic UAV simulator that can be coupled with tracking methods. Our benchmark provides the first evaluation of many state-of-the-art and popular trackers on 123 new and fully annotated HD video sequences captured from a low-altitude aerial perspective. Among the compared trackers, we determine which ones are the most suitable for UAV tracking both in terms of tracking accuracy and run-time. The simulator can be used to evaluate tracking algorithms in real-time scenarios before they are deployed on a UAV “in the field”, as well as, generate synthetic but photo-realistic tracking datasets with automatic ground truth annotations to easily extend existing real-world datasets. Both the benchmark and simulator are made publicly available to the vision community on our website to further research in the area of object tracking from UAVs. (https://ivul.kaust.edu.sa/Pages/pub-benchmark-simulator-uav.aspx.).
1,277 citations
TL;DR: 3D-printed D2NNs are created that implement classification of images of handwritten digits and fashion products, as well as the function of an imaging lens at a terahertz spectrum.
Abstract: Deep learning has been transforming our ability to execute advanced inference tasks using computers. Here we introduce a physical mechanism to perform machine learning by demonstrating an all-optical diffractive deep neural network (D2NN) architecture that can implement various functions following the deep learning-based design of passive diffractive layers that work collectively. We created 3D-printed D2NNs that implement classification of images of handwritten digits and fashion products, as well as the function of an imaging lens at a terahertz spectrum. Our all-optical deep learning framework can perform, at the speed of light, various complex functions that computer-based neural networks can execute; will find applications in all-optical image analysis, feature detection, and object classification; and will also enable new camera designs and optical components that perform distinctive tasks using D2NNs.
1,145 citations
TL;DR: The goal is to provide a survey that will help researchers to better position their own work in the context of existing solutions, and to help newcomers and practitioners in computer graphics to quickly gain an overview of this vast field.
Abstract: This paper provides a comprehensive overview of urban reconstruction. While there exists a considerable body of literature, this topic is still under active research. The work reviewed in this survey stems from the following three research communities: computer graphics, computer vision and photogrammetry and remote sensing. Our goal is to provide a survey that will help researchers to better position their own work in the context of existing solutions, and to help newcomers and practitioners in computer graphics to quickly gain an overview of this vast field. Further, we would like to bring the mentioned research communities to even more interdisciplinary work, since the reconstruction problem itself is by far not solved.
445 citations
TL;DR: A TO methodology that will lead to designs requiring significantly reduced support structures, and the concept of support structure topological sensitivity is introduced, combined with performance sensitivity to result in a TO framework that maximizes performance, subject to support structure constraints.
Abstract: There is significant interest today in integrating additive manufacturing (AM) and topology optimization (TO). However, TO often leads to designs that are not AM friendly. For example, topologically optimized designs may require significant amount of support structures before they can be additively manufactured, resulting in increased fabrication and clean-up costs.In this paper, we propose a TO methodology that will lead to designs requiring significantly reduced support structures. Towards this end, the concept of support structure topological sensitivity is introduced. This is combined with performance sensitivity to result in a TO framework that maximizes performance, subject to support structure constraints. The robustness and efficiency of the proposed method is demonstrated through numerical experiments, and validated through fused deposition modeling, a popular AM process. Addresses additive manufacturing support structure constraint in topology optimization.Introduces topological sensitivity for support structures.Combines support structure sensitivity with performance sensitivity.Proposes a robust and efficient algorithm for support structure constrained topology optimization.
248 citations
References
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Book•
01 Jun 1974
TL;DR: Since the lm function provides a lot of features it is rather complicated so it is going to instead use the function lsfit as a model, which computes only the coefficient estimates and the residuals.
Abstract: Since the lm function provides a lot of features it is rather complicated. So we are going to instead use the function lsfit as a model. It computes only the coefficient estimates and the residuals. Now would be a good time to read the help file for lsfit. Note that lsfit supports the fitting of multiple least squares models and weighted least squares. Our function will not, hence we can omit the arguments wt, weights and yname. Also, changing tolerances is a little advanced so we will trust the default values and omit the argument tolerance as well.
