Related papers: Deriving thin-film averaged equations using comput…
Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations…
The isentropic compressible Cahn-Hilliard-Navier-Stokes equations is a system of fourth-order partial differential equations that model the evolution of some binary fluids under convection. The purpose of this paper is the design of…
Deep image watermarking, which refers to enabling imperceptible watermark embedding and reliable extraction in cover images, has been shown to be effective for copyright protection of image assets. However, existing methods face limitations…
We propose Derivative Learning (DERL), a supervised approach that models physical systems by learning their partial derivatives. We also leverage DERL to build physical models incrementally, by designing a distillation protocol that…
In this work, we propose a systematic derivation of normal forms for dispersive equations using decorated trees introduced in arXiv:2005.01649. The key tool is the arborification map which is a morphism from the Butcher-Connes-Kreimer Hopf…
We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as…
The Whittle likelihood is a widely used and computationally efficient pseudo-likelihood. However, it is known to produce biased parameter estimates for large classes of models. We propose a method for de-biasing Whittle estimates for…
Given a map $\Xi\colon U(\mathfrak{g})\rightarrow A$ of associative algebras, with $U(\mathfrak{g})$ the universal enveloping algebra of a (complex) finite-dimensional reductive Lie algebra $\mathfrak{g}$, the restriction functor from…
Explicit representations of densities for linear parabolic partial differential equations are useful in order to design computation schemes of high accuracy for a considerable class of diffusion models. Approximations of lower order based…
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
The spectral decomposition of the elastic wave operator in a layered isotropic half-space is derived by means of standard functional analytic methods. Particular attention is paid to the coupled $P$-$SV$ waves. The problem is formulated…
A well-known technique in estimating probabilities of rare events in general and in information theory in particular (used, e.g., in the sphere-packing bound), is that of finding a reference probability measure under which the event of…
In this paper we explore a numerical scheme for a nonlinear fourth order system of partial differential algebraic equations that describes the dynamics of slender inextensible elastica as they arise in the technical textile industry.…
The thin runback water films driven by the gas flow, the pressure gradient and the gravity on the iced aircraft surface are investigated in this paper. A three-dimensional film flow model based on Finite Volume Method (FVM) and the…
Symbolic regression (SR) methods have been extensively investigated to explore explicit algebraic Reynolds stress models (EARSM) for turbulence closure of Reynolds-averaged Navier-Stokes (RANS) equations. The deduced EARSM can be readily…
We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is…
It is well known that building analytical performance models in practice is difficult because it requires a considerable degree of proficiency in the underlying mathematics. In this paper, we propose a machine-learning approach to derive…
Umbrella sampling efficiently yields equilibrium averages that depend on exploring rare states of a model by biasing simulations to windows of coordinate values and then combining the resulting data with physical weighting. Here, we…
Credibility building activities in computational research include verification and validation, reproducibility and replication, and uncertainty quantification. Though orthogonal to each other, they are related. This paper presents…