A Quantum Annealing-Driven Multi-Scale Optimization Framework for Nonlinear Electromagnetic Field Analysis
Abstract
This study proposes an efficient quantum annealing-driven multi-scale optimization framework for solving global optimization problems in nonlinear electromagnetic field analysis. The framework first establishes a unified mathematical model of the nonlinear electromagnetic field. This unified model describes the multi-physics coupling behavior through Maxwell's equations and nonlinear constitutive relations. Based on variational principles, the model transforms the electromagnetic field governing equations into an energy functional minimization problem. Simultaneously, the finite element method is used for spatial discretization. To handle the non-convexity in multi-scale parameter inversion, the objective function is mapped to a time-varying Hamiltonian. This is equivalently transformed into a quadratic unconstrained binary optimization model. This operation enables quantum annealing for solution. For strongly nonlinear objective functions, this study introduces incremental encoding and quantum approximation strategies, and achieves efficient processing through iterative linearization and dynamic updates. In experimental verification of seven multi-scale electromagnetic systems, including nonlinear ferromagnetic coils, high-frequency motor magnetic fields, and magnetostrictive actuators, the proposed method demonstrates significant advantages. Experimental results show that, in seven test cases, the objective function value obtained by this method is on average 18.7 % lower…
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