Gradient-Informed Machine Learning in Electromagnetics

2026-01-26

AI Summary

This work addresses the high computational cost of high-fidelity electromagnetic simulations—such as those based on the finite element method—which hinders real-time or repeated analysis of nonlinear, non-affine parametrized models, particularly where conventional reduced-order methods struggle. To overcome this limitation, the authors propose a non-intrusive surrogate modeling framework that synergistically integrates isogeometric analysis (IGA), proper orthogonal decomposition (POD), and gradient-enhanced Gaussian process regression (GPR). Notably, this approach explicitly incorporates the analytical parameter sensitivities provided by IGA into the GPR formulation for the first time, enabling efficient and accurate surrogate modeling of nonlinear parametrized permanent magnet synchronous machines. The method substantially improves both the accuracy and training efficiency of the surrogate model, thereby overcoming key bottlenecks of traditional reduction techniques in handling complex parameter dependencies and offering a viable pathway for real-time optimization and design of electromagnetic devices.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Simulation techniques such as the finite element method are essential for designing electrical devices, but their computational cost can be prohibitive for repeated or real-time computations. Projection-based model order reduction techniques mitigate this by reducing the model size and complexity, yet face challenges when extended to nonlinear or non-affine parametric models. In this work, Isogeometric Analysis (IGA) is combined with proper orthogonal decomposition and Gaussian process regression to construct a non-intrusive surrogate model of a parametric nonlinear model of a permanent magnet synchronous machine. The differentiable nature of IGA allows for computationally efficient extraction of parametric sensitivities, which are leveraged for gradient-enhanced surrogate modeling.

Problem

• model order reduction
• nonlinear parametric models
• computational cost
• electromagnetics simulation
• surrogate modeling

Innovation

• Isogeometric Analysis
• Gradient-enhanced surrogate modeling
• Proper Orthogonal Decomposition
• Gaussian Process Regression
• Parametric sensitivity