Artificial Intelligence leveraging Computational Electromagnetics

Dnr:

NAISS 2024/5-222

Type:

NAISS Medium Compute

Principal Investigator:

Jonas Ekman

Affiliation:

Luleå tekniska universitet

Start Date:

2024-04-29

End Date:

2024-11-01

Primary Classification:

20299: Other Electrical Engineering, Electronic Engineering, Information Engineering

Secondary Classification:

10105: Computational Mathematics

Tertiary Classification:

10399: Other Physics Topics

Maxwell's equations are the basis of many applications that have led to rapid improvements in human life over the last two centuries. Therefore, their solution is still of extreme interest today in the design of systems and devices used in daily life. It is well known that they can be resolved by resorting to their integral formulation. This translates into the need to solve integral equations that use the concept of Green's function and require the calculation of integrals that describe the electric and magnetic field interactions between currents and charges localized in elementary regions of volume and surface. The calculation of these integrals is typically very time-consuming, even if parallel calculation means are used. In the case of orthogonal meshes, analytical formulas are very quick to calculate but have a validity limited to the quasi-static regime and cannot be used in cases where propagation phenomena are important. Furthermore, their application is not possible in the case of non-orthogonal meshes, which are more flexible in the description of complex geometries. For example, in the case of tetrahedral meshes, there are no analytical formulas, and the interaction integrals are normally calculated numerically with a consequent increase in calculation times. Machine learning techniques have been widely used to capture the response of electrical/electromagnetic systems in certain regions of the computing domain, called gates, as geometric and physical parameters (e.g., frequency) vary. However, we are unaware of the use of machine learning aimed at capturing the dependence of the interaction integrals on the geometric parameters that describe a pair of tetrahedra and on the basis functions that describe the current field inside them. Therefore, we propose a project aiming to develop deep learning techniques that are able to quickly calculate these integrals as the geometric characteristics of the tetrahedral elementary domains, their relative position, and the current basis functions vary. The accuracy and efficiency of the proposed technique will be validated on realistic structures by comparing the results with those obtained using commercial tools and those obtained through the rigorous calculation of the coupling coefficients. The developed model can then be used within direct and iterative electromagnetic solvers, avoiding the heavy use of numerical integration, to analyze complex systems that adopt tetrahedral meshes.
The project will be carried out by Jonas Ekman and Danesh Daroui. Our group has been awarded two grants by Vetenskapsrådet in the past (2006 and 2018) for our work on computational electromagnetics.