Low-dimensional Design Research Articles

A Gaussian process based surrogate approach for the optimization of cylindrical targets

Simulating direct-drive inertial confinement experiments presents significant computational challenges, both due to the complexity of the codes required for such simulations and the substantial computational expense associated with target design studies. Machine learning models, and in particular, surrogate models, offer a solution by replacing simulation results with a simplified approximation. In this study, we apply surrogate modeling and optimization techniques that are well established in the existing literature to one-dimensional simulation data of a new cylindrical target design containing deuterium–tritium fuel. These models predict yields without the need for expensive simulations. We find that Bayesian optimization with Gaussian process surrogates enhances sampling efficiency in low-dimensional design spaces but becomes less efficient as dimensionality increases. Nonetheless, optimization routines within two-dimensional and five-dimensional design spaces can identify designs that maximize yield, while also aligning with established physical intuition. Optimization routines, which ignore constraints on hydrodynamic instability growth, are shown to lead to unstable designs in 2D, resulting in yield loss. However, routines that utilize 1D simulations and impose constraints on the in-flight aspect ratio converge on novel cylindrical target designs that are stable against hydrodynamic instability growth in 2D and achieve high yield.

Diffusion model-based inverse design for thermal transparency

Generative models in the field of artificial intelligence and their applications and deployment have demonstrated their great strength in the past few years. Of the vast spectrum of generative models, diffusion probabilistic models have proven to be particularly powerful and productive, transforming notions such as text-to-image and text-to-video generation from ideas into practical applications. In our previous works, we proposed a thermal metamaterial-based periodic interparticle interaction mechanism for heat management, with a specific application in thermal transparency. To address the challenging problems associated with the inverse design of thermal metamaterial structures, we employed an autoencoder-based machine learning approach and a reinforcement learning-based approach successfully. In this work, we demonstrate that our particular problems with the inverse design of thermal metamaterial-based periodic lattices for the realization of thermal transparency can also be reframed and efficiently solved by training a generative diffusion probabilistic model that can generate the design parameters corresponding to the desired response. Furthermore, we show that for a specific response, multiple sets of design parameters can be obtained by simply performing multiple inferences with the generative diffusion probabilistic model, enabling us to select the ones that can be more economical to fabricate and implement. Our work is among the first to use a diffusion model for the inverse design of thermal metamaterial-based structures and demonstrates the effectiveness of generating low-dimensional design parameters through a diffusion model.

Inverse design of transmission-type linear-to-circular polarization control metasurface based on deep learning

To solve the time-consuming and complex design problems, the deep learning method is used to realize the inverse predictive design of a transmission-type linear-to-circular polarization control metasurface (TLCPCM). Firstly, the target-generation neural network model (TGNNM) is constructed based on a fully connected neural network. The model selects the critical features of the required electromagnetic performance as design targets, and maps low-dimensional design targets to high-dimensional electromagnetic performance. Secondly, taking the output data of the TGNNM as input data, an inverse-mapping neural network model (IMNNM) is constructed by a convolutional neural network. The prediction performance of the IMNNM is compared with two other inverse-mapping models. The research results show that the IMNNM outperforms the other two networks. Finally, combining TGNNM and IMNNM, four sets of TLCPCM structural parameters are predicted. The research results show that the electromagnetic performances of the metasurface determined by the predicted structural parameters are generally consistent with the given design targets. On this basis, one experimental sample is manufactured. The measurement results are consistent with the simulation results. The research results demonstrate the validity and feasibility of the inverse predictive design method proposed in this paper.

Novel three-dimensional simplified numerical simulation method of a compact precooler for hypersonic precooled air-breathing engine

The revolutionary thermal cycle of precooled air-breathing engines has led to the application of a compact tubular precooler. A novel three-dimensional simplified numerical simulation method for a compact tube precooler is proposed. The unique aspect of this method is the integration of low-dimensional design method of the precooler with three-dimensional simulation technique. The method includes a segmented model to discretize the precooler into sub-precoolers, with corresponding performance calculation programs for circumferential uniform and non-uniform airflows in the circumferential direction. The heat transfer and pressure drop are then simulated using a combination of the distributed heat source method and porous model. The developed method was verified with previous experiments, and showed good agreement. In addition, the flow and heat transfer characteristics of the precooler were investigated under both circumferential uniform and non-uniform inlet conditions. The results show that the radial total temperature distortion intensity at the outlet of the precooler is 0.087 and 0.073 under uniform and non-uniform inlet conditions, respectively. Additionally, the intensity of circumferential total temperature distortion increases from 0.004 under uniform inlet conditions to 0.029 under non-uniform inlet conditions. Overall, this method provides an accurate evaluation of the precooler during the engineering design phase.

