Related papers: Optimal, scalable forward models for computing gra…
A model for the static weak-field macroscopic medium is analyzed and the equation for the macroscopic gravitational potential is derived. This is a biharmonic equation which is a non-trivial generalization of the Poisson equation of…
Advancements in tools like Shapely 2.0 and Triton can significantly improve the efficiency of spatial similarity computations by enabling faster and more scalable geometric operations. However, for extremely large datasets, these…
It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns…
Recent work introduced a robust computational framework combining embedded mathematical structures, advanced optimization, and neural network architecture, leading to the discovery of multiple unstable self-similar solutions for key fluid…
We compute the accuracy at which a LISA-like space-based gravitational wave detector will be able to observe deviations from General Relativity in the low frequency approximation. To do so, we introduce six correction parameters that…
[Abridged] We present a novel technique, dubbed FiEstAS, to estimate the underlying density field from a discrete set of sample points in an arbitrary multidimensional space. FiEstAS assigns a volume to each point by means of a binary tree.…
We study the growth of structures in modified gravity models where the Poisson equation and the relationship between the two Newtonian potentials are modified by explicit functions of space and time. This parameterisation applies to the…
Modeling of collisionless galactic systems is based on the N-body model, which requires large computational resources due to the long-range nature of gravitational forces. The most common method for calculating gravity is the TreeCode…
Minimum residual methods such as the least-squares finite element method (FEM) or the discontinuous Petrov--Galerkin method with optimal test functions (DPG) usually exclude singular data, e.g., non square-integrable loads. We consider a…
We derive the most general mimetic scalar-tensor theory assuming a healthy "seed" action and accounting for the constraints on the speed of gravitational-wave propagation arising from the GW170817 event. By analysing linear perturbations…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
Since self-gravity is crucial in the structure formation of the universe, many hydrodynamics simulations with the effect of self-gravity have been conducted. The multigrid method is widely used as a solver for the Poisson equation of the…
To complete a previous paper, the probability density functions of the center-of-gravity as positioning algorithm are derived with classical methods. These methods, as suggested by the textbook of Probability, require the preliminary…
In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the…
MAXCUT defines a classical NP-hard problem for graph partitioning and it serves as a typical case of the symmetric non-monotone Unconstrained Submodular Maximization (USM) problem. Applications of MAXCUT are abundant in machine learning,…
Empirical Bayes methods are widely used for large-scale estimation and inference in the Poisson means problem. Existing results establish theoretical properties of the nonparametric maximum likelihood estimator (NPMLE) for optimal posterior…
Standard finite element discretizations of the Richards equation may violate the discrete minimum principle, producing unphysical negative saturations. While existing bound-preserving methods typically rely on computationally expensive…
We propose a novel approach for solving inverse-problems with high-dimensional inputs and an expensive forward mapping. It leverages joint deep generative modelling to transfer the original problem spaces to a lower dimensional latent…
We introduce a new code, ECOSMOG, to run N-body simulations for a wide class of modified gravity and dynamical dark energy theories. These theories generally have one or more new dynamical degrees of freedom, the dynamics of which are…
We develop a method for multidimensional optimisation using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimising functional correspond to fixed points of the…