Inverse Design Problem Research Articles

An even-load-distribution design for composite bolted joints using a novel circuit model and neural network

Due to the brittle feature of carbon fiber reinforced plastic laminates, mechanical multi-joint within these composite components shows uneven load distribution for each bolt, which weakens the strength advantage of composite laminates. In order to reduce this defect and achieve the goal of even load distribution in mechanical joints, we propose a machine learning-based framework as an optimization method. Since that the friction effect has been proven to be a significant factor in determining bolt load distribution, our framework aims at providing optimal parameters including bolt-hole clearances and tightening torques for a minimum unevenness of bolt load. A novel circuit model is established to generate data samples for the training of artificial networks at a relatively low computational cost. A database for all the possible inputs in the design space is built through the machine learning model. The optimal dataset of clearances and torques provided by the database is validated by both the finite element method, circuit model, and an experimental measurement based on the linear superposition principle, which shows the effectiveness of this general framework for the optimization problem. Then, our machine learning model is further compared and worked in collaboration with commonly used optimization algorithms, which shows a potential of greatly increasing computational efficiency for the inverse design problem.

RANGE-GAN: Design Synthesis Under Constraints Using Conditional Generative Adversarial Networks

Abstract Typical engineering design tasks require the effort to modify designs iteratively until they meet certain constraints, i.e., performance or attribute requirements. Past work has proposed ways to solve the inverse design problem, where desired designs are directly generated from specified requirements, thus avoid the trial and error process. Among those approaches, the conditional deep generative model shows great potential since 1) it works for complex high-dimensional designs and 2) it can generate multiple alternative designs given any condition. In this work, we propose a conditional deep generative model, Range-GAN, to achieve automatic design synthesis subject to range constraints. The proposed model addresses the sparse conditioning issue in data-driven inverse design problems by introducing a label-aware self-augmentation approach. We also propose a new uniformity loss to ensure generated designs evenly cover the given requirement range. Through a real-world example of constrained 3D shape generation, we show that the label-aware self-augmentation leads to an average improvement of14% on the constraint satisfaction for generated 3D shapes, and the uniformity loss leads to a 125% average increase on the uniformity of generated shapes' attributes. This work laid the foundation for data-driven inverse design problems where we consider range constraints and there are sparse regions in the condition space.

Reinforcement learning approach to thermal transparency with particles in periodic lattices

Implementing thermal transparency by using thermal metamaterials, with its potential applications in real-world scenarios, has been a promising field attracting many theoretical and experimental studies. The implementation of thermal transparency, as well as other thermal metamaterial-based applications, often requires solving an inverse design problem to calculate optimal design parameters. In this paper, we propose a periodic interparticle interaction mechanism to realize thermal transparency, in which particles are arranged in periodic lattices with symmetric interactions and anisotropic thermal conductivities. We reframe the inverse design problem of calculating the design parameters of such a periodic interparticle system into a reinforcement learning problem. The essence of our reinforcement learning-based approach is to train an intelligent agent that can vary the design parameters in a series of time steps toward the realization of thermal transparency. Compared to our previous effort to solve the same problem with an autoencoder-based approach, the reinforcement learning-based approach requires significantly less computational resources and thus demonstrates its potential to alleviate the “curse of dimensionality.” We also discuss the cause for the superior computational efficiency of the reinforcement learning-based approach over the autoencoder-based approach, and the possibility of extending the use of our reinforcement learning-based approach to solve other inverse design problems.

3D weaving with curved ribbons

Basket weaving is a traditional craft for creating curved surfaces as an interwoven array of thin, flexible, and initially straight ribbons. The three-dimensional shape of a woven structure emerges through a complex interplay of the elastic bending behavior of the ribbons and the contact forces at their crossings. Curvature can be injected by carefully placing topological singularities in the otherwise regular weaving pattern. However, shape control through topology is highly non-trivial and inherently discrete, which severely limits the range of attainable woven geometries. Here, we demonstrate how to construct arbitrary smooth free-form surface geometries by weaving carefully optimized curved ribbons. We present an optimization-based approach to solving the inverse design problem for such woven structures. Our algorithm computes the ribbons' planar geometry such that their interwoven assembly closely approximates a given target design surface in equilibrium. We systematically validate our approach through a series of physical prototypes to show a broad range of new woven geometries that is not achievable by existing methods. We anticipate our computational approach to significantly enhance the capabilities for the design of new woven structures. Facilitated by modern digital fabrication technology, we see potential applications in material science, bio- and mechanical engineering, art, design, and architecture.

