Circuit-based Inverse Design of Metastructured MIMO Devices

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.

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

Inverse design optimization of the spatial distribution of emissivity for radiative transfer problems based on adjoint method

A new consistent direct-iterative method is proposed for the solution of the aerodynamic inverse design problem. These popular design procedures couple analysis and shape-prediction methods to iteratively determine the design geometry. The proposed method includes a new shape-prediction technique; this unique method uses the identical governing equations and numerical techniques as those used in the analysis portion of the design procedure. The new design method was evaluated with an upwind cell-centered finite-volume formulation of the two-dimensional Euler equations. Inverse design test problems were conducted with a symmetric channel for which the design variable was a channel-wall ramp angle, theta, that is nominally 5 deg. Target geometries were defined with ramp-angle perturbations of delta theta = 2, 10, and 20 percent. With a supersonic inlet Mach number of 2, the new design method accurately predicted all target geometries. The inverse design solutions were obtained in a computationally efficient manner; the average design solution required less than seven iterations and approximately twice the computational effort as a comparable analysis solution. (Author)

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

We report a series of deep learning models to solve complex forward and inverse design problems in molecular modeling and design. Using both diffusion models inspired by nonequilibrium thermodynamics and attention-based transformer architectures, we demonstrate a flexible framework to capture complex chemical structures. First trained on the Quantum Machines 9 (QM9) dataset and a series of quantum mechanical properties (e.g., homo, lumo, free energy, and heat capacity), we then generalize the model to study and design key properties of deep eutectic solvents (DESs). In addition to separate forward and inverse models, we also report an integrated fully prompt-based multi-task generative pretrained transformer model that solves multiple forward, inverse design, and prediction tasks, flexibly and within one model. We show that the multi-task generative model has the overall best performance and allows for flexible integration of multiple objectives, within one model, and for distinct chemistries, suggesting that synergies emerge during training of this large language model. Trained jointly in tasks related to the QM9 dataset and DESs, the model can predict various quantum mechanical properties and critical properties to achieve deep eutectic solvent behavior. Several combinations of DESs are proposed based on this framework.

We consider the diffraction of a time-harmonic wave incident upon a grating (or periodic) structure. We study mathematical issues that arise in the direct modeling, inverse, and optimal design problems. Particular attention is paid to the variational approach and to finite-element methods. For the direct problem various results on existence, uniqueness, and numerical approximations of solutions are presented. Convergence properties of the variational method and sensitivity to TM polarization are examined. Our recent research on inverse diffraction problems and optimal design problems is also discussed.

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.

Computational Intelligence Systems (CIS) is one of advanced softwares. CIS has been important position for solving single-objective / reverse / inverse and multi-objective design problems in engineering. The paper hybridise a CIS for optimisation with the concept of Nash-Equilibrium as an optimisation pre-conditioner to accelerate the optimisation process. The hybridised CIS (Hybrid Intelligence System) coupled to the Finite Element Analysis (FEA) tool and one type of Computer Aided Design (CAD) system, GiD is applied to solve an inverse engineering design problem, reconstruction of High Lift Systems (HLS). Numerical results obtained by the hybridised CIS are compared to the results obtained by the original CIS. The benefits of using the concept of Nash-Equilibrium are clearly demonstrated in terms of solution accuracy and optimisation efficiency.

Electronic band structure contains a wealth of information on the electronic properties of a solid and is routinely computed. However, the more difficult problem of designing a solid with a desired band structure is an outstanding challenge. In order to address this inverse band structure design problem, we devise an approach using materials database screening with materials attributes based on the constituent elements, nominal electron count, crystal structure, and thermodynamics. Our strategy is tested in the context of thermoelectric materials, for which a targeted band structure containing both flat and dispersive components with respect to crystal momentum is highly desirable. We screen for thermodynamically stable or metastable compounds containing d8 transition metals coordinated by anions in a square planar geometry in order to mimic the properties of recently identified oxide thermoelectrics with such a band structure. In doing so, we identify 157 compounds out of a total of more than half a million candidates. After further screening based on electronic band gap and structural anisotropy, we explicitly compute the band structures for the several of the candidates in order to validate the approach. We successfully find two new oxide systems that achieve the targeted band structure. Electronic transport calculations on these two compounds, Ba2PdO3 and La4PdO7, confirm promising thermoelectric power factor behavior for the compounds. This methodology is easily adapted to other targeted band structures and should be widely applicable to a variety of design problems.

