Inverse Design Problem Research Articles

Methodology for finding the virtual center of mass of the aircraft

There are types of aircraft for which the geometric shapes are primarily due to “hard” infrastructural constraints. The secondary nature of aerodynamic requirements makes it possible to deviate from the traditional design task. And move on to the Inverse Design Problem. A solution that allows you to reduce the number of design iterations and narrow the search for a rational solution in the Pareto-optimal area. These aircraft include vertical takeoff and landing aircraft. After analyzing the characteristics of moment-inertia units obtained after an analytical experiment, it shows that the introduction of a virtual center of mass makes it possible to reduce the radius of action of the inertial forces of the aircraft. A sequence of absolute advantages in terms of the moment of inertia of the nodes has been obtained, for example, a more optimal location of the target load, fuel tanks and power plant, which provides an advantage in the mass of the aircraft up to 7-8%, only due to the rational moment of inertia of the layout relative to the virtual center of mass. In an aircraft, the moment of inertia depends to the fifth power on the change in its linear size

Inverse design of truss lattice materials with superior buckling resistance

Manipulating the architecture of materials to achieve optimal combinations of properties (inverse design) has always been the dream of materials scientists and engineers. Lattices represent an efficient way to obtain lightweight yet strong materials, providing a high degree of tailorability. Despite massive research has been done on lattice architectures, the inverse design problem of complex phenomena (such as structural instability) has remained elusive. Via deep neural network and genetic algorithm, we provide a machine-learning-based approach to inverse-design non-uniformly assembled lattices. Combining basic building blocks, our approach allows us to independently control the geometry and topology of periodic and aperiodic structures. As an example, we inverse-design lattice architectures with superior buckling performance, outperforming traditional reinforced grid-like and bio-inspired lattices by ~30–90% and 10–30%, respectively. Our results provide insights into the buckling behavior of beam-based lattices, opening an avenue for possible applications in modern structures and infrastructures.

A Multi-Category Inverse Design Neural Network and Its Application to Diblock Copolymers

In this work, we design a multi-category inverse design neural network to map ordered periodic structures to physical parameters. The neural network model consists of two parts, a classifier and Structure-Parameter-Mapping (SPM) subnets. The classifier is used to identify structures, and the SPM subnets are used to predict physical parameters for desired structures. We also present an extensible reciprocal-space data augmentation method to guarantee the rotation and translation invariant of periodic structures. We apply the proposed network model and data augmentation method to two-dimensional diblock copolymers based on the Landau–Brazovskii model. Results show that the multi-category inverse design neural network has high accuracy in predicting physical parameters for desired structures. Moreover, the idea of multi-categorization can also be extended to other inverse design problems.

Harnessing interpretable machine learning for holistic inverse design of origami

This work harnesses interpretable machine learning methods to address the challenging inverse design problem of origami-inspired systems. We established a work flow based on decision tree-random forest method to fit origami databases, containing both design features and functional performance, and to generate human-understandable decision rules for the inverse design of functional origami. First, the tree method is unique because it can handle complex interactions between categorical features and continuous features, allowing it to compare different origami patterns for a design. Second, this interpretable method can tackle multi-objective problems for designing functional origami with multiple and multi-physical performance targets. Finally, the method can extend existing shape-fitting algorithms for origami to consider non-geometrical performance. The proposed framework enables holistic inverse design of origami, considering both shape and function, to build novel reconfigurable structures for various applications such as metamaterials, deployable structures, soft robots, biomedical devices, and many more.

