arXiv subjects

Soumaya Elkantassi

Publications and source records attributed to Soumaya Elkantassi.

5 recordsLinked to original sources

arXiv2026

A Finite Element Method for Fluctuating Navier--Stokes Equations

We introduce a finite-element framework for simulating thermal fluctuations in compressible fluids governed by the fluctuating Navier-Stokes equations. The method is designed to preserve the fundamental fluctuation-dissipation balance at the discrete level. This is achieved by defining the stochastic forcing term in the weak formulation, ensuring its covariance is proportional to the discrete viscous dissipation operator. A nodal quadrature rule is employed to eliminate unphysical mesh-scale correlations. The time integration is performed using the Crank-Nicolson scheme to maintain numerical stability and accuracy. The proposed approach is numerically validated in one, two, and three spatial dimensions, demonstrating its capability to correctly capture equilibrium fluctuation statistics across various discretisation parameters.

cond-mat.stat-mech↗

arXiv2026

A Physics-Informed Neural Network with a Modified Lorentzian Activation for Nonlocal Gradient-Flow Equations in Dynamic Density Functional Theory

We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations arising in dynamic density functional theory (DDFT). Such equations are challenging for standard PINN methods because they involve nonlinearities, nonlocal interaction terms, and an underlying gradient-flow structure, often leading to slow convergence and difficult optimization. We adapt the PINN methodology to DDFT gradient-flow equations and introduce two computational components: a modified Lorentzian activation function that behaves approximately linearly for small inputs and decays toward zero as the input magnitude increases, and a precomputed discrete operator for evaluating the nonlocal convolution term efficiently during training. The method is tested on four examples in one and two space dimensions. In the first example, the exact stationary solution is known, while in the remaining cases the neural-network approximations are validated against reference solutions computed using continuous and discontinuous Galerkin finite element discretizations. Accuracy and physical consistency are assessed through $L^1$, $L^2$, and $L^\infty$ errors, together with mass conservation and free-energy dissipation. The results show that the proposed activation function accelerates convergence relative to the standard $\tanh$ function, while the overall framework maintains good agreement with the reference solutions and captures the expected gradient-flow behaviour. These findings demonstrate the potential of the proposed PINN framework for solving nonlocal gradient-flow equations arising in DDFT.

math.NA↗

arXiv2025

Inference on the Miss Distance in a Conjunction

Over the last quarter-century, spacecraft conjunction assessment has focused on a quantity associated by its advocates with collision probability. This quantity has a well-known dilution feature, where it is small when uncertainty is large, giving rise to false confidence that a conjunction is safe when it is not. An alternative approach to conjunction assessment is to assess the missed detection probability that the best available information indicates the conjunction to be safe, when it is actually unsafe. In other words, the alternative seeks to answer the question of whether unknowable errors in the best available data might be especially unlucky. A proper implementation of this alternative avoids dilution and false confidence. Implementations of the alternative use either significance probabilities (p-values) associated with a null hypothesis that the miss distance is small, or confidence intervals on the miss distance. Both approaches rely on maximum likelihood principles to deal with nuisance variables, rather than marginalization. This paper discusses the problems with the traditional approach, and summarizes other work that developed the alternative approach. The paper presents examples of application of the alternatives using data from actual conjunctions experienced in operations, including synthetic scaling to highlight contrasts between the alternative and the traditional approach.

stat.AP↗

arXiv2025

Statistical Inference on the Miss Distance Compared to Collision Probability for Conjunction Analysis

Satellite conjunctions involving near misses of space objects are increasingly common, especially with the growth of satellite constellations and space debris. Accurate risk analysis for these events is essential to prevent collisions and manage space traffic. Traditional methods for assessing collision risk, such as calculating the so-called collision probability, are widely used but have limitations, including counterintuitive interpretations when uncertainty in the state vector is large. To address these limitations, we build on an alternative approach proposed by Elkantassi and Davison (2022) that uses a statistical model allowing inference on the miss distance between two objects in the presence of nuisance parameters. This model provides significance probabilities for a null hypothesis that assumes a small miss distance and allows the construction of confidence intervals, leading to another interpretation of collision risk. In this study, we compare this approach with the traditional use of pc across a large, NASA-provided dataset of real conjunctions, in order to evaluate its reliability and to refine the statistical framework to improve its suitability for operational decision-making. We also discuss constraints that could limit the practical use of such alternative approaches.

stat.AP↗

arXiv2022

Space Oddity? A Statistical Formulation of Conjunction Assessment

Satellite conjunctions involving "near misses" of space objects are becoming increasingly likely. One approach to risk analysis for them involves the computation of the collision probability, but this has been regarded as having some counter-intuitive properties and its interpretation has been debated. This paper formulates an approach to satellite conjunction based on a simple statistical model and discusses inference on the miss distance between the two objects, both when the relative velocity can be taken as known and when its uncertainty must be taken into account. It is pointed out that the usual collision probability estimate can be badly biased, but that highly accurate inference on the miss distance is possible. The ideas are illustrated with case studies and Monte Carlo results that show its excellent performance.

stat.AP↗