Three-dimensional data-driven magnetostatic field computation using real-world measurement data

Abstract

Purpose The purpose of this paper is to present the applicability of data-driven solvers to computationally demanding three-dimensional problems and their practical usability when using real-world measurement data. Design/methodology/approach Instead of using a hard-coded phenomenological material model within the solver, the data-driven computing approach reformulates the boundary value problem such that the field solution is directly computed on raw measurement data. The data-driven formulation results in a double minimization problem based on Lagrange multipliers, where the sought solution must conform to Maxwell’s equations while at the same time being as close as possible to the available measurement data. The data-driven solver is applied to a three-dimensional model of a direct current electromagnet. Findings Numerical results for data sets of increasing cardinality verify that the data-driven solver recovers the conventional solution. Additionally, the practical usability of the solver is shown by using real-world measurement data. This work concludes that the data-driven magnetostatic finite element solver is applicable to computationally demanding three-dimensional problems, as well as in cases where a prescribed material model is not available. Originality/value Although the mathematical derivation of the data-driven problem is well presented in the referenced papers, the application to computationally demanding real-world problems, including real measurement data and its rigorous discussion, is missing. The presented work closes this gap and shows the applicability of data-driven solvers to challenging, real-world test cases.

Data‐driven model‐free modified nodal analysis circuit solver

“…In such cases, it is indeed difficult to establish a meaningful error norm between the data-driven and the conventional approach, primarily because the true behavior of the elements is unknown, thus making unclear what should be considered as the definitive reference point or ground truth. 17 Furthermore, the required level of accuracy is highly dependent on the specific use case. In addition to errors stemming from finite data, there are numerous other error sources to consider, such as timediscretization, mathematical modeling of the physical problem, and general numerical approximations, to name but a few.…”

“…contributions in the field of magnetic field simulation. [15][16][17] The original model-free data-driven formulation 8 and its derived works are characterized by a partial differential equation (PDE), which is either elliptic or parabolic.…”

Hybrid Modeling: Towards the Next Level of Scientific Computing in Engineering

“…3, the measured material data can be found in [1]. Further information on the simulated geometries is given in [7,13,14]. The CAD model and network simulation setup explained in Sect.…”

“…3 Data-driven field simulation [7,13,14] This section is about data-driven field simulation for magnetostatic problems. Here, datadriven simulation is meant in the context of simulations directly on the material data and was first introduced in [26].…”

“…A computationally demanding 3D inductor model was considered in [14], where realworld measurement data [1] was employed for the iron part. For comparison, an extended Brauer model [22] was constructed on the measurement data and utilized in a standard Newton solver.…”