Design of double layer protective coatings: Finite element modeling and machine learning approximations

Thin film-composed coatings can significantly improve the mechanical and tribological properties of spacecraft friction units. In this regard, protection by ion-plasma coatings has become one of the most used options and well-established technologies. However, design of coatings that remain effective over multiple usages, is a challenge. Improving their production requires a large number of parameters to be optimized and many verification experiments to be set up. We exploited machine learning algorithm to solve the problem of double layer coatings optimization with respect to a set of mechanical properties (hardness, Young's modulus, Poisson's ratio, and yield stress). The training dataset was constructed using the adaptive sampling algorithm and numerical simulation of indentation in ANSYS for coatings of different compositions and thicknesses. The machine learning approximation provided significant accuracy (R2 > 0.96) in predicting the coating hardness based on the mechanical properties of its individual layers. The feature importance analysis of the Extra Trees algorithm was used to define the parts of the indentation curve that carry information about the properties of individual coating layers. We have also addressed the inverse problem of coatings design in terms of the required hardness. Our findings demonstrate that only tandem approach to the cross-validation task permitted correct estimation of error in the presence of multiple ambiguous solutions. The value of error was smaller than 0.15 GPa. Being comprehensive, the proposed methodology can be applied to design optimal multilayer coatings in terms of their mechanical properties for friction units in aviation and rocketry-astronautics.

Ultrafast inverse design of quantum dot optical spectra via a joint TD-DFT learning scheme and deep reinforcement learning

Here, we report a case study on inverse design of quantum dot optical spectra using a deep reinforcement learning algorithm for the desired target optical property of semiconductor CdxSeyTex−y quantum dots. Machine learning models were trained to predict the optical absorption and emission spectra by using the training dataset by time dependent density functional theory simulation. We show that the trained deep deterministic policy gradient inverse design agent can infer the molecular structure with an accuracy of less than 1 Å at a fixed computational time of milliseconds and up to 100–1000 times faster than the conventional heuristic particle swam optimization method. Most of the effective inverse design problems based on the surrogate machine learning and reinforcement learning model have been focused on the field of nano-photonics. Few attempts have been made in the field of quantum optical system in a similar manner. For the first time, our results, to our knowledge, provide concrete evidence that for computationally challenging tasks, a well-trained deep reinforcement learning agent can replace the existing quantum simulation and heuristics optimization tool, enabling fast and scalable simulations of the optical property of nanometer sized semiconductor quantum dots.

Design of Pulse Forming Systems for Pulsed Electromagnetic Manufacturing Applications

Electromagnetic (EM) manufacturing techniques are currently being used to manufacture several industrial components with both tubular and sheet metal workpieces. The deformation behavior of the workpiece in an EM manufacturing process is governed by the spatial distribution and the temporal behavior of the magnetic pressure acting on it. This article considers the specific inverse problem of pulsed power source design from the output objective temporal force waveform required for final mechanical deformation in the workpiece. It presents a novel method using direct transcription formulation to calculate the necessary input needed to generate the desired temporal variation in the magnetic pressure on the workpiece. The required controlling parameters for the rise time control, the peak pressure control, and the fall time control are identified. A model waveform has been proposed for the temporal variations of the EM force on the workpiece, followed by the technique to synthesize the tooling coil current using direct collocation methods. The suitable pulsed power circuit topology is then identified, and a curve fitting method is proposed to exactly achieve the desired temporal features of the force profile. Without loss of generality, the technique is experimentally validated for the free-forming process of sheet metal using a uniform pressure tooling coil (UPTC).

Discrete global optimization algorithms for the inverse design of silicon photonics devices

The photonics community counts on inverse design approaches to provide new designs of miniaturized photonic components. Although the structures are composed of two materials only, the dominant method used to tackle such a problem is to make the problem continuous through a relaxation of the binary constraint and to use a gradient-based approach. Global optimization algorithms working on continuous problems actually often fail to produce satisfying solutions in such a context characterized by a large number of parameters – especially when space is discretized into a large number of pixels or voxels. However, we show here for three different photonics problems that global discrete optimization algorithms, which are adapted to this kind of problems, can provide efficient solutions which are relatively regular, physically understandable and close to being buildable. Such algorithms constitute overlooked but valuable tools for inverse design problems. Our preferred method is using a starting point provided by a gradient based algorithm, and run an optimization using Lengler’s algorithm equipped with a simple smoothing operator to make the algorithm aware of the physical nature of the problem.