Global Aerodynamic Topology Optimization using Dimensionality Reduction Methods

In recent years, topology optimizations have attracted attention as advanced optimization methods with higher degree of freedom to represent various topologies. These methods can automatically propose innovative/optimal topologies. Therefore, the topology optimization can be an efficient tool to extract innovative design insights. In general, the topology optimizations become high-dimensional optimization problems. This increases the possibility to represent optimal topologies, while requires a large number of performance evaluations to solve the optimization problems. In this study, we investigate the introduction of dimensionality reduction methods that can replace a high-dimensional design space with a low-dimensional design space in order to reduce the computational cost to solve the topology optimization problems. Proper orthogonal decomposition and active subspace method are considered as the dimensionality reduction methods in this study. As a result, it is confirmed that the computational cost can be reduced by using the dimensionality reduction methods.

Microstructure design using machine learning generated low dimensional and continuous design space

The cornerstone of materials design is the design space used in solving materials related optimization problems. Materials design strategies often involve evaluating properties of materials with selected design variables. Because a microstructure comprises a high dimensional data, dimensionality reduction using principal component analysis or multi-dimensional scaling has become a common practice in generating low dimensional design variables. Unfortunately, generation of microstructures is not guaranteed using design variables formulated using popular dimensionality reduction techniques. These design variables are limited to the initial dataset used for dimensionality reduction, resulting in a discontinuous design space. This shortcoming severely constrains design flexibility and can hamper the performance of design strategies. To address this limitation, we propose the use of the latent space of a convolutional autoencoder trained with synthetic dual phase (DP) microstructures as low dimensional and continuous design space. Once the design space is established, Bayesian optimization is adopted to search for optimal microstructures that exhibit maximal tensile strength. The strength of each microstructure is approximated using microstructure based finite element method. To take full advantage of the continuous design space, a second Bayesian optimization with a refined search space is adopted. The second Bayesian optimization resulted in higher maximum strength value and fewer number of data necessary to find the optimal microstructure compared to Bayesian optimization without search space refinement. Furthermore, multiple microstructures exhibiting strengths comparable to that of the optimal microstructure can be identified within the refined search space, providing significant flexibility in microstructure design.

Bayesian Approach to Probabilistic Design Space Characterization: A Nested Sampling Strategy

Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space characterization, which determine a feasibility probability that can be used as a measure of reliability and risk by the practitioner. An adaptation of nested sampling---a Monte Carlo technique introduced to compute Bayesian evidence---is presented. The nested sampling algorithm maintains a given set of live points through regions with increasing probability feasibility until reaching a desired reliability level. It furthermore leverages efficient strategies from Bayesian statistics for generating replacement proposals during the search. Features and advantages of this algorithm are demonstrated by means of a simple numerical example and two industrial case studies. It is shown that nested sampling can outperform conventional Monte Carlo sampling and be competitive with flexibility-based optimization techniques in low-dimensional design space problems. Practical aspects of exploiting the sampled design space to reconstruct a feasibility probability map using machine learning techniques are also discussed and illustrated. Finally, the effectiveness of nested sampling is demonstrated on a higher-dimensional problem, in the presence of a complex dynamic model and significant model uncertainty.

On the Influence of the Interaction Laws of a Dynamical Particle System for Sample Optimization

Abstract The presented paper investigates the effect of the formulation of the energy potential of a dynamical particle system used for the optimization of statistical point sampling. The dynamical particle system, originally developed as a physical analogy to the Audze-Eglajs (AE) optimization criterion and its periodical modification (PAE), effectively demonstrated that the originally proposed energy potential performs well only in poorly applicable scenarios featuring low-dimensional design domains filled with a rather high number of design points. A remedy is presented which involves a refined formulation of the energy potential, as well as its derivation. The reasoning behind this approach is also dealt with in detail.

