Computational Tools for Differentiable Multi-Physics Electric Machine Models
Andrés Beltrán-Pulido, Dionysios Aliprantis (Elmore Family School of Electrical & Computer Engineering), Ilias Bilionis (School of Mechanical Engineering, Purdue University
This research project is focused on developing a computational framework for differentiable multi-physics electric machine (EM) models to enable efficient and accurate modeling, analysis, and design for various applications (e.g., electric vehicles). Our goal is to create computationally efficient EM models for solving partial differential equations-constrained optimization problems. Significant progress has been made in developing a method for constructing an analytical representation of complex EM geometries. A main contribution is the development of a signed distance function (SDF)-based representation to define the geometry of an EM analytically in two-dimensional (2-D) problems. The device regions are defined using indicator functions, constructed by combining and transforming SDF primitives. We have demonstrated this method with a hairpin PMSM in a case study (see Figure 1) and published the accompanying code in [1].
An advantage of the proposed method is the flexibility it provides in the parameterization of EM geometry. Thus, it can be employed as part of a parametric-based EM optimization process. Additionally, since the proposed mesh-less method involves analytical expressions that are straightforward to compute, it is suitable for application with other emerging approaches to model electromagnetic devices, such as physics-informed neural networks (PINNs) [2]. Moving forward, we aim to refine and extend the optimization framework, particularly to include (parametric) electromagnetic physics analysis. We will leverage the PINN framework to solve the quasi-magnetostatic problem across various geometries, yielding a physics-informed, differentiable model for rapidly predicting the EM electromagnetic fields. In addition, we will compare the predicted fields with finite element simulations to further validate and enhance our methodology. We expect this effort to yield openly available codes and methods, extensive simulation data sets, and journal publication

Figure 1. 8-pole PMSM stator (top) and rotor (bottom) geometry parameterization (half pole is shown) [1].
[2] A. Beltrán-Pulido, I. Bilionis and D. Aliprantis, “Physics-Informed Neural Networks for Solving Parametric Magnetostatic Problems,” in IEEE Transactions on Energy Conversion, vol. 37, no. 4, pp. 2678-2689, Dec. 2022.