A practical general flow for a detection or design problem is to combine a Maxwell solver with some kind of optimization method. The connection between the two is formed by a parametrization, e.g. regarding geometry and materials, of the scene in the computational domain and a mathematical measure that measures the distance between the intended or measured response and the response of the system is for the current parameter values. The optimization method is tasked with driving this measure to zero as much as possible. The Maxwell solver provides the evaluation of the system’s response for the current values of the parameters. Depending on the type of optimization method, the Maxwell solver also computes the derivatives of the response with respect to the parameters.
Such a flow is an iterative process that requires multiple evaluations of the system response by the Maxwell solver. In many cases, many of such evaluations are need to solve the design or detection problem. Further, the Maxwell solver usually determines the computation time required to solve the inverse problem. In such cases, the Maxwell solver plays the pivotal role in this process and its properties largely determine the potential of solving the inverse problem. Therefore, the EMPMC lab invests in constructing Maxwell solvers with a range of properties suitable for this type of task. Examples include the LEGO method to enable local optimization approaches, geometrically differentiable Maxwell solvers via the spatial spectral method, and time-domain solvers to address wide-frequency-band responses.
In case of design problems, we often face additional challenges. One aspect is the generation of the initial design or blueprint, which precedes the introduction of parameters. An initial design is often guided by simplified design rules and technology constraints and this phase of the design process is often referred to as synthesis. In some cases, synthesis can also be more or less automated. An example is the construction of a sparse array topology in a MIMO radar, see e.g. [1]. A second aspect in design problems is the robustness of the solution, which concerns the question of how sensitive a design is for variations due to e.g. manufacturing tolerances. For this reason, we also research stochastic modeling and uncertainty quantification approaches, integrated with a Maxwell solver, see e.g. [2,3].
[1] Syeda, R., van Beurden, M. C., & Smolders, A. B. (2021) doi.org/10.1049/mia2.12129
[2] Barzegar, E., Eijndhoven, van, S. J. L., & Beurden, van, M. C. (2015) doi.org/10.2528/PIERB14111304
[3] Barzegar, E. (2024). Effect of uncertainty in electromagnetic media and its design implications. research.tue.nl/en/publications/effect-of-uncertainty-in-electromagnetic-media-and-its-design-imp