On the efficient determination of optimal Bayesian experimental designs using ABC: A case study in optimal observation of epidemics

We present a new method for determining optimal Bayesian experimental designs, which we refer to as ABCdE. ABCdE uses Approximate Bayesian Computation to calculate the utility of possible designs. For problems with a low-dimensional design space, it evaluates the designs’ utility in less computation time compared to existing methods. We apply ABCdE to stochastic epidemic models. Optimal designs evaluated using ABCdE are compared to those evaluated using existing methods for the stochastic death and susceptible–infectious (SI) models. We present the Bayesian optimal experimental designs for the susceptible–infectious–susceptible (SIS) model using ABCdE.

Analysis of gene expression programming for approximation in engineering design

To reduce the computational cost of implementing computer-based simulations and analyses in engineering design, a variety of metamodeling techniques have been developed and used for the construction of metamodels. Metamodels, also called approximation models and surrogate models, can be used to make a replacement of the expensive simulation codes for design and optimization. In this paper, gene expression programming (GEP) algorithm in the evolutionary computing area is investigated as an alternative metamodeling technique to provide the approximation of a design space. The approximation performance of GEP is tested on some low-dimensional mathematical and engineering problems. A comparative study is conducted on GEP and three common metamodeling techniques in engineering design (i.e., response surface methodology (RSM), kriging and radial basis functions (RBF)) for the approximation of the low-dimensional design space. Multiple evaluation criteria are considered in the comparison: accuracy, robustness, transparency and efficiency. Two different sample sizes are adopted: small and large. Comparative results indicate that GEP can achieve the most accurate and robust approximation of a low-dimensional design space for small sample sets. For large sample sets, GEP also presents good prediction accuracy and high robustness. Moreover, the transparency of GEP is the best since it can provide clear function relationships and factor contributions by means of compact expressions. As a novel metamodeling technique, GEP shows great promise for metamodeling applications in a low-dimensional design space, especially when only a few sample points are selected and used for training.

Optimization of Processing Parameters in Injection Molding Based on Adaptive Ant Colony Algorithm

An optimization method, integrating correlation degree, response surface method and ant colony algorithm, is proposed for exploring optimal parameters with the molding quality evaluation of warpage amount in injection molding. Initially, a novel formula calculating correlation degree is brought forth on the basis of the definition of distance and place value, and the parameters are chosen using the correlation degree method. Then the approximate model of the injection molding process is constructed by Kriging model with the determined parameters. Finally, the adaptive genetic algorithm and the ant colony algorithm are adopted to solve the optimization problem respectively, and injection molding tests are experimentally performed to validate the optimization results of parameters in injection molding. The experimental results demonstrate that the ant colony algorithm is superior to the genetic algorithm in solving the optimization problem for the low-dimensional design variables vector and the short coding length.

Metamodeling for High Dimensional Simulation-Based Design Problems

Computational tools such as finite element analysis and simulation are widely used in engineering, but they are mostly used for design analysis and validation. If these tools can be integrated for design optimization, it will undoubtedly enhance a manufacturer’s competitiveness. Such integration, however, faces three main challenges: (1) high computational expense of simulation, (2) the simulation process being a black-box function, and (3) design problems being high dimensional. In the past two decades, metamodeling has been intensively developed to deal with expensive black-box functions, and has achieved success for low dimensional design problems. But when high dimensionality is also present in design, which is often found in practice, there lacks of a practical method to deal with the so-called high dimensional, expensive, and black-box (HEB) problems. This paper proposes the first metamodel of its kind to tackle the HEB problem. This paper integrates the radial basis function with high dimensional model representation into a new model, RBF-HDMR. The developed RBF-HDMR model offers an explicit function expression, and can reveal (1) the contribution of each design variable, (2) inherent linearity/nonlinearity with respect to input variables, and (3) correlation relationships among input variables. An accompanying algorithm to construct the RBF-HDMR has also been developed. The model and the algorithm fundamentally change the exponentially growing computation cost to be polynomial. Testing and comparison confirm the efficiency and capability of RBF-HDMR for HEB problems.