Related papers: Differential Geometric Foundations for Power Flow …
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…
In recent years, Neural Operators(NO) have gradually emerged as a popular approach for solving Partial Differential Equations (PDEs). However, their application to large-scale engineering tasks suffers from significant computational…
Some differential equations are considered in the context of Synthetic Differential Geometry. Here, this means that not only nilpotent infinitesimals, but also the formation of function spaces, is exploited. In particular, we utilize…
We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…
This paper surveys results found by the authors in the previous papers (see for example, A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical layer flows of a viscid fluid, Journal of Geometry and Physics, 130,…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
We present a simple algorithm for differentiable rendering of surfaces represented by Signed Distance Fields (SDF), which makes it easy to integrate rendering into gradient-based optimization pipelines. To tackle visibility-related…
This paper proposes a graph computation based sequential power flow calculation method for Line Commutated Converter (LCC) based large-scale AC/DC systems to achieve a high computing performance. Based on the graph theory, the complex AC/DC…
Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…
Quantum solutions to differential equations represent quantum data -- states that contain relevant information about the system's behavior, yet are difficult to analyze. We propose a toolbox for reading out information from such data, where…
A new computational algorithm, the discrete singular convolution (DSC), is introduced for computational electromagnetics. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied.…
Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the…
Two dimensional passive scalar turbulence is studied by means of a k-space diffusion model based on a third order differential approximation. This simple description of local nonlinear interactions in Fourier space is shown to present a…
Accurate and efficient prediction of multi-scale flows remains a formidable challenge. Constructing theoretical models and numerical methods often involves the design and optimization of parameters. While gradient descent methods have been…
In this paper we develop a new approach to the design of direct numerical methods for multidimensional problems of the calculus of variations. The approach is based on a transformation of the problem with the use of a new class of…
During the process of teaching the concept of derivative, it is common and natural to refer to geometric interpretations, such as the use of the tangent line and the maximum and minimum points of a function, to illustrate the scope of the…
We present an energy/entropy stable and high order accurate finite difference (FD) method for solving the nonlinear (rotating) shallow water equations (SWEs) in vector invariant form using the newly developed dual-pairing and…
A variational technique is used to derive analytical expressions for the sensitivity of several geometric indicators of flow separation to steady actuation. Considering the boundary layer flow above a wall-mounted bump, the six following…