Registered Data
Contents
- 1 [CT069]
- 1.1 [02321] Anisotropic perimeter approximation for topology optimization
- 1.2 [00680] Computing p-Harmonic Descent Directions for Shape Optimization
- 1.3 [00619] Optimal Transport for Positive and Unlabeled Learning
- 1.4 [00122] Exact expansion of functions using partial derivatives: sensitivity analysis
[CT069]
- Session Time & Room
- Classification
- CT069 (1/1) : Manifolds and measure-geometric topics (49Q)
[02321] Anisotropic perimeter approximation for topology optimization
- Session Time & Room : 4E (Aug.24, 17:40-19:20) @F403
- Type : Contributed Talk
- Abstract : Perimetric type functionals are known to be difficult to handle directly within topology optimization algorithms because of their high sensitivity to topology changes. I will present a Gamma-convergence approximation of an anisotropic variant of the perimeter which is built upon the solution of an elliptic boundary value problem. I will discuss the advantages of such a construction over local approximations, and show applications to the optimal design of supports in additive manufacturing.
- Classification : 49Q10, 49Q20, 49Q05
- Format : Talk at Waseda University
- Author(s) :
- Samuel Amstutz (Ecole polytechnique)
- Beniamin Bogosel (Ecole polytechnique)
[00680] Computing p-Harmonic Descent Directions for Shape Optimization
- Session Time & Room : 4E (Aug.24, 17:40-19:20) @F403
- Type : Contributed Talk
- Abstract : Recent development in shape optimization suggests enhanced results by using a $p$-harmonic approach to determine descent directions. Therefore, we present the extension of an algorithm to solve the occurring vector-valued $p$-Laplace problem subject to a boundary force without requiring an iteration over the order $p$ and thus compute higher-order solutions efficiently. Results are verified by numerical experiments in a fluid dynamic setting.
- Classification : 49Q10, 49M41
- Format : Talk at Waseda University
- Author(s) :
- Henrik Wyschka (University of Hamburg)
- Martin Siebenborn (University of Hamburg)
- Winnifried Wollner (University of Hamburg)
[00619] Optimal Transport for Positive and Unlabeled Learning
- Session Time & Room : 4E (Aug.24, 17:40-19:20) @F403
- Type : Contributed Talk
- Abstract : Positive and unlabeled learning (PUL) aims to train a binary classifier based on labeled positive samples and unlabeled Samples, which is challenging due to the unavailability of negative training samples. This talk will introduce a novel optimal transport model with a regularized marginal distribution for PUL. By using the Frank-Wolfe algorithm, the proposed model can be solved properly. Extensive experiments showed that the proposed model is effective and can be used in meteorological applications.
- Classification : 49Q22, 68T01
- Format : Talk at Waseda University
- Author(s) :
- Jie ZHANG (University of Hong Kong)
- Yuguang YAN (Guangdong University of Technology)
- Michael Ng (University of Hong Kong)
[00122] Exact expansion of functions using partial derivatives: sensitivity analysis
- Session Time & Room : 4E (Aug.24, 17:40-19:20) @F403
- Type : Contributed Talk
- Abstract : Expansions of functions such as Taylor’ series, ANOVA and anchored decompositions are widely used for approximating and analyzing complex mathematical models. We propose a novel and exact expansion of functions using their cross-partial derivatives, the distribution functions and densities of the input variables. In uncertainty quantification and multivariate sensitivity analysis, such expansion allows for developing a dimension-free computation of sensitivity indices for dynamic models, and for proposing new lower and upper bounds of total indices.
- Classification : 49Q12, 46G10, 46G99
- Format : Online Talk on Zoom
- Author(s) :
- Matieyendou LAMBONI (université de Guyane)