A physics-guided machine learning for multifunctional wave control in active metabeams

Design space exploration can reveal the underlying structure of design problems of interest. In a set-based approach, for example, exploration can identify sets of designs or regions of the design space that meet specific performance requirements. For some problems, promising designs may cluster in multiple regions of the design space, and the boundaries of those clusters may be irregularly shaped and difficult to predict. Visualizing the promising regions can clarify the design space structure, but design spaces are typically high-dimensional, making it difficult to visualize the space in three dimensions. Techniques have been introduced to map high-dimensional design spaces to low-dimensional, visualizable spaces. Before the promising regions can be visualized, however, the first task is to identify how many clusters of promising designs exist in the high-dimensional design space. Unsupervised machine learning methods, such as spectral clustering, have been utilized for this task. Spectral clustering is generally accurate but becomes computationally intractable with large sets of candidate designs. Therefore, in this paper a technique for accurately identifying clusters of promising designs is introduced that remains viable with large sets of designs. The technique is based on spectral clustering but reduces its computational impact by leveraging the Nyström Method in the formulation of self-tuning spectral clustering. After validating the method on a simplified example, it is applied to identify clusters of high performance designs for a high-dimensional negative stiffness metamaterials design problem.

An inverse design process has the potential to positively impact the difficulties of the traditional iterative process if the design candidates are ``explicitly'' generated from target performance metrics. The explicit inverse design methods can not only bypass the time-consuming iterative process, it can also allow the designer to explore the design space beyond their initial intended target performance in a much more efficient manner. With recent advances in Machine Learning new methods have revolutionized the inverse design process. However, the current approaches struggle with high-dimensional design space, require large amounts of high-fidelity training data, and have difficulty dealing with ill-posed, ill-conditioned issues. In this work we developed a Probabilistic Machine Learning for Inverse Design of Aerodynamic Systems (Pro-ML IDeAS) framework that overcomes these challenges and achieves the desired outcome with limited budget. The framework follows a two-step process. In the first step an efficient probabilistic generative model of the forward process is built using limited data. In the second step a surrogate of the inverse process is built using Invertible Neural Network (INN) using the data sampled from the generative model. In this work, we will demonstrate the framework on analytical functions and aerodynamic design of gas turbine airfoils.

PurposeAerodynamic shape optimisation is a complex problem usually governed by transonic non-linear aerodynamics, a high dimensional design space and high computational cost. Consequently, the use of a numerical simulation approach can become prohibitive for some applications. This paper aims to propose a computationally efficient multi-fidelity method for the optimisation of two-dimensional axisymmetric aero-engine nacelles.Design/methodology/approachThe nacelle optimisation approach combines a gradient-free algorithm with a multi-fidelity surrogate model. Machine learning based on artificial neural networks (ANN) is used as the modelling technique because of its ability to handle non-linear behaviour. The multi-fidelity method combines Reynolds-averaged Navier Stokes and Euler CFD calculations as high- and low-fidelity, respectively.FindingsRatios of low- and high-fidelity training samples to degrees of freedom of nLF/nDOFs = 50 and nHF/nDOFs = 12.5 provided a surrogate model with a root mean squared error less than 5% and a similar convergence to the optimal design space when compared with the equivalent CFD-in-the-loop optimisation. Similar nacelle geometries and aerodynamic flow topologies were obtained for down-selected designs with a reduction of 92% in the computational cost. This highlights the potential benefits of this multi-fidelity approach for aerodynamic optimisation within a preliminary design stage.Originality/valueThe application of a multi-fidelity technique based on ANN to the aerodynamic shape optimisation problem of isolated nacelles is the key novelty of this work. The multi-fidelity aspect of the method advances current practices based on single-fidelity surrogate models and offers further reductions in computational cost to meet industrial design timescales. Additionally, guidelines in terms of low- and high-fidelity sample sizes relative to the number of design variables have been established.

Functional commonalities across product families have been considered by a large body of product family design community but this concept is not widely used in design. For a designer, a functional family refers to a set of designs evaluated based on the same set of qualities; the embodiments and the design spaces may differ, but the semantics of what is being measured (e.g., strength of a spring) remain the same. Based on this functional behaviour we introduce a product family hierarchy, where the designs can be classified into phenomenological design family, functional part family and embodiment part family. And then, we consider the set of possible performances of interest to the user at the embodiment level, and use multi-objective optimisation to identify the non-dominated solutions or the Pareto-front. The designs lying along this front are mapped to the design space, which is usually far higher in dimensionality, and then clustered in an unsupervised manner to obtain candidate product groupings which the designer may inspect to arrive at portfolio decisions. We highlight and discuss two recently suggested techniques for this purpose. First, with help of dimensionality reduction techniques, we show how these clusters in low-dimensional manifolds embedded in the high-dimensional design space. We demonstrate this process on three different designs (water faucets, compression springs and electric motors), involving both continuous and discrete design variables. Second, with the help of a data analysis of Pareto-optimal solutions, we decipher common design principles that constitute the product portfolio solutions. We demonstrate this so-called ‘innovization’ principles on a spring design problem. The use of multi-objective optimisation (evolutionary and otherwise) is the key feature of both approaches. The approaches are promising and further research should pave their ways to better design and manufacturing activities.