How to see hidden patterns in metamaterials with interpretable machine learning

Machine learning models can assist with metamaterials design by approximating computationally expensive simulators or solving inverse design problems. However, past work has usually relied on black box deep neural networks, whose reasoning processes are opaque and require enormous datasets that are expensive to obtain. In this work, we develop two novel machine learning approaches to metamaterials discovery that have neither of these disadvantages. These approaches, called shape-frequency features and unit-cell templates, can discover 2D metamaterials with user-specified frequency band gaps. Our approaches provide logical rule-based conditions on metamaterial unit-cells that allow for interpretable reasoning processes, and generalize well across design spaces of different resolutions. The templates also provide design flexibility where users can almost freely design the fine resolution features of a unit-cell without affecting the user’s desired band gap.

Fast Design Space Exploration of Nonlinear Systems: Part I

System design tools are often only available as input–output blackboxes: for a given design as input, they compute an output representing system behavior. Blackboxes are intended to be run in the forward direction. This article presents a new method of solving the “inverse design problem,” namely, given requirements or constraints on output, find an input that also optimizes an objective function. This problem is challenging for several reasons. First, blackboxes are not designed to be run in reverse. Second, inputs and outputs can be discrete and continuous. Third, finding designs concurrently satisfying a set of requirements is hard because designs satisfying individual requirements may conflict with each other. Fourth, blackbox evaluations can be expensive. Finally, evaluations can sometimes fail to produce an output due to nonconvergence of underlying numerical algorithms. This article presents CNMA, a new method of solving the inverse problem that overcomes these challenges. CNMA tries to sample only the part of the design space relevant to solving the inverse problem, leveraging the power of neural networks, mixed-integer linear programs, and a new learning-from-failure feedback loop. This article also presents a parallel version of CNMA that improves the efficiency and quality of solutions over the sequential version and tries to steer it away from local optima. CNMA’s performance is evaluated against conventional optimization methods for seven nonlinear design problems of 8 (two problems), 10, 15, 36 and 60 real-valued dimensions and one with 186 binary dimensions. Conventional methods evaluated are stable, off-the-shelf implementations of the Bayesian optimization with the Gaussian Processes, Nelder–Mead, and Random Search. The first two do not even produce a solution for problems that are high dimensional, having both discrete and continuous variables or whose blackboxes fail to return values for some inputs. CNMA produces solutions for all problems. When conventional methods do produce solutions, CNMA improves upon their performance by 1%–87%.

QOptCraft: A Python package for the design and study of linear optical quantum systems

The manipulation of the quantum states of light in linear optical systems has multiple applications in quantum optics and quantum computation. The package QOptCraft gives a collection of methods to solve some of the most usual problems when designing quantum experiments with linear interferometers. The methods include functions that compute the quantum evolution matrix for n photons from the classical description of the system and inverse methods that, for any desired quantum evolution, will either give the complete description of the experimental system that realizes that unitary evolution or, when this is impossible, the complete description of the linear system which approximates the desired unitary with a locally minimal error. The functions in the package include implementations of different known decompositions that translate the classical scattering matrix of a linear system into a list of beam splitters and phase shifters and methods to compute the effective Hamiltonian that describes the quantum evolution of states with n photons. The package is completed with routines for useful tasks like generating random linear optical systems, computing matrix logarithms, and quantum state entanglement measurement via metrics such as the Schmidt rank. The routines are chosen to avoid usual numerical problems when dealing with the unitary matrices that appear in the description of linear systems. Program summaryProgram Title: QOptCraftCPC Library link to program files:https://doi.org/10.17632/r24hszggf4.1Developer's repository link:https://github.tel.uva.es/juagar/qoptcraftLicensing provisions: Apache-2.0Programming language: Python 3 v3.9.5:0a7dcbd, May 3 2021 17:27:52Supplementary material:: User's manual at https://github.tel.uva.es/juagar/qoptcraft/-/blob/main/QOptCraft_V1.1_user_guide.pdfNature of problem: The evolution of the quantum states of light in linear optical devices can be computed from the scattering matrix of the system using a few alternative points of view. Apart from being able to compute the evolution through a known optical system, it is interesting to consider the less studied inverse problem of design: finding the optical system which gives or approximates a desired evolution. Linear optical systems are limited and can only provide a small subset of all the physically possible quantum transformations on multiple photons. Choosing the best approximation for the evolutions that cannot be achieved with linear optics is not trivial.This software deals with the analysis of the quantum evolution of multiple photons in linear optical devices and the design of optical setups that achieve or approximate a desired quantum evolution.Solution method: We have automated multiple computation processes regarding quantum experiments via linear optic devices. The methods rely on the properties of the groups and algebras that describe the problem of light evolution in linear system.The library QOptCraft for Python 3 includes known numerical methods for decomposing an optical system into beam splitters and phase shifters and methods to give the quantum evolution of system classically described by a scattering matrix using either the Heisenberg picture evolution of the states, a description based on the permanents of certain matrices or the evolution from the effective Hamiltonian of the system. It also provides methods for the design of achievable evolutions, using the adjoint representation, and for approximating quantum evolutions outside the reach of linear optics with an iterative method using Toponogov's comparison theorem from differential geometry. The package is completed with useful functions that deal with systems including losses and gain, described with quasiunitary matrices, the generation of random matrices and stable implementations of the matrix logarithm.Additional comments including restrictions and unusual features: The package is designed to work with intermediate scale optical systems. Due to the combinatorial growth in the state space with the number of photons and modes involved, there is an upper limit on the efficiency of any classical calculation. QOptCraft serves as a design tool to explore the building blocks of photonic quantum computers, optical systems that generate useful quantum states of light for their use in metrology or other applications or the design of quantum optics experiments to probe the foundations of quantum mechanics.

