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Recently, the deep learning technology has been successfully applied in the field of image compression, leading to superior rate-distortion performance. However, a challenge of many learning-based approaches is that they often achieve…
Score-based diffusion models currently constitute the state of the art in continuous generative modeling. These methods are typically formulated via overdamped or underdamped Ornstein--Uhlenbeck-type stochastic differential equations, in…
We propose to model physical effects at the sharp density interface between atmosphere and ocean with the help of diffuse interface approaches for multiphase flows with variable densities. We use the variable-density model proposed in…
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…
In this paper, a centred universal high-order finite volume method for solving hyperbolic balance laws is presented. The scheme belongs to the family of ADER methods where the Generalized Riemann Problems (GRP) is a building block. The…
In this note we present the current status of the derivation of a viscous Serre-Green-Naghdi system. For this goal, the flow domain is separated into two regions. The upper region is governed by inviscid Euler equations, while the bottom…
We prove locally in time the existence of the unique smooth solution (including smooth interface) to the multidimensional free boundary problem for the thin film equation in the case of partial wetting. We also obtain the Schauder estimates…
X-ray reflectivity (XRR) is a powerful and popular scattering technique that can give valuable insight into the growth behavior of thin films. In this study, we show how a simple artificial neural network model can be used to predict the…
The Wasserstein barycenter problem is to compute the average of $m$ given probability measures, which has been widely studied in many different areas; however, real-world data sets are often noisy and huge, which impedes its applications in…
We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the…
This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional…
The shallow water equations describing the motion of thin liquid film on the rotating cylinder surface are obtained. These equations are the analog of the modified Boussinesq equations for shallow water and the Korteweg-de Vries equation.…
Machine learning techniques have been applied to enhance turbulence modeling in recent years. However, the "black box" nature of most machine learning techniques poses significant interpretability challenges in improving turbulence models.…
Accurate on-orbit reliability prediction for satellite electronics is often hindered by limited data availability, varying operational conditions, and considerable unit-to-unit variability. To overcome these obstacles, this paper proposes a…
This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial…
Semi-empirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semi-empirical model still in widespread use in chemistry is H\"uckel's…
A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
For the evolution of a compressible fluid in spherical symmetry on a Schwarzschild curved background, we design a class of well-balanced numerical algorithms with first-order or second-order of accuracy. We treat both the relativistic…
The non-parametric version of Amari's dually affine Information Geometry provides a practical calculus to perform computations of interest in statistical machine learning. The method uses the notion of a statistical bundle, a mathematical…