Simulation-based design optimization utilizes computational models that rely on assumptions and approximations. There is a need therefore, to ensure that the obtained designs will exhibit the desired behavior as anticipated given the model predictions. The common approach to accomplish that is to validate the utilized computational models prior to the design optimization process. However, this is practically an impossible task especially for design problems with high-dimensional design and parameter spaces. We have recently proposed a different approach for maximizing confidence in the designs generated during a sequential simulation-based optimization process based on calibrating the computational models when necessary and within local subdomains of the design space. In that work, the size of the local domains was held fixed and not linked to uncertainty, and the confidence in designs was quantified using Bayesian hypothesis testing. In this article, we present an improved methodology. Specifically, we use a statistical methodology to account for uncertainty and to determine the size of the local domains at each stage of the sequential design optimization process using parametric bootstrapping that involves maximum likelihood estimators of model parameters. The sequential process continues until the local domain does not change from stage to stage during the design optimization process, ensuring convergence to an optimal design. The proposed methodology is illustrated with the design of a thermal insulator using one-dimensional, linear heat conduction in a solid slab with heat flux boundary conditions.

The nanoparticle corona phase (CP) offers a unique materials design space for constructs capable of molecular recognition (MR) for sensing applications. Single-walled carbon nanotube (SWCNT) CPs have the additional ability to transduce MR through its band gap photoluminescence (PL). DNA oligonucleotides are well-known to disperse SWCNTs through forming CPs and can be manufactured with molecular precision. Nevertheless, no generalized scheme exists for the de novo prediction of SWCNT MR based on these CPs due to their sequence-dependent three-dimensional complexity.In aquaculture, there exist a pressing need for rapid tests for the detection of commonly harmful adulterants such as metal ions and small molecule antibiotics. Through a screening process, we found that DNA-SWCNTs offer a rich design space for MR capable of differentiating divalent metal ions. We also created best practices for the study of colloidal SWCNT analyte responses involve mitigating the effects of ionic strength, dilution kinetics, laser power and analyte response kinetics.Next, we generated the largest DNA-SWCNT PL response library of 1408 elements against 4 adulterant targets. We leveraged machine learning (ML) techniques and used both local features (LFs) and high-level features (HLFs) of the DNA sequences were utilized as model inputs. Out-of-sample analysis of our ML model showed significant correlations between model predictions and actual sensor responses for 6 out of the 8 tested experimental conditions. Furthermore, models utilizing both LFs and HLFs show improvement over that with HLFs alone, demonstrating that DNA-SWCNT CP engineering is more complex than simply specifying general DNA molecular properties. Taken as a whole, we detail the feasibility and utility of a ML-guided approach for nanoparticle CP engineering with relatively few experiments within a high-dimensional design space.

Global optimization in optical design is particularly challenging for aspheric and freeform surfaces due to their complex, non-symmetric nature and the presence of numerous local minima in high-dimensional design spaces. Traditional optimization methods often struggle to efficiently escape these local minima, leading to suboptimal solutions. To address this, we propose the Simple Saddle Point Detection (SSPD) Algorithm, which enhances optimization by systematically identifying transition points that connect different design regions. By leveraging these pathways, the algorithm enables a more structured exploration of the design space, improving the convergence toward high-performance solutions. This study applies the SSPD approach to optimize complex optical systems, including catadioptric and multiple (folded) imaging mirror systems, where conventional methods face significant limitations. The results demonstrate that this approach is highly effective in refining aspheric and freeform optical designs, facilitating more efficient and reliable global optimization. Finally, we present the global search results as a closed network, highlighting the capability of SSPD to navigate complex design landscapes and achieve superior optical performance.

Aerodynamic shape optimization plays a fundamental role in aircraft design. However, useful parameterizations of shapes for engineering models often result in high-dimensional design spaces which can create challenges for both local and global optimizers. In this paper, we employ an active subspace method (ASM) to discover and exploit low-dimensional, monotonic trends in the quantity of interest as a function of the design variables. The trend enables us to eciently and eectively nd an optimal design in appropriate areas of the design space. We apply this approach to the ONERA-M6 transonic wing, parameterized with 50 Free-Form Deformation (FFD) design variables. Given an initial set of 300 designs, the ASM discovered a low-dimensional linear subspace of the input space that explained the majority of the variability in the drag and lift coecients. This revealed a global trend that we exploited to nd an optimal design with reduced computational cost.

Multifunctional materials that balance mechanical resilience and fluid dynamic efficiency are critical in engineering applications, yet their synergistic optimization remains challenging due to inherent trade-offs, computational expense, and high-dimensional design spaces. Inspired by the skeleton of the deep-sea sponge Euplectella aspergillum, this work presents an automated framework integrating Finite Element Analysis for mechanics, Computational Fluid Dynamics for flow behavior, and multi-objective Bayesian optimization. Leveraging high-performance computing, the framework efficiently explores complex design spaces to identify Pareto-optimal solutions. Optimized lattices achieve an average 140% increase in critical buckling load across a range of volume fractions relative to baseline designs, while simultaneously reducing drag, lift, and vortex shedding at porosities as low as 5%. We fabricate selected designs via stereolithography and validate them through compression experiments and particle image velocimetry, showing agreement with simulations. By jointly optimizing mechanics and fluidics, this work establishes a scalable methodology for designing lightweight, high-performance architected materials.

The optimization of analog integrated circuit synthesis is inherently a multi-objective problem, requiring the global optimum to satisfy all critical performance constraints. Classical genetic algorithms, although widely applied in analog design, often suffer from slow convergence and premature stagnation in high-dimensional design spaces. To overcome these limitations, this study proposes an Enhanced Adaptive Quantum Genetic Algorithm (EA-QGA), which integrates quantum computation principles with classical evolutionary strategies. Implemented using true quantum gate operations on IBM Qiskit simulators, the EA-QGA leverages a compact population, rapid convergence behavior, and global search efficiency inherent to quantum computing. The framework is evaluated on three benchmark analog circuits