Related papers: Inverse methods for freeform optical design
Our goal is to develop a flux limiter of the Flux-Corrected Transport method for a nonconservative convection-diffusion equation. For this, we consider a hybrid difference scheme that is a linear combination of a monotone scheme and a…
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
We revisit the classical problem of 3D shape interpolation and propose a novel, physically plausible approach based on Hamiltonian dynamics. While most prior work focuses on synthetic input shapes, our formulation is designed to be…
On the space of probability densities, we extend the Wasserstein geodesics to the case of higher-order interpolation such as cubic spline interpolation. After presenting the natural extension of cubic splines to the Wasserstein space, we…
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of…
We formulate an optimization problem of Hamiltonian design based on the variational principle. Given a variational ansatz for a Hamiltonian we construct a loss function to be minimised as a weighted sum of relevant Hamiltonian properties…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
We discuss structure-preserving model order reduction for port-Hamiltonian systems based on an approximation of the full-order state by a linear combination of ansatz functions which depend themselves on the state of the reduced-order…
Among $\R^3$-valued triples of random vectors $(X,Y,Z)$ having fixed marginal probability laws, what is the best way to jointly draw $(X,Y,Z)$ in such a way that the simplex generated by $(X,Y,Z)$ has maximal average volume? Motivated by…
We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex…
Designing physical artifacts that serve a purpose - such as tools and other functional structures - is central to engineering as well as everyday human behavior. Though automating design has tremendous promise, general-purpose methods do…
Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography (PAT), we study in this work inverse coefficient problems for a semilinear radiative transport equation and its diffusion approximation with…
This paper introduces two variational formulations for a model of robust optimal transport, that is, the problem of designing optimal transport networks that are resilient to potential damages, balancing construction costs against the…
In this paper a set of analytic formulae are presented with which the partial derivatives of the flux obscuration function can be evaluated -- for planetary transits and eclipsing binaries -- under the assumption of quadratic limb…
In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
In a physical design problem, the designer chooses values of some physical parameters, within limits, to optimize the resulting field. We focus on the specific case in which each physical design parameter is the ratio of two field…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…