Deep learning approach for designing acoustic absorbing metasurfaces with high degrees of freedom

The advent of the acoustic metasurfaces offered an unprecedented expansion of our ability to manipulate and structure sound waves for many exotic functionalities. However, the metasurface designs require deep expertise in acoustics and highly intensive iterative computations using the Finite Element Method. In this work, we use a two-dimensional convolutional neural network to model complex metasurface absorber structures under oblique wave incidences. The proposed network architecture is capable of computing the absorption spectra with a large number of design degrees of freedom. Further, we implement a conditional generative adversarial network to solve the inverse design problem. When fed with an input set of predefined absorption spectra, the constructed generative network produces candidate designs of metasurface absorbers that match on-demand spectra with high fidelity. We demonstrate the capability of the implemented network architecture by designing a metasurface absorber operating at 82 Hz for oblique wave incidences with a thickness of λ/64. To implement the deep learning methods for acoustic designs, the main challenge is to generate large and high-quality training dataset using numerical simulations. To mitigate this issue, we implement data augmentation. The presented approaches open new avenues to automate the design process of metasurfaces and enable a much more generalized and broader scope of optimal designs that go beyond acoustics applications.

Inverse design of acoustic metasurfaces using space-filling points

Acoustic metasurfaces are two-dimensional materials that impart non-trivial amplitude and phase shifts on incident acoustic waves at a predetermined frequency. While acoustic metasurfaces enable extraordinary wavefront engineering capabilities, they are not developed well enough to independently control the amplitude and phase of reflected and transmitted acoustic waves simultaneously, which are governed by their geometry. We aim to solve the inverse design problem of finding a geometry to achieve a specified set of acoustic properties. The geometry is modeled by discretizing the continuous space into a finite number of elements, where each element can either be filled with air or solid material. Full wave simulations are performed to obtain the acoustic properties for a given geometry. It is computationally infeasible to simulate all geometries. To address this challenge, we develop an experimental design-based algorithm to efficiently perform the simulations. The algorithm starts with a few geometries and adaptively adds geometries to the set, such that they fill the entire space of the desired acoustic properties using a small fraction of the possible geometries. We find that the geometry needs to have at least 7 × 7 elements to obtain any given acoustic property with a tolerance of 5.4% of its maximum range. This is achieved by simulating 24 000 geometries using the proposed algorithm, which is only 4.2×10−9% of the 563 × 1012 possible geometries. The method provides a general solution to the inverse design problem that can be extended to control more acoustic properties.