Study on realizing the personalized customization of bra cup by solving the inverse problem of bra cup design

In the process of bra cup customization, the matching between bra cup surface and breast shape largely depends on the practical experience of designers. To achieve effective customization, this study proposes an inverse design method. This method prescribes the surface of the main test section and subsequently optimizes the corresponding shape of the bra cup, thus minimizing the supremum of pressure in the target region. The optimization framework is mainly based on the particle swarm optimization algorithm and Kriging surrogate model. The inner surface of the bra cup represents the study model, and the three-dimensional morphology of the bra cup is characterized by the free-form deformation. The result exhibits a reduction of 22.51% in the pressure of the design cup as compared to the body size cup. The developed method can contribute to the engineering and personalized customization of the bra cup, thus further improving the fitting of the bra cup.

Inverse design of mode-locked fiber laser by particle swarm optimization algorithm

A wide variety of laser applications, that often require radiation with specific characteristics, and relative flexibility of laser configurations offer a prospect of designing systems with the parameters on demand. The inverse laser design problem is to find the system architecture that provides for the generation of the desired laser output. However, typically, such inverse problems for nonlinear systems are sensitive to the computation of the gradients of a target (fitness) function making direct back propagation approach challenging. We apply here particle swarm optimization algorithm that does not rely on the gradients of the fitness function to the design of a fiber 8-figure laser cavity. This technique allows us to determine the laser cavity architectures tailored to generating on demand pulses with duration in the range of 1.5–105 ps and spectral width in the interval 0.1–20.5 nm. The proposed design optimisation algorithm can be applied to a variety of laser applications, and, more generally, in a range of engineering systems with flexible adjustable configurations and the outputs on demand.

Efficient One-Shot Technique for Adjoint-Based Unsteady Optimization

A computationally efficient one-shot approach with a low memory footprint is presented for unsteady optimization. The proposed technique is based on a novel and unique approach that combines local-in-time and fixed-point iteration methods to advance the unconverged primal and adjoint solutions forward and backward in time to evaluate the sensitivity of the globally time-integrated objective function. This is in some ways similar to the piggyback iterations in which primal and adjoint solutions are evaluated at a frozen design. During each cycle, the primal, adjoint, and design update problems are solved to advance the optimization problem. This new coupled approach is shown to provide significant savings in the memory footprint while reducing the computational cost of primal and adjoint evaluations per design cycle. The method is first applied to an inverse design problem for the unsteady lid-driven cavity. Following this, vortex suppression and mean drag reduction for a circular cylinder in crossflow is considered. Both of these objectives are achieved by optimizing the rotational speeds for steady or periodically oscillating excitations. For all cases presented in this work, the proposed technique is shown to provide significant reductions in memory as well as computational time. It is also shown that the unsteady optimization problem converges to the same optimal solution obtained using a conventional approach.

Vertical and horizontal pullout capacity of mooring lines embedded in very soft clays

Mooring lines are widely used to connect offshore platforms to anchors embedded in the seabed. The configuration of the inverse catenary formed by mooring lines influences the installation of the anchors, the load capacity and the anchors failure mode. For this reason, a proper understanding of the soil-chain interaction is a requirement for an accurate prediction of the configuration of the inverse catenary. This paper presents the main results of a laboratory investigation program carried out on a scale-reduced model to study the interaction mechanism between clay and the steel chain of different diameters, lengths and stiffness. Some aspects related to the inverse catenary and tension distribution, such as the shaft and base resistances, adhesion and bearing capacity factors, effective width in sliding, strain-softening, and displacement at the maximum load were extensively discussed herein. Comparisons between these results and the background experimental data used to support general engineering practice have been made for the different aspects investigated. The chain geometry, stiffness, direction of chain displacement and soil properties influence the behavior of the measured curves and, consequently, the corresponding soil-chain interaction. From a practical point of view, the results presented are beneficial for understanding the chain-soil interaction and show an explicit potential to contribute to the optimization of the offshore foundation engineering involving inverse catenary design problems.

Simplifying inverse materials design problems for fixed lattices with alchemical chirality.

Brute-force compute campaigns relying on demanding ab initio calculations routinely search for previously unknown materials in chemical compound space (CCS), the vast set of all conceivable stable combinations of elements and structural configurations. Here, we demonstrate that four-dimensional chirality arising from antisymmetry of alchemical perturbations dissects CCS and defines approximate ranks, which reduce its formal dimensionality and break down its combinatorial scaling. The resulting "alchemical" enantiomers have the same electronic energy up to the third order, independent of respective covalent bond topology, imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of CCS and enables the establishment of trends without empiricism for any materials with fixed lattices. We demonstrate the efficacy for three cases: (i) new rules for electronic energy contributions to chemical bonding; (ii) analysis of the electron density of BN-doped benzene; and (iii) ranking over 2000 and 4 million BN-doped naphthalene and picene derivatives, respectively.

