Related papers: Constrained Transport Algorithms for Numerical Rel…
The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular…
Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…
A new integration scheme, combining the stability and the precision of usual pseudo-spectral codes with the locality of finite differences methods, is introduced. It turns out to be particularly suitable for the study of front and…
We generalise Phinney's 'practical theorem' to account for modified graviton dispersion relations motivated by certain cosmological scenarios. Focusing on specific examples, we show how such modifications can induce characteristic localised…
We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Bianchi I universe. We discuss and employ basic concepts such as Dirac observables, Dirac brackets, gauge-fixing conditions,…
Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…
A new lattice based scheme for numerical relativity will be presented. The scheme uses the same data as would be used in the Regge calculus (eg. a set of leg lengths on a simplicial lattice) but it differs significantly in the way that the…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear programming, our method is based on a dynamical formulation…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
Discrete ordinate ($S_N$) and filtered spherical harmonics ($FP_N$) based schemes have been proven to be robust and accurate in solving the Boltzmann transport equation but they have their own strengths and weaknesses in different physical…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
Gradients have been exploited in proposal distributions to accelerate the convergence of Markov chain Monte Carlo algorithms on discrete distributions. However, these methods require a natural differentiable extension of the target discrete…
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 formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…
An open source software package for simulating thermal neutron propagation in geometry is presented. In this system, neutron propagation can be treated by either the particle transport method or the ray-tracing method. Supported by an…
We present the new Guided Moments ($\texttt{GM}$) formalism for neutrino modeling in astrophysical scenarios like core-collapse supernovae and neutron star mergers. The truncated moments approximation ($\texttt{M1}$) and Monte-Carlo…
A discretization of a continuum theory with constraints or conserved quantities is called mimetic if it mirrors the conserved laws or constraints of the continuum theory at the discrete level. Such discretizations have been found useful in…
We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard…