Call for Papers "SPECIAL ISSUE: Machine Learning Based Solutions of Partial Differential Equations"

Partial Differential Equations (PDEs) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In order to solve PDEs that represent real systems to an acceptable degree, analytical methods are usually not enough. One has to resort to discretization methods. For engineering problems, probably the best known option is the Finite Element Method (FEM). However, powerful alternatives such as mesh-ree methods, Isogeometric Analysis (IGA) or Finite Difference Methods (FDM) are also available, just to name a few. A new route to solve PDEs is so called physics-informed neural networks that make use of machine learning based activation functions as approximators. There is great flexibility to define their structure and important advances in the architecture and the efficiency of the algorithms to implement them make such approaches a very interesting alternative to “classical” methods such as FEM. The goal of the SI is on numerical solutions of PDEs taking advantage of ML approaches. Physics informed neural networks or ML based approaches to improve existing approaches such as FEM or IGA are the main focus of this SI. Furthermore, manuscripts dealing with the following topics are particularly welcome:

Theory and applications of neural networks (NN) or similar approaches for the solution of PDEsNN approaches for the solution of inverse or optimization problemsData-driven constitutive models exploiting NN or similar methods.Stochastic approaches based on NN or similar methods.

Papers will be published online upon acceptance, regardless of the special Issue publication date.

Welcome your contributions!

Guest Editors:

Prof. Dr.-Ing. Timon Rabczuk

Chair of Computational Mechanics,

Bauhaus University Weimar, Germany

Prof. Xiaoying Zhuang

Sofja Kovalevskaja Group Leader,

Institute of Continuum Mechanics,

Leibniz University Hannover, Germany


Machine Learning based solutions of partial differential equations

Guest Editors

Timon Rabczuk and Xiaoying Zhuang

Number of Manuscript

15 to 20

Deadline of paper submission


Articles reach production by


Manuscript guidelines

Submission online (with 2020PDE in the article title)