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In the simulation of differential-algebraic equations (DAEs), it is essential to employ numerical schemes that take into account the inherent structure and maintain explicit or hidden algebraic constraints without altering them. This paper…
Recently, various evolutionary partial differential equations (PDEs) with a mixed derivative have been emerged and drawn much attention. Nonetheless, their PDE-theoretical and numerical studies are still in their early stage. In this paper,…
Differential equations are fundamental to modeling dynamic systems in physics, engineering, biology, and economics. While analytical solutions are ideal, most real-world problems necessitate numerical approaches. This study conducts a…
This paper proposes and analyzes an accelerated inexact dampened augmented Lagrangian (AIDAL) method for solving linearly-constrained nonconvex composite optimization problems. Each iteration of the AIDAL method consists of: (i) inexactly…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
A new general Lie-algebraic approach is proposed to solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras $su_{pd}(2)$ as their dynamic symmetry algebras. The method makes use of an…
Supervised fine-tuning enhances the problem-solving abilities of language models across various mathematical reasoning tasks. To maximize such benefits, existing research focuses on broadening the training set with various data augmentation…
The quest for analytical solutions to differential equations has traditionally been constrained by the need for extensive mathematical expertise. Machine learning methods like genetic algorithms have shown promise in this domain, but are…
We present preconditioning techniques to solve linear systems of equations with a block two-by-two and three-by-three structure arising from finite element discretizations of the fictitious domain method with Lagrange multipliers. In…
The paper describes development (improvement/extension) approaches for composite (modular) systems (as combinatorial reengineering). The following system improvement/extension actions are considered: (a) improvement of systems component(s)…
In this paper, we propose some algorithms for analytical solution construction to nonlinear polynomial partial differential equations with constant function coefficients. These schemes are based on one-(single), two- (double) or three-…
This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…
Discrete Differential Equations (DDEs) are functional equations that relate polynomially a power series $F(t,u)$ in $t$ with polynomial coefficients in a "catalytic" variable $u$ and the specializations, say at $u=1$, of $F(t,u)$ and of…
Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…
Aligning theoretical atomistic structural models of materials with available experimental data presents a significant challenge for disordered systems. The configurational space to navigate is vast, and faithful realizations require large…
Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…
The Denoising Autoencoder (DAE) enhances the flexibility of the data stream method in exploiting unlabeled samples. Nonetheless, the feasibility of DAE for data stream analytic deserves an in-depth study because it characterizes a fixed…
Table Structure Recognition is an essential part of end-to-end tabular data extraction in document images. The recent success of deep learning model architectures in computer vision remains to be non-reflective in table structure…
Surrogate modeling is of great practical significance for parametric differential equation systems. In contrast to classical numerical methods, using physics-informed deep learning methods to construct simulators for such systems is a…
The analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap (PBG) structures and plasmonically active nanostructures to metamaterials. To achieve an accurate…