Inverse design of electromagnetic devices using topological derivative method

This paper deals with an inverse source problem governed by the Poisson equation. The aim is to reconstruct multiple anomalies from internal observation data within an arbitrary sub-region. The considered model problem is motivated by various applications such as the identification of geological anomalies underneath the Earth’s surface. To overcome the ill-posedness, the inverse problem is formulated as a self-regularized topology optimization one. A least-square functional measuring the misfit between the observed quantities and the values provided by the model problem is introduced. The misfit function involves a regularization term penalizing the relative perimeter of the unknown domain. Finally, it is minimized with respect to a finite number of circular-shaped anomalies. The existence and stability of the solution to the inverse problem are demonstrated. The reconstruction process is based on the topological derivative method. The variation of the shape functional with respect to a small geometric perturbation is studied, and the leading terms of a second-order topological asymptotic expansion are derived. A non-iterative reconstruction algorithm is developed via the minimization of the obtained asymptotic formula with respect to the location and size parameters of the unknown set of anomalies. The efficiency and accuracy of the proposed approach are justified by some numerical experiments.

In this work, an inverse design method for multiinput multi-output (MIMO) metastructured devices is developed. Large-scale inverse design problems are difficult to solve directly and often require heuristic methods or design optimization to find a solution. Inherent errors introduced by heuristic methods makes design optimization a more promising route to the realization of high performance devices. Here, a fast frequency domain solver for grids of Y-parameter matrices is developed. The solver is used together with an adjoint-based optimization routine to solve inverse metastructured design problems. The design procedure is demonstrated through the realization of a planar beamforming network for a multi-beam antenna.

Interpretable Forward and Inverse Design of Particle Spectral Emissivity Using Common Machine-Learning Models

PurposeThe purpose of this study is sensitivity analysis of the L2-norm and H1-seminorm of the solution of a diffusive–convective–reactive problem to topological changes of the underlying material.Design/methodology/approachThe topological derivative method is used to devise a simple and efficient topology design algorithm based on a level-set domain representation method.FindingsRemarkably simple analytical expressions for the sensitivities are derived, which are useful for practical applications including heat exchange topology design and membrane eigenvalue maximization.Originality/valueThe topological asymptotic expansion associated with a diffusive–convective–reactive equation is rigorously derived, which is not available in the literature yet.

Image segmentation is one of the most challenging problems in non-destructive testing (NDT) for industrial quality control where digitized radiographs or X-ray computerized tomography images are usually concerned in. The topological derivative based segmentation algorithms can be do well in these images with low signal to noise and contrast to noise ratio but the results are heavily affected by the image homogeneity and election of cost function. Note that the defects in these images usually lie in a very small area. An expensive computational cost with undesired result would be gained if segmenting were done on the whole image domain. Therefore a new strategy in this paper is proposed to remedy this problem. First the image is roughly segmented into a set of regions using pyramid linking. Then the scale parameters of cost function are computed for every sub region based on properties of the region. Finally, refinement can be performed on the sub regions using topological derivative method. The proposed algorithm has been demonstrated by several cases.

Simulation Based Engineering Science (SBES) is an evolving interdisciplinary research area rooted in the methods for modeling multiscale, multi-physics events. The objective in SBES is to develop methodologies that are foundational to designing multiscale systems by accounting for phenomena at multiple scales of lengths and time. Some of the key challenges faced in SBES include lack of methods for bridging various time and length scales, management of models and uncertainty associated with them, management of huge amount and variety of information, and methods for efficient decision making based on the available models. Although efforts have been made to address some of these challenges for individual application domains, a domain independent framework for addressing these challenges associated with multiscale problems is not currently available in the literature. In this paper, we make a clear distinction between multiscale modeling and multiscale design. Multiscale modeling deals with efficient integration of information from multiscale models to gain a holistic understanding of the system, whereas multiscale design deals with efficient utilization of information to satisfy design objectives. Our focus in this paper is on multiscale design. In order to address the challenges associated with multiscale design, we propose a domain independent strategy that is based on understanding the generic interaction patterns between models at multiple scales. The design strategy outlined in this paper has as its foundation a systems-based approach for designing design processes (meta-design) and robust design. The concepts are illustrated with a multiscale design problem from materials domain.