A model-based method has been developed for the performance simulation and conceptual design of rocket-type pulse detonation engines (PDEs). A reduced-order model (ROM) has been generated based on the high order singular value decomposition of a data tensor obtained from CFD computations. This ROM could be used to solve the direct (performance) and inverse (design) problems in the context of the early phases of pulse detonation engine design. Output performance parameters are predicted from prescribed input operation/geometry parameters in the direct problem, and vice versa in the inverse problem. The focus of this method is industrial application in situations where large parametric searches are to be performed with a reasonable level of fidelity at a low computational cost. It was found that the performance and conceptual design tool thus developed provides results that deviate, on average, by less than 10% from the CFD results. Regarding practical implementation, the method allows for shifting the heavier computational load off-line. In this way, when working on-line, the user can obtain results in less than a second for every single case. The main contribution of this study is showing that a model-based approach that combines CFD and tensor decomposition has the potential to extract a maximum of information from a given computational effort. This characteristic makes the method of interest for early design phases in the aerospace industry.

Deep learning surrogate models have shown promise in modeling complex physical phenomena such as photonics, fluid flows, molecular dynamics and material properties. However, standard neural networks assume finite-dimensional inputs and outputs, and hence, cannot withstand a change in resolution or discretization between training and testing. We introduce Fourier neural operators that can learn operators, which are mappings between infinite dimensional spaces. They are discretization-invariant and can generalize beyond the discretization or resolution of training data. They can efficiently solve partial differential equations (PDEs) on general geometries. We consider a variety of PDEs for both forward modeling and inverse design problems, as well as show practical gains in the lithography domain.

Traditional computational approaches to design chemical species are limited by the need to compute properties for a vast number of candidates, e.g., by discriminative modeling. Therefore, inverse design methods aim to start from the desired property and optimize a corresponding chemical structure. From a machine learning viewpoint, the inverse design problem can be addressed through so-called generative modeling. Mathematically, discriminative models are defined by learning the probability distribution function of properties given the molecular or material structure. In contrast, a generative model seeks to exploit the joint probability of a chemical species with target characteristics. The overarching idea of generative modeling is to implement a system that produces novel compounds that are expected to have a desired set of chemical features, effectively sidestepping issues found in the forward design process. In this contribution, we overview and critically analyze popular generative algorithms like generative adversarial networks, variational autoencoders, flow, and diffusion models. We highlight key differences between each of the models, provide insights into recent success stories, and discuss outstanding challenges for realizing generative modeling discovered solutions in chemical applications.

Inverse design strategies for buckling-guided assembly of 3D surfaces based on topology optimization

Introduction A very efficient formulation for the inverse design of two-dimensional turbomachinery blades in turbulent transonic flow conditions is presented. The proposed optimization technique employs a highly accurate space discretization scheme for the accurate computation of the flow solution and of the objective function. The sensitivity derivatives are evaluated very efficiently by using a discrete adjoint formulation. The use of an auxiliary dissipative flow solver in the adjoint equations, rather than the accurate basic flow solver, allows a robust evaluation of the sensitivity derivatives, even in presence of shocks and of numerical noise. Moreover, if the variable prescribed on the blade surface is the pressure, as usual, a simplified inviscid formulation of the adjoint problem can be used, even in the real case of turbulent flows. The entire procedure is termed progressive optimization, because both the flow computation and the iterative solution of the adjoint problem, based on the addition of an artificial time-dependent term in the adjoint equations, are brought to convergence while approaching the optimum. The idea of the simultaneous convergence of all iterative solutions suggests also the use of progressively finer grids for the progressive computation of the flow field; the cost of the adjoint problem is strongly reduced by solving the adjoint equations always at the coarsest level. The proposed approach has been tested on the inverse design of a two-dimensional turbine blade in turbulent transonic flow conditions, both with fixed stagger angle and with fixed outlet angle of the camberline. The numerical results demonstrate that the methodology is robust and highly efficient, with a converged design optimization produced in no more than the amount of computational work needed to perform from 0.7 to 1.3 converged flow analyses on the finest grid. 'Associate Professor. ^Professor and Department Head, AIAA senior member. Copyright © 2000 by L. A. Catalano and A. Dadone. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. Until few years ago, the optimization of the aerodynamic efficiency of turbomachinery bladings has been mostly approached by subsequent improvements based on the experience of the designers, each one of them followed by expensive and timeconsuming wind tunnel tests. For such a reason, the recent development of automatic tools based on the numerical solution of the flow equations and on an optimization process for the shape changes has greatly attracted the interest of turbomachinery designers. Due to the complex flow patterns about turbomachinery bladings, these numerical methods have been first developed and applied to the inverse and the direct design of airfoils; some of them have been later extended to the optimization of turbine and compressor blades. Nevertheless, many of the inverse design methods for turbomachinery bladings currently used are based on the use of a transpiration model', which cannot be extended to the direct design of the blade. For such a reason, the authors find very attractive to extend more general metodologies, already developed and tested for the optimization of airfoils or wings, to the design of turbomachinery bladings. In the application of these methods to transonic flows, typical of high-load bladings, a major difficulty commonly arises: the objective function is generally noisy or non-smooth, so that the convergence of standard optimization techniques may be compromised or even prevented, as shown in Ref. 3 for the case of a transonic nozzle. In such situations a standard finite-difference approach for design sensitivities or an alternative route based on the solution of a set of sensitivity equations' may result in an optimization process hung up at one of the many local minima artificially created by the shock shifting. The adjoint procedure proposed by Jameson et al overcomes this problem by effectively smoothing the objective function, which however may change the result of the optimization process, as outlined in Ref. 7. An alternative smoothing procedure which operates only on the design sensitivities and not on the objective function itself is proposed in Ref. 8, where it is (c)2000 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. shown to be effective and efficient in designing transonic diffusers and airfoils by using two-dimensional inviscid flow equations. A second, very important challenge is the development of an optimization technique able to converge to the optimum in a computational work corresponding to few flow analyses. Indeed, most existing methodologies are based on a sequence of global iterations, each one of them requiring a computation of the converged flow field, a solution for the sensitivity derivatives and an appropriate update of the design variables. The repeated solution of the flow equations typical of such a serial approach results in a high computational cost of the entire design procedure. The efficiency of the smoothing procedure developed in Ref. 8 has been recently improved by introducing a progressive optimization strategy''', whereby the optimization process is based on partially converged flow solutions with the aim to converge the flow solution while converging the design problems. In particular, in Ref. 11 this efficient approach is applied to the inverse design of turbine blades in inviscid transonic flow conditions. In Refs. 9 — 1 2 , the adjoint equations are solved using a direct solver, appropriate for two-dimensional flow problems, but not effective for three-dimensional flow problems. The extension to three dimensions has been considered in Ref. 13, where the progressive procedure suggested in Ref. 9 is modified by adding a time derivative in the adjoint equations, and by solving them iteratively. in a progressive manner quite similar to the one employed for the flow equations. The smoothing procedure and the use of partially converged flow solutions as well as of partially converged adjoint equation solutions in the progressive optimization implies that the optimization process is based on approximate values of the gradient of the objective function. Another example of approximate design sensitivity has been discussed by Matsuzawa and Hafez, where adjoint equations based on an inviscid flow formulation have been used successfully to determine approximate gradients of the objective function for airfoil inverse design in laminar flow conditions. The aim of the present paper is to apply all of the aforementioned strategies that contribute to improve the robustness and the efficiency of the optimization process to the inverse design of two-dimensional cascades in turbulent flow conditions. The final goal is to validate the robustness and efficiency of the outlined procedure also for this important class of design problems and, more importantly, to perform a first important step towards the development of an automatic tool for the direct optimization of turbomachinery bladings in real flow conditions. The adjoint equations will be derived using an inviscid solver involving a traditional centered scheme with added numerical viscosity. The inviscid formulation will be used in order to preserve the simplicity of the adjoint equations. Moreover, an additional time derivative will be introduced in order to solve the time dependent adjoint equations progressively in time. Finally, the flow equations will be solved on a progressively finer mesh, while the adjoint equations will be always solved on the coarsest mesh in order to reduce the cost of the computation of the gradient of the objective function to a few percents of the total cost of the optimization procedure. The following sections will be devoted to the description of the main ingredients of the proposed approach, that will be tested on the inverse design of a two-dimensional turbine blade in turbulent transonic flow conditions, both with fixed stagger angle and with fixed outlet angle of the camberline.