6,956 citations
Book•
01 Feb 1996
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
Abstract: Preface 1. Introduction. Problems to be considered Characteristics of 'real-world' problems Finite-precision arithmetic and measurement of error Exercises 2. Nonlinear Problems in One Variable. What is not possible Newton's method for solving one equation in one unknown Convergence of sequences of real numbers Convergence of Newton's method Globally convergent methods for solving one equation in one uknown Methods when derivatives are unavailable Minimization of a function of one variable Exercises 3. Numerical Linear Algebra Background. Vector and matrix norms and orthogonality Solving systems of linear equations-matrix factorizations Errors in solving linear systems Updating matrix factorizations Eigenvalues and positive definiteness Linear least squares Exercises 4. Multivariable Calculus Background Derivatives and multivariable models Multivariable finite-difference derivatives Necessary and sufficient conditions for unconstrained minimization Exercises 5. Newton's Method for Nonlinear Equations and Unconstrained Minimization. Newton's method for systems of nonlinear equations Local convergence of Newton's method The Kantorovich and contractive mapping theorems Finite-difference derivative methods for systems of nonlinear equations Newton's method for unconstrained minimization Finite difference derivative methods for unconstrained minimization Exercises 6. Globally Convergent Modifications of Newton's Method. The quasi-Newton framework Descent directions Line searches The model-trust region approach Global methods for systems of nonlinear equations Exercises 7. Stopping, Scaling, and Testing. Scaling Stopping criteria Testing Exercises 8. Secant Methods for Systems of Nonlinear Equations. Broyden's method Local convergence analysis of Broyden's method Implementation of quasi-Newton algorithms using Broyden's update Other secant updates for nonlinear equations Exercises 9. Secant Methods for Unconstrained Minimization. The symmetric secant update of Powell Symmetric positive definite secant updates Local convergence of positive definite secant methods Implementation of quasi-Newton algorithms using the positive definite secant update Another convergence result for the positive definite secant method Other secant updates for unconstrained minimization Exercises 10. Nonlinear Least Squares. The nonlinear least-squares problem Gauss-Newton-type methods Full Newton-type methods Other considerations in solving nonlinear least-squares problems Exercises 11. Methods for Problems with Special Structure. The sparse finite-difference Newton method Sparse secant methods Deriving least-change secant updates Analyzing least-change secant methods Exercises Appendix A. A Modular System of Algorithms for Unconstrained Minimization and Nonlinear Equations (by Robert Schnabel) Appendix B. Test Problems (by Robert Schnabel) References Author Index Subject Index.
6,831 citations
Book•
01 Mar 1983
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
Abstract: Preface 1. Introduction. Problems to be considered Characteristics of 'real-world' problems Finite-precision arithmetic and measurement of error Exercises 2. Nonlinear Problems in One Variable. What is not possible Newton's method for solving one equation in one unknown Convergence of sequences of real numbers Convergence of Newton's method Globally convergent methods for solving one equation in one uknown Methods when derivatives are unavailable Minimization of a function of one variable Exercises 3. Numerical Linear Algebra Background. Vector and matrix norms and orthogonality Solving systems of linear equations-matrix factorizations Errors in solving linear systems Updating matrix factorizations Eigenvalues and positive definiteness Linear least squares Exercises 4. Multivariable Calculus Background Derivatives and multivariable models Multivariable finite-difference derivatives Necessary and sufficient conditions for unconstrained minimization Exercises 5. Newton's Method for Nonlinear Equations and Unconstrained Minimization. Newton's method for systems of nonlinear equations Local convergence of Newton's method The Kantorovich and contractive mapping theorems Finite-difference derivative methods for systems of nonlinear equations Newton's method for unconstrained minimization Finite difference derivative methods for unconstrained minimization Exercises 6. Globally Convergent Modifications of Newton's Method. The quasi-Newton framework Descent directions Line searches The model-trust region approach Global methods for systems of nonlinear equations Exercises 7. Stopping, Scaling, and Testing. Scaling Stopping criteria Testing Exercises 8. Secant Methods for Systems of Nonlinear Equations. Broyden's method Local convergence analysis of Broyden's method Implementation of quasi-Newton algorithms using Broyden's update Other secant updates for nonlinear equations Exercises 9. Secant Methods for Unconstrained Minimization. The symmetric secant update of Powell Symmetric positive definite secant updates Local convergence of positive definite secant methods Implementation of quasi-Newton algorithms using the positive definite secant update Another convergence result for the positive definite secant method Other secant updates for unconstrained minimization Exercises 10. Nonlinear Least Squares. The nonlinear least-squares problem Gauss-Newton-type methods Full Newton-type methods Other considerations in solving nonlinear least-squares problems Exercises 11. Methods for Problems with Special Structure. The sparse finite-difference Newton method Sparse secant methods Deriving least-change secant updates Analyzing least-change secant methods Exercises Appendix A. A Modular System of Algorithms for Unconstrained Minimization and Nonlinear Equations (by Robert Schnabel) Appendix B. Test Problems (by Robert Schnabel) References Author Index Subject Index.
6,217 citations
Book•
01 Feb 1987
4,897 citations
TL;DR: L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables, intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems.
Abstract: L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems. L-BFGS-B can also be used for unconstrained problems and in this case performs similarly to its predessor, algorithm L-BFGS (Harwell routine VA15). The algorithm is implemented in Fortran 77.
2,776 citations