While fractal boundaries and their ability to describe irregularity have been intensively studied, only a few studies are available on wave propagation in a medium where a fractal or quasi fractal pattern is embedded. Acoustical propagation in 1D or 2D domains can be modeled using Time Domain Finite Differences or in Frequency domain with Finite element methods. The fractal object is then considered as a subwavelength set of scatterers, and the problem becomes a multiple scattering one leading to acoustic localization. So, as some important part of the energy remains trapped inside the fractal pattern, imaging such a medium becomes difficult and imaging such complex media with classical tools as B-scan or comparable methods is not sufficient. The resolution of the inverse problem of wave propagation can then be achieved with the help of the more efficient imaging methods related with Time Reversal. Using the concept of topological derivative as defined in Time Domain Topological Energy and Fast Topological Imaging Method, respectively, in Time domain and Frequency domain is powerful in that case. Examples in 1D and 2D will be presented including the image obtained for a sliced sponge.

Hybrid on‐load tap changers (OLTCs) are attractive solutions for the smooth change in voltage without current interruption in the converter transformer. This paper proposes a systematic topology derivation method of hybrid OLTC. To begin with, the topology derivation principle of OLTC is studied according to graph theory and equivalent electrical network theory, and the basic structure of OLTCs is constructed. Based on the topology derivation and optimization method, some hybrid OLTC topologies are derived. Particularly, a new hybrid star‐type parallel three‐switch OLTC topology with independent intellectual property rights is investigated in detail. Then, the optimal timing control is designed to reduce the time of current flow and shorten the overall switching time. Circuit simulation results show that arc‐free and reliable switching can be realized in the new topology. In addition, the losses and the heat generated during the switching process are calculated, and the impact of the phase between the stage voltage and system current on the loss and electrical stress is studied. Furthermore, the comparison between the proposed topology and other topologies is carried out to show the advantages of the proposed topology. Finally, Saber circuit simulation will be carried out to verify the theoretical and numerical analysis results.

Designing a monochromatic spatially-structured light field that recovers the pre-specified profile of optical force (OF) exerted on a particle is an inverse problem. It usually requires high dimensional optimization and involves lengthy calculations, thus remaining little studied despite decades of research on OF. We report here the first attempt to attack this inverse design problem. The modus operandi relies on the back-propagation algorithm, which is facilitated by the currently available machine learning framework, and, in particular, by an exact and efficient expression of OF that shows only polynomial and trigonometric functional dependence on the engineered parameters governing the structured light field. Two illustrative examples are presented in which the inversely designed structured light fields reproduce, respectively, a predefined spatial pattern of OF and a negative longitudinal OF in a transversely trapping area.

The employment of topological derivative concept is considered to propose a new optimization algorithm for the inverse conductivity problem. Since this inverse problem is nonlinear and ill-posed it is necessary to incorporate a prior knowledge about the unknown conductivity. In particular, we apply the Bayes theorem to add the assumption that we have just one small ball-shaped inclusion, which must be at a certain distance from the boundary of the domain. As the main emphasis of this paper is to investigate numerically the proposed approach, we shall use the meshless method of fundamental solutions to present some numerical results.

Mechanical metamaterials - engineered materials whose behavior is defined by their internal structure rather than their base material - have received great at- tention for the unusual properties they can exhibit. However, while the forward problem of predicting the mechanical behavior of a given metamaterial can be reliably done through simulation or experiments, the inverse problem - designing metamaterials with specific properties - remains difficult, especially for heteroge- neous metamaterials composed of multiple unit cells. This dissertation explores the use of generative machine learning to address this inverse design problem. The first part of the work investigates how inverse and generative models can be conditioned to produce unit cells with prescribed mechanical properties and how they can be used to generate multiple valid solutions for the same target. This is examined using a curved-beam metamaterial, which allows a compact geometric representation without complex design restrictions. The effect these restrictions have on the generative models is investigated in the second part. For this, a number of generative models—Variational Autoencoders, Generative Adversarial Networks, and Diffusion Models—are evaluated on a kirigami metamaterial where dependencies between the cuts cause intricate design constraints. The final part covers the challenges that arise when generative models are applied to heteroge- neous metamaterials, in which multiple unit cells are combined to create spatially varying mechanical properties. The results show that the applicability of generative models for the design of metamaterials strongly depends on the choice of geometric parameterization. Generative models make assumptions about their input data that generally hold for images, but can be invalid for metamaterials when complex dependencies be- tween the input parameters exist. B-splines can provide a representation without those dependencies and are therefore well suited to be paired up with generative models. Furthermore, it is also important how these geometrical parameters are sampled to create the training data for the generative models, as this sampling also affects the distribution of the properties in the training data. Overall, while generative machine learning models prove effective for the inverse design of mechanical metamaterials their successful application requires careful parameterization and selection of the training data.

