All papers published in this volume have been reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected ...of a proceedings journal published by IOP Publishing.• Type of peer review: Single Anonymous• Conference submission management system: Morressier• Number of submissions received: 86• Number of submissions sent for review: 53• Number of submissions accepted: 48• Acceptance Rate (Submissions Accepted / Submissions Received × 100): 55.8• Average number of reviews per paper: 1.0416666666666667• Total number of reviewers involved: 32• Contact person for queries:Name: Michail TodorovEmail: mditod@gmail.comAffiliation: EAC4AMiTaNS - Mathematical Modelling and Numerical Methods
This article offers a comprehensive overview of the results obtained through numerical methods in solving the minimal surface equation, along with exploring the applications of minimal surfaces in ...science, technology, and architecture. The content is enriched with practical examples highlighting the diverse applications of minimal surfaces.
The Multi-Mission Maximum Likelihood framework (ThreeML) is a Python-based software package designed for multi-wavelength data analysis in high-energy astronomy. Integrating X-ray and gamma-ray data ...from various instruments, along with measurements at lower wavelengths, is essential for unlocking the full potential of observational data. However, the lack of standardization and unique challenges posed by each instrument often complicate the process of combining data from multiple sources. ThreeML addresses these challenges with its flexible, plugin-based structure, allowing for the seamless inclusion of data from diverse observatories in their native formats. Leveraging astromodels, a versatile modeling framework, ThreeML enables separate handling of source modeling and data access from likelihood optimization, facilitating a flexible combination of both aspects. Moreover, in addition to frequentist maximum likelihood analysis, ThreeML supports Bayesian analysis through posterior distribution sampling.
Abstract
In this work we study some characteristics of growth functions of the logistic type. The standard logistic function and the 2-logistic growth function are solutions of ordinary differential ...equations derived from the perspective of reaction network theory. These solutions are compared in terms of their shape. We are interested in the new 2-logistic probability distribution and its characteristics. Using the tools of reaction network theory and numerical methods we derive some properties of this distribution.
In this article, amplitude, and vibrational characteristics of a rotating fiber metal laminated microdisk are presented. The current microstructure is modeled as a flexible microdisk surrounded by ...the two-parameter viscoelastic foundation. The centrifugal and coriolis effects due to the rotation are considered. The strains and stresses can be determined via the third-order shear deformable theory. For accessing to size-effects, the nonlocal strain gradient theory is used. The boundary conditions are derived through governing equations of the laminated rotating microdisk using an energy method known as Hamilton's principle and finally are solved using a numerical method based generalized differential quadrature method.
Summary
In the present paper, structure‐preserving numerical methods for finite strain thermoelastodynamics are proposed. The underlying variational formulation is based on the general equation for ...nonequilibrium reversible‐irreversible coupling (GENERIC) formalism and makes possible the free choice of the thermodynamic state variable. The notion “GENERIC consistent space discretization” is introduced, which facilitates the design of Energy‐Momentum‐Entropy (EME) consistent schemes. In particular, three alternative EME schemes result from the present approach. These schemes are directly linked to the respective choice of the thermodynamic variable. Numerical examples confirm the structure‐preserving properties of the newly developed EME schemes, which exhibit superior numerical stability.
The article from this special issue was previously published in International Journal for Numerical Methods in Engineering, Volume 112, Issue 11, 2017. For completeness we are including the title ...page of the article. The full text of the article can be read in Issue 112:11 on Wiley Online Library: http://onlinelibrary.wiley.com/doi/10.1002/nme.5569/full
We introduce a class of Sparse, Physics-based, and partially Interpretable Neural Networks (SPINN) for solving ordinary and partial differential equations (PDEs). By reinterpreting a traditional ...meshless representation of solutions of PDEs we develop a class of sparse neural network architectures that are partially interpretable. The SPINN model we propose here serves as a seamless bridge between two extreme modeling tools for PDEs, namely dense neural network based methods like Physics Informed Neural Networks (PINNs) and traditional mesh-free numerical methods, thereby providing a novel means to develop a new class of hybrid algorithms that build on the best of both these viewpoints. A unique feature of the SPINN model that distinguishes it from other neural network based approximations proposed earlier is that it is (i) interpretable, in a particular sense made precise in the work, and (ii) sparse in the sense that it has much fewer connections than typical dense neural networks used for PDEs. Further, the SPINN algorithm implicitly encodes mesh adaptivity and is able to handle discontinuities in the solutions. In addition, we demonstrate that Fourier series representations can also be expressed as a special class of SPINN and propose generalized neural network analogues of Fourier representations. We illustrate the utility of the proposed method with a variety of examples involving ordinary differential equations, elliptic, parabolic, hyperbolic and nonlinear partial differential equations, and an example in fluid dynamics.
•An interpretable sparse neural network architecture for solving PDEs.•More efficient than DNN based methods on account of sparsity of the network.•Bridge between traditional meshless methods and DNNs.•Implicit mesh adaptivity; works also for non-smooth problems.•Provides a general framework for developing new hybrid algorithms for PDEs.
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