Parameterized reinforcement learning for optical system optimization

Engineering a physical system to feature designated characteristics states an inverse design problem, which is often determined by several discrete and continuous parameters. If such a system must feature a particular behavior, the mentioned combination of both, discrete and continuous, parameters results in a challenging optimization problem that requires an extensive search for an optimal system design. However, if the corresponding inverse design problem can be reformulated as a parameterized Markov decision process, reinforcement learning (RL) provides a heuristic framework to solve it. In this work, we use multi-layer thin films as an example of the aforementioned optimization problems and consider three design parameters: Each of the thin film layer’s dielectric material (discrete) and thickness (continuous), as well as the total number of layers (discrete). While recent methods merely determine the optimal thicknesses and—less commonly—the layers’ materials, our approach optimizes the total number of stacked layers as well. In summary, we further develop a Q-learning variant to solve inverse design optimization and thereby outperform human experts and current approaches like needle-point optimization or naive RL. For this purpose, we propose an exponentially transformed reward signal that eases policy search and enables constrained optimization. Moreover, the learned Q-values contain information about the optical properties of multi-layer thin films, which allows us a physical interpretation or what-if analysis and thus enables explainability.

Inverse design of an optical film filter by a recurrent neural adjoint method: an example for a solar simulator

Inverse design of photonic nanostructures based on machine learning (ML) methods has recently attracted much attention. An artificial neural network (ANN) showcases good performance on the photonic inverse design problem. However, there are still many unsolved issues regarding an efficient way to find a geometry that yields the target response by data-driven ML approaches. The design of air mass (AM) 1.5G filters for solar simulators represents such a challenging case. Here, we propose and show that a recurrent neural adjoint method is efficient in optimizing a multilayer optical filter for that purpose. Two examples of inverse design and optimization for an AM 1.5G filter with S i 3 N 4 / S i O 2 and ( S i 3 N 4 / S i O 2 )/( T a 2 O 5 / S i O 2 ) films at a different spectrum band (e.g., λ = 280 n m − 800 n m and λ = 280 n m − 1350 n m ) have been demonstrated. By comparing several strategies based on ANN approaches, a generic and efficient scheme is presented for photonic multilayer film structure engineering, which we believe could be applied to various photonic device designs.

A Differential Evaporation Model to Predict Chemistry Change of Additively Manufactured Metals

The desire for increased performance and functionality has introduced additional complexities to the design and fabrication of additively manufactured (AM) parts. However, addressing these needs would require improved control over local properties during the fabrication process. In this regard, differential evaporation is an inherent characteristic in metal AM processes, directly influencing local chemistry, material properties, functionality, and performance. In the present work, a differential evaporation model (DEM) is presented for laser powder bed fusion (LPBF) AM to predict and control the effect of evaporation on chemistry and properties on local and part-wide scales. The DEM model is coupled with an analytical thermal model that is calibrated against 51.2 Ni [at.%] nickel titanium SMA single-track experiments and a multi-layer model that accounts for the AM part’s multi-layer design and the inherent melt pool overlap and chemistry propagation. The combined hierarchical model, consisting of the thermal, evaporation, and multi-layer components, is used to predict location-specific chemistry for LBPF AM fabrication of 50.8 Ni [at.%] nickel titanium shape memory alloys(NiTi SMAs). Model predictions are validated with values obtained from multi-layer experiments on a commercial LPBF system, resulting in a root mean square error (RMSE) of 0.25 Ni [at.%] for predicted Ni content. Additionally, martensitic transformation temperature, Ms, is calculated and compared with empirical data, resulting in an RMSE of 18.6 K. A practical account of the cumulative and propagative thermal-induced evaporation effect on location-specific chemistry is made through this linkage of models. Fundamentally, this model chain has also provided a solution to the forward modeling problem, enabling steps to be taken towards resolving the inverse design problem of deter-mining processing parameters based on desired location-specific properties.

