Double Accelerated Convergence ZNN with Noise-Suppression for Handling Dynamic Matrix Inversion

Matrix inversion is commonly encountered in the field of mathematics. Therefore, many methods, including zeroing neural network (ZNN), are proposed to solve matrix inversion. Despite conventional fixed-parameter ZNN (FPZNN), which can successfully address the matrix inversion problem, it may focus on either convergence speed or robustness. So, to surmount this problem, a double accelerated convergence ZNN (DAZNN) with noise-suppression and arbitrary time convergence is proposed to settle the dynamic matrix inversion problem (DMIP). The double accelerated convergence of the DAZNN model is accomplished by specially designing exponential decay variable parameters and an exponential-type sign-bi-power activation function (AF). Additionally, two theory analyses verify the DAZNN model’s arbitrary time convergence and its robustness against additive bounded noise. A matrix inversion example is utilized to illustrate that the DAZNN model has better properties when it is devoted to handling DMIP, relative to conventional FPZNNs employing other six AFs. Lastly, a dynamic positioning example that employs the evolution formula of DAZNN model verifies its availability.

Three-dimensional transient electromagnetic inversion with optimal transport

Transient electromagnetic method (TEM), as one of the essential time-domain electromagnetic prospecting approaches, has the advantage of expedition, efficiency and convenience. In this paper, we study the transient electromagnetic inversion problem of different geological anomalies. First, Maxwell’s differential equations are discretized by the staggered finite-difference (FD) method; then we propose to solve the TEM inversion problem by minimizing the Wasserstein metric, which is related to the optimal transport (OT). Experimental tests based on the layered model and a 3D model are performed to demonstrate the feasibility of our proposed method.

Radon Inversion Problem for Holomorphic Functions on Circular, Strictly Convex Domains

In this paper we study the so-called Radon inversion problem in bounded, circular, strictly convex domains with $${\mathcal {C}}^2$$ C 2 boundary. We show that given $$p>0$$ p > 0 and a strictly positive, continuous function $$\Phi $$ Φ on $$\partial \Omega $$ ∂ Ω , by use of homogeneous polynomials it is possible to construct a holomorphic function $$f \in {\mathcal {O}}(\Omega )$$ f ∈ O ( Ω ) such that $$\displaystyle \smallint _0^1 |f(zt)|^pdt = \Phi (z)$$ ∫ 0 1 | f ( z t ) | p d t = Φ ( z ) for all $$z \in \partial \Omega $$ z ∈ ∂ Ω . In our approach we make use of so-called lacunary K-summing polynomials (see definition below) that allow us to construct solutions with in some sense extremal properties.

The Radon Inversion Problem for Holomorphic Functions in the Unit Disc

This paper deals with the so-called Radon inversion problem formulated in the following way: Given a $$p>0$$ p > 0 and a strictly positive function H continuous on the unit circle $${\partial {\mathbb {D}}}$$ ∂ D , find a function f holomorphic in the unit disc $${\mathbb {D}}$$ D such that $$\int _0^1|f(zt)|^pdt=H(z)$$ ∫ 0 1 | f ( z t ) | p d t = H ( z ) for $$z \in {\partial {\mathbb {D}}}$$ z ∈ ∂ D . We prove solvability of the problem under consideration. For $$p=2$$ p = 2 , a technical improvement of the main result related to convergence and divergence of certain series of Taylor coefficients is obtained.

Toward a fully resolved volume of fluid simulation of the phase inversion problem

This paper presents an enstrophy-resolved simulation of the phase inversion problem using the volume of fluid (VOF) method. This well-known benchmark for modeling multiphase flows features a buoyancy-driven unsteady motion of a light fluid into a heavy one followed by several large- and small-scale interfacial processes such as deformation, ligament formation, interface breakup, and coalescence. A fully resolved description of such flow is advantageous for a priori and a posteriori evaluations when developing new subgrid-scale closure models for large eddy simulation of two-phase flows. However, most of the previous attempts in performing the direct numerical simulation of this problem have been unsuccessful to reach grid-independent high-order flow statistics such as enstrophy. The key contribution of this paper lies in proposing a new converging configuration for this problem by reducing the Reynolds and Weber numbers. The new setup reaches grid convergence for all the flow characteristics on a $$512^3$$ 512 3 grid. Particularly, the enstrophy which has always revealed a grid-dependent behavior in all the previous studies converges for the proposed setup. Also, we analyze the temporal evolution of interfacial structures including the statistics of the total interfacial area during the process on different grid resolutions. First, no convergence on the interfacial area is observed and the possible reasons for lack of convergence are discussed. The potential remedies are investigated through a comprehensive parameter study. The findings highlight that (i) the enstrophy always converges for these moderate Re and We numbers, and (ii) the convergence of the total interfacial area is sensitive to the choice of initial and wall boundary conditions. Then, a new setup based on this sensitivity analysis is proposed that succeeded in full convergence for enstrophy and a partial convergence for the total interfacial area. The numerical simulations were carried out using the VOF solvers of OpenFOAM with a comparison between the algebraic and geometric schemes. Besides, the convergence of size distribution of dispersed structures is investigated. The present study provides insight into the possible directions toward a DNS of phase inversion problem with all the flow and interfacial structures resolved, which is essential for the future development of multiphase flow models.