Simulation and optimization of magnetoelastic thin shells

Magnetoelastic thin shells exhibit great potential in realizing versatile functionalities through a broad range of combination of material stiffness, remnant magnetization intensity, and external magnetic stimuli. In this paper, we propose a novel computational method for forward simulation and inverse design of magnetoelastic thin shells. Our system consists of two key components of forward simulation and backward optimization. On the simulation side, we have developed a new continuum mechanics model based on the Kirchhoff-Love thin-shell model to characterize the behaviors of a megnetolelastic thin shell under external magnetic stimuli. Based on this model, we proposed an implicit numerical simulator facilitated by the magnetic energy Hessian to treat the elastic and magnetic stresses within a unified framework, which is versatile to incorporation with other thin shell models. On the optimization side, we have devised a new differentiable simulation framework equipped with an efficient adjoint formula to accommodate various PDE-constraint, inverse design problems of magnetoelastic thin-shell structures, in both static and dynamic settings. It also encompasses applications of magnetoelastic soft robots, functional Origami, artworks, and meta-material designs. We demonstrate the efficacy of our framework by designing and simulating a broad array of magnetoelastic thin-shell objects that manifest complicated interactions between magnetic fields, materials, and control policies.

Data-driven design of thin-film optical systems using deep active learning.

A deep learning aided optimization algorithm for the design of flat thin-film multilayer optical systems is developed. The authors introduce a deep generative neural network, based on a variational autoencoder, to perform the optimization of photonic devices. This algorithm allows one to find a near-optimal solution to the inverse design problem of creating an anti-reflective grating, a fundamental problem in material science. As a proof of concept, the authors demonstrate the method's capabilities for designing an anti-reflective flat thin-film stack consisting of multiple material types. We designed and constructed a dielectric stack on silicon that exhibits an average reflection of 1.52 %, which is lower than other recently published experiments in the engineering and physics literature. In addition to its superior performance, the computational cost of our algorithm based on the deep generative model is much lower than traditional nonlinear optimization algorithms. These results demonstrate that advanced concepts in deep learning can drive the capabilities of inverse design algorithms for photonics. In addition, the authors develop an accurate regression model using deep active learning to predict the total reflectivity for a given optical system. The surrogate model of the governing partial differential equations can then be broadly used in the design of optical systems and to rapidly evaluate their behavior.

Inverse airfoil design method for generating varieties of smooth airfoils using conditional WGAN-gp

Machine learning models are recently adopted to generate airfoil shapes. A typical task is to obtain airfoil shapes that satisfy the required lift coefficient. These inverse design problems can be solved by generative adversarial networks (GAN). However, the shapes obtained from ordinal GAN models are not smooth; hence, flow analysis cannot be conducted. Therefore, Bézier curves or smoothing methods are required. This study employed conditional Wasserstein GAN with gradient penalty (cWGAN-gp) to generate smooth airfoil shapes without any smoothing method. In the proposed method, the cWGAN-gp model outputs a shape that indicates the specified lift coefficient. Then, the results obtained from the proposed model are compared with those of ordinal GANs and variational autoencoders; in addition, the proposed method outputs the smoothest shape owing to the earth mover's distance used in cWGAN-gp. By adopting the proposed method, no additional smoothing method is required to conduct flow analysis.

End-to-end prediction of multimaterial stress fields and fracture patterns using cycle-consistent adversarial and transformer neural networks