Utilizing computer vision and artificial intelligence algorithms to predict and design the mechanical compression response of direct ink write 3D printed foam replacement structures

Additive Manufacturing (AM) of porous polymeric materials, such as foams, recently became a topic of intensive research due their unique combination of low density, impressive mechanical properties, and stress dissipation capabilities. Conventional methods for fabricating foams rely on complex and stochastic processes, making it challenging to achieve precise architectural control of structured porosity. In contrast, AM provides access to a wide range of printable materials, where precise spatial control over structured porosity can be modulated during the fabrication process enabling the production of foam replacement structures (FRS). Current approaches for designing FRS are based on intuitive understanding of their properties or an extensive number of finite element method (FEM) simulations. These approaches, however, are computationally expensive and time consuming. Therefore, in this work, we present a novel methodology for determining the mechanical compression response of direct ink write (DIW) 3D printed FRS using a simple cross-sectional image. By obtaining measurement data for a relatively small number of samples, an artificial neural network (ANN) was trained, and a computer vision algorithm was used to make inferences about foam compression characteristics from a single cross-sectional image. Finally, a genetic algorithm (GA) was used to solve the inverse design problem, generating the AM printing parameters that an engineer should use to achieve a desired compression response from a DIW printed FRS. The methods developed herein present an avenue for entirely autonomous design and analysis of additively manufactured structures using artificial intelligence.

Sample-efficient deep learning for accelerating photonic inverse design

Data-driven techniques like deep learning (DL) are currently being explored for inverse design problems in photonics (especially nanophotonics) to deal with the vast search space of materials and nanostructures. Many challenges need to be overcome to fully realize the potential of this approach; current workflows are specific to predefined shapes and require large upfront investments in dataset creation and model hyperparameter search. We report an improved workflow for DL based acceleration of evolutionary optimizations for scenarios where past simulation data is nonexistent or highly inadequate and demonstrate its utility considering the example problem of multilayered thin-film optics design. For obtaining sample-efficiency in surrogate training, novel training loss functions that emphasize a model’s ability to predict a structurally similar spectral response rather than minimizing local approximation error are proposed. The workflow is of interest to extend the ambit of DL based optics design to complicated structures whose spectra are computationally expensive to calculate.

Artificial Neural Network-Based Prediction of the Optical Properties of Spherical Core-Shell Plasmonic Metastructures.

The substitution of time- and labor-intensive empirical research as well as slow finite difference time domain (FDTD) simulations with revolutionary techniques such as artificial neural network (ANN)-based predictive modeling is the next trend in the field of nanophotonics. In this work, we demonstrated that neural networks with proper architectures can rapidly predict the far-field optical response of core–shell plasmonic metastructures. The results obtained with artificial neural networks are comparable with FDTD simulations in accuracy but the speed of obtaining them is between 100–1000 times faster than FDTD simulations. Further, we have proven that ANNs does not have problems associated with FDTD simulations such as dependency of the speed of convergence on the size of the structure. The other trend in photonics is the inverse design problem, where the far-field optical response of a spherical core–shell metastructure can be linked to the design parameters such as type of the material(s), core radius, and shell thickness using a neural network. The findings of this paper provide evidence that machine learning (ML) techniques such as artificial neural networks can potentially replace time-consuming finite domain methods in the future.

Reinforcement learning in discrete action space applied to inverse defect design

Reinforcement learning (RL) algorithms that include Monte Carlo Tree Search (MCTS) have found tremendous success in computer games such as Go, Shiga and Chess. Such learning algorithms have demonstrated super-human capabilities in navigating through an exhaustive discrete action search space. Motivated by their success in computer games, we demonstrate that RL can be applied to inverse materials design problems. We deploy RL for a representative case of the optimal atomic scale inverse design of extended defects via rearrangement of chalcogen (e.g. S) vacancies in 2D transition metal dichalcogenides (e.g. MoS2). These defect rearrangements and their dynamics are important from the perspective of tunable phase transition in 2D materials i.e. 2H (semi-conducting) to 1T (metallic) in MoS2. We demonstrate the ability of MCTS interfaced with a reactive molecular dynamics simulator to efficiently sample the defect phase space and perform inverse design—starting from randomly distributed S vacancies, the optimal defect rearrangement of defects corresponds a line defect of S vacancies. We compare MCTS performance with evolutionary optimization i.e. genetic algorithms and show that MCTS converges to a better optimal solution (lower objective) and in fewer evaluations compared to GA. We also comprehensively evaluate and discuss the effect of MCTS hyperparameters on the convergence to solution. Overall, our study demonstrates the effectives of using RL approaches that operate in discrete action space for inverse defect design problems.

Fast inverse design of microstructures via generative invariance networks.