Multiscale design dealing with a 2-scale material and product system is implemented by employing the probabilistic distribution matching probabilistic analytical target cascading method (PATC-PCE) in this paper. PATC-PCE allows design autonomy at each scale subsystem by formulating the multiscale design system as a multilevel design structure. The probabilistic distribution matching strategy in PATC-PCE can quantify the stochastic interrelated responses accurately enough. Comparative study on a multiscale bracket design problem shows that the results obtained by our method are very close to the benchmark values. PATC-PCE is demonstrated to be highly effective and applicable on multi-scale design.

Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately described by fractional differential equations, which involves fractional derivatives in time or/and space. The fractional derivatives describe either history mechanism or long range interactions of particle motions at a microscopic level. The new physics can change dramatically the behavior of the forward problems. For example, the solution operator of the time fractional diffusion diffusion equation has only limited smoothing property, whereas the solution for the space fractional diffusion equation may contain weak singularity. Naturally one expects that the new physics will impact related inverse problems in terms of uniqueness, stability, and degree of ill-posedness. The last aspect is especially important from a practical point of view, i.e., stably reconstructing the quantities of interest. In this paper, we employ a formal analytic and numerical way, especially the two-parameter Mittag-Leffler function and singular value decomposition, to examine the degree of ill-posedness of several ‘classical’ inverse problems for fractional differential equations involving a Djrbashian–Caputo fractional derivative in either time or space, which represent the fractional analogues of that for classical integral order differential equations. We discuss four inverse problems, i.e., backward fractional diffusion, sideways problem, inverse source problem and inverse potential problem for time fractional diffusion, and inverse Sturm–Liouville problem, Cauchy problem, backward fractional diffusion and sideways problem for space fractional diffusion. It is found that contrary to the wide belief, the influence of anomalous diffusion on the degree of ill-posedness is not definitive: it can either significantly improve or worsen the conditioning of related inverse problems, depending crucially on the specific type of given data and quantity of interest. Further, the study exhibits distinct new features of ‘fractional’ inverse problems, and a partial list of surprising observations is given below. (a) Classical backward diffusion is exponentially ill-posed, whereas time fractional backward diffusion is only mildly ill-posed in the sense of norms on the domain and range spaces. However, this does not imply that the latter always allows a more effective reconstruction. (b) Theoretically, the time fractional sideways problem is severely ill-posed like its classical counterpart, but numerically can be nearly well-posed. (c) The classical Sturm–Liouville problem requires two pieces of spectral data to uniquely determine a general potential, but in the fractional case, one single Dirichlet spectrum may suffice. (d) The space fractional sideways problem can be far more or far less ill-posed than the classical counterpart, depending on the location of the lateral Cauchy data. In many cases, the precise mechanism of these surprising observations is unclear, and awaits further analytical and numerical exploration, which requires new mathematical tools and ingenuities. Further, our findings indicate fractional diffusion inverse problems also provide an excellent case study in the differences between theoretical ill-conditioning involving domain and range norms and the numerical analysis of a finite-dimensional reconstruction procedure. Throughout we will also describe known analytical and numerical results in the literature.

Purpose – The purpose of this paper is to present a simple approach for calculation of the sensitivities in the free-form inverse design problems. The approach is based on the analogy with the similar tasks used in the signal-processing analysis. In the proposed case it is not required to solve an adjoint problem as in the most of the similar optimization tasks. The simulation engine used in the background is a Fast Boundary Element Method. The approach is validated on some known benchmark problems. Design/methodology/approach – Inverse design is recognized nowadays as a crucial scientific grand challenge. Contrary to the conventional approach (“Given the structure, find the properties”) it purses a new paradigm (“Given the desired property, find the structure”). Inverse class of problems has a broad application area, from the material-, medical-, bio- to the engineering-class of problems. When dealing with the inverse design in free-form optimization of the engineering problems the typical approach is to calculate the adjoint problem. Calculation of the adjoint problem mostly requires the costly calculation of the gradients, which makes the whole optimization procedure rather expensive due to the high computational burden required for their solution. Findings – In this paper it is proposed a novel Simple Sensitivity Approach to get in a fast way the response (sensitivity) function of the analyzed structure. The simulation engine used in the background is the Fast Boundary Element Method. Originality/value – Novel approach for inverse design when performing the free-form optimization of engineering problems.

Development and validation of a hybrid aerodynamic design method for curved diffusers using genetic algorithm and ball-spine inverse design method