Differentiable Cosimulator for Electrically Reconfigurable Structures

Electrically reconfigurable metasurfaces (MTS) for magnetic resonance imaging (MRI) can exhibit many degrees of freedom. Each tunable parameter affects the final response of the metasurface to an impinging magnetic field. Thus, the configuration of the electric parameters significantly affects the manner in which metasurfaces shape the overall magnetic field distribution. Owing to the high number of parameters and the mutual coupling, shaping the field in a target way can be a nontrivial and time-consuming challenge. This paper introduces a novel CUDA-enabled PyTorch-based framework (available open-source on github.com) designed for the gradient-based optimization of such reconfigurable electromagnetic structures with electrically tunable parameters. Traditional optimization techniques for these structures often rely on non-gradient-based methods, which limit their efficiency and flexibility. The proposed framework leverages automatic differentiation, facilitating the application of gradient-based optimization methods. This approach is particularly advantageous for embedding within deep learning frameworks, which enables sophisticated optimization strategies. We demonstrate the effectiveness of the framework through comprehensive simulations involving resonant structures with tunable parameters. The key contributions include the efficient solution to the inverse problem. The performance of the framework is validated using three different resonant structures: a single-loop copper wire (single unit cell) and an 8x1 as well as an 8x8 array of resonant unit cells with multiple inductively coupled unit cells (one-dimensional (1d) and two-dimensional (2d) metasurfaces). The results show precise control over an individual component of the magnetic field normal to the surface of each resonant structure, achieving target field strengths with minimal error.