Related papers: Improved Initial Guesses for Numerical Solutions o…
We present an algorithm to obtain the maximum likelihood estimates of the correlation parameters of elliptical copulas. Previously existing methods for this task were either fast but only approximate or exact but very time-consuming,…
This short note describes the tentative form of a finite-dimensional optimization problem that may be of use in a second-generation proof of the Kepler conjecture. In the original 1998 proof of the Kepler conjecture, the form of the…
Can a machine or algorithm discover or learn Kepler's first law from astronomical sightings alone? We emulate Johannes Kepler's discovery of the equation of the orbit of Mars with the Rudolphine tables using AI Feynman, a physics-inspired…
It is well known that Newton's method can have trouble converging if the initial guess is too far from the solution. Such a problem particularly occurs when this method is used to solve nonlinear elliptic partial differential equations…
The interpretation of cosmological observables requires the use of increasingly sophisticated theoretical models. Since these models are becoming computationally very expensive and display non-trivial uncertainties, the use of standard…
We present and analyze a discontinuous Galerkin method for the numerical solution of a class of second-order linear mixed-type partial differential equations, i.e. equations that change their nature from elliptic to hyperbolic through the…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
This paper offers a contemporary and comprehensive perspective on the classical algorithms utilized for the solution of minimum-time problem for linear systems (MTPLS). The use of unified notations supported by visual geometric…
Numerical solutions to Newton's equations of motion for chaotic self gravitating systems of more than 2 bodies are often regarded to be irreversible. This is due to the exponential growth of errors introduced by the integration scheme and…
Recent developments in computational power and machine learning techniques motivate their use in many different astrophysical research areas. Consequently, many machine learning models have been trained to classify exoplanet transit signals…
We present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in $\sqrt{N \beta/{\cal Z}}$ and polynomial in…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
This article introduces an enhancement to the Grover search algorithm to speed up computing the probability of finding good states. It suggests incorporating a rotation phase angle determined mathematically from the derivative of the model…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…
In this paper, we design a new iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithm is that it requires only one strongly convex programming problem at each iteration.…
The classical fuel-optimal two-impulse rendezvous problem between Keplerian orbits is revisited from a family-based perspective. Conventional approaches often yield isolated optimal solutions whose mutual relationships remain unclear; yet,…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
We consider the fundamental problem of solving quadratic systems of equations in $n$ variables, where $y_i = |\langle \boldsymbol{a}_i, \boldsymbol{x} \rangle|^2$, $i = 1, \ldots, m$ and $\boldsymbol{x} \in \mathbb{R}^n$ is unknown. We…