The problem of the efficient design of material microstructures exhibiting desired properties spans a variety of engineering and science applications. The ability to rapidly generate microstructures that exhibit user-specified property distributions can transform the iterative process of traditional microstructure-sensitive design. We reformulate the microstructure design process using a constrained generative adversarial network (GAN) model. This approach explicitly encodes invariance constraints within GANs to generate two-phase morphologies for photovoltaic applications obeying design specifications: specifically, user-defined short-circuit current density and fill factor combinations. Such invariance constraints can be represented by differentiable, deep learning-based surrogates of full physics models mapping microstructures to photovoltaic properties. Furthermore, we propose a multi-fidelity surrogate that reduces expensive label requirements by a factor of five. Our framework enables the incorporation of expensive or non-differentiable constraints for the fast generation of microstructures (in 190 ms) with user-defined properties. Such proposed physics-aware data-driven methods for inverse design problems can be used to considerably accelerate the field of microstructure-sensitive design.

Thermal transparency with periodic particle distribution: A machine learning approach

The periodic interparticle interaction mechanism has been previously proposed for heat management, especially the practical application of thermal transparency. In our mechanism for engineering and manipulating thermal metamaterials, particles are arranged in periodic lattices with symmetric interactions. In this work, we relax the constraints in the previous work and allow rectangle lattice and arbitrary relative positioning between the two types of particles. We use a machine learning-based approach to solve the inverse design problem by training autoencoders to compress the dimensionalities of both the design space and the response space and training a neural network tailored for the inverse design problem. We employ the finite-element method for generating the training set for the neural network and for validating the calculated design parameters for a given thermal transparency problem. We also discuss the possibility of extending the machine learning-based workflow to other problems, such as thermal camouflage.

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

The inverse design is one of the aerodynamic design methods, in which the pressure distribution along the wall is known, and the duct geometry is unknown. To obtain the best geometry by the inverse design, the target pressure distribution along the walls should be optimum. This paper presents an aerodynamic design of diffusers by optimizing the wall pressure distribution and applying it to the ball-spine inverse design method. A code was first developed to solve the boundary layer equations using the integration method, and then incorporated into a genetic algorithm to optimize the wall pressure distribution to achieve the maximum pressure recovery without separation occurrence. Depending on the type of the duct, a series of constraints was applied to the wall pressure distributions during the optimization process. The optimized pressure distribution was considered as the target pressure distribution for the inverse design problem. The duct geometry changes during the inverse design process to reach one satisfying the target pressure distribution. An offline connection was observed between the ball-spine inverse design method and the genetic algorithm. The boundary layer code was the medium for this offline connection. The optimized wall pressure distribution and inverse design process were evaluated for a straight diffuser and three S-shaped diffusers with different height to length ratios. The results revealed the robustness of the offline link of the inverse design and the genetic algorithm for the optimal aerodynamic design of ducts.

Modified Butterworth Filters in Solving the Inverse Problem of Analytical Design of Optimal Controllers

In this work, for linear stationary one-dimensional control objects, the inverse problem of analytical design of optimal controllers (ADOC) is considered, which consists in determining the weight coefficients of the quadratic functional of the optimality of the control process that provide the closed-loop control system with the specified values of the time of transient processes and overshoot. The time of the transient process (regulation time) of the synthesized system is understood in the sense of the classical theory of automatic control and is determined using a " tube" , the value of which is taken, in contrast to known works, equal to the required (desired) small value of the system overshoot of a few percent (2—5 %). The equality of the percentage values characterizing the " tube" and the desired overshoot of the synthesized system is a necessary condition for the maximum response rate of linear dynamic systems and, accordingly, ensures the unambiguity of the solution of the considered inverse ADOC problem in the class of fast-response systems. The proposed solution method provides for the transformation of the ADOC problem to the canonical form, in which the control object is described by a matrix differential equation in the Frobenius form, and the quality functional is defined as the integral of the sum of the products of the object’s canonical phase coordinates, as well as the square of the control signal with appropriate weight coefficients. It is shown that the solution of the inverse canonical ADOC problem is determined by the values of only three nonzero weight coefficients of the criterion, and one of them has a single value. The values of the other two coefficients are proposed to be found in the process of modeling the synthesized optimal control system from the conditions of providing for it a given control time and a given overshoot. To obtain numerical estimates of the two main weight coefficients of the quadratic quality criterion, the solution of the ADOC problem is considered with the limiting increase in the values of these weight coefficients. By the limiting solution of the ADOC problem, the transfer functions of dynamic systems with the limiting (maximum) speed are determined, which have a given overshoot of 4.321 %. The dynamical systems described by these transfer functions are called modified Butterworth filters due to the fact that the well-known Butterworth filters are obtained as their special case with a zero value of a certain constant. The parameters and indicators of the dynamics of these filters up to the sixth order are presented in the table. Using the indicators of Butterworth filters, numerical estimates of the weight coefficients of the quadratic quality criterion are established. Transfer functions of modified Butterworth filters are recommended to be used as reference transfer functions of synthesized high-speed control systems.