Related papers: A Lagrangian shape and topology optimization frame…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
In this paper we introduce a theoretical framework for semi-discrete optimization using ideas from optimal transport. Our primary motivation is in the field of deep learning, and specifically in the task of neural architecture search. With…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We propose dynamical optimal transport (OT) problems constrained in a parameterized probability subset. In application problems such as deep learning, the probability distribution is often generated by a parameterized mapping function. In…
A material-based, i.e., Lagrangian, methodology for exact integration of flux by volume-preserving flows through a surface has been developed recently in [Karrasch, SIAM J. Appl. Math., 76 (2016), pp. 1178-1190]. In the present paper, we…
Numerical simulations of the air in the atmosphere and water in the oceans are essential for numerical weather prediction. The state-of-the-art for performing these fluid simulations relies on an Eulerian viewpoint, in which the fluid…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
Designs generated by density-based topology optimization (TO) exhibit jagged and/or smeared boundaries, which forms an obstacle to their integration with existing CAD tools. Addressing this problem by smoothing or manual design adjustments…
A semi-Lagrangian Characteristic Mapping method for the solution of the tracer transport equations on the sphere is presented. The method solves for the solution operator of the equations by approximating the inverse of the diffeomorphism…
A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
Topology optimization methods have widely been used in various industries, owing to their potential for providing promising design candidates for mechanical devices. However, their applications are usually limited to the objects which do…
Generative Design (GD) combines artificial intelligence (AI), physics-based modeling, and multi-objective optimization to autonomously explore and refine engineering designs. Despite its promise in aerospace, automotive, and other…
We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…
Flavor-tagging calibrations are often provided either as scale factors measured at a finite set of working points or as binned corrections to a chosen one-dimensional discriminant. However, this approach falls short of providing continuous,…
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…
To be applicable to real world scenarios trajectory planning schemes for mobile autonomous systems must be able to efficiently deal with obstacles in the area of operation. In the context of optimization based trajectory planning and…
Planning trajectories for automated vehicles in urban environments requires methods with high generality, long planning horizons, and fast update rates. Using a path-velocity decomposition, we contribute a novel planning framework, which…