The prediction of stress, strain fields or fracture patterns, along with other physical quantities as a function of boundary conditions and material microstructure, is an important objective of various physics-based simulation methods like finite element models or molecular dynamics modeling. However, such simulations may be expensive and can be costly in their execution, limiting their application to solve inverse design problems, or in the discovery of novel materials that feature a desirable performance. In other fields of studies, such as in mechanobiology, field data can often not be calculated due to a lack of models to begin with; where experimental observations may be the only source of insight. Here we introduce a data-driven method to relate input microstructures and field data using an alternative approach, enabled by deep learning, to predict complex mechanical fields directly based on input microstructure data. We report two approaches to solve said problem, first using cycle-consistent adversarial neural networks trained on unpaired images of microstructures and physical fields, and second, using a Perceiver neural networks based on an attention mechanism based on paired images, implemented in a transformer neural network. Due to the cycle consistent nature of the GAN model we can immediately make forward (from microstructure to stress field) and backward (from stress field to microstructure) predictions, offering an avenue for inverse material design. The Perceiver model, implementing an efficient transformer model that can be scaled to very large input and output data, shows strong generalizability and can be successfully applied to scenarios distinct from those in the training set. We demonstrate the model in several sample microstructures including a set of small cracks (voids) to predict both stress fields and fracture patterns, as well as in a composite microstructure of a soft matrix and rigid inclusions, and in a series of solutions to the inverse problem facilitated by the cycle consistent GAN model. The applications of the models include biomimetic biotechnology (e.g. bone-tendon-inspired attachments and gradients), armor materials, mechanobiology, soft robotics, and lightweight resilient and tough structural systems.

Deep Reinforcement Learning for Molecular Inverse Problem of Nuclear Magnetic Resonance Spectra to Molecular Structure.

Spectroscopy is the study of how matter interacts with electromagnetic radiation. The spectra of any molecule are highly information-rich, yet the inverse relation of spectra to the corresponding molecular structure is still an unsolved problem. Nuclear magnetic resonance (NMR) spectroscopy is one such critical technique in the scientists' toolkit to characterize molecules. In this work, a novel machine learning framework is proposed that attempts to solve this inverse problem by navigating the chemical space to find the correct structure given an NMR spectra. The proposed framework uses a combination of online Monte Carlo tree search (MCTS) and a set of graph convolution networks to build a molecule iteratively. Our method can predict the structure of the molecule ∼80% of the time in its top 3 guesses for molecules with <10 heavy atoms. We believe that the proposed framework is a significant step in solving the inverse design problem of NMR spectra.

Inverse molecular design from first principles: Tailoring organic chromophore spectra for optoelectronic applications.

The discovery of molecules with tailored optoelectronic properties, such as specific frequency and intensity of absorption or emission, is a major challenge in creating next-generation organic light-emitting diodes (OLEDs) and photovoltaics. This raises the following question: How can we predict a potential chemical structure from these properties? Approaches that attempt to tackle this inverse design problem include virtual screening, active machine learning, and genetic algorithms. However, these approaches rely on a molecular database or many electronic structure calculations, and significant computational savings could be achieved if there was prior knowledge of (i) whether the optoelectronic properties of a parent molecule could easily be improved and (ii) what morphing operations on a parent molecule could improve these properties. In this Perspective, we address both of these challenges from first principles. We first adapt the Thomas-Reiche-Kuhn sum rule to organic chromophores and show how this indicates how easily the absorption and emission of a molecule can be improved. We then show how by combining electronic structure theory and intensity borrowing perturbation theory we can predict whether or not the proposed morphing operations will achieve the desired spectral alteration, and thereby derive widely applicable design rules. We go on to provide proof-of-concept illustrations of this approach to optimizing the visible absorption of acenes and the emission of radical OLEDs. We believe that this approach can be integrated into genetic algorithms by biasing morphing operations in favor of those that are likely to be successful, leading to faster molecular discovery and greener chemistry.

Improved bidirectional networks for nanostructure color design

Localized optical resonances in silicon nanostructures have been increasingly used in color printing. By changing the geometric parameters of the silicon nanostructures to obtain different structural colors, it is possible to get a larger coverage range than the sRGB color gamut in the CIE color space, and achieve ultra-high-resolution color printing. However, the design of specific colors involves iterative optimization of geometric parameters, which is computationally expensive. Thus, it is very challenging to obtain millions of different colors in the color space. In this paper, we trained a feature-crossed neural network with attention mechanism to predict the structural color produced by random silicon nano truncated cones with high accuracy. On the problem of inverse design, we improve the loss function of the tandem network, which solves the non-uniqueness problem in the inverse design process and avoids the tandem net from falling into the wrong solution space. Our model can accurately predict millions of different color points in the CIE color gamut. In addition, the proposed methods can be easily extended to solve the optimization design problems in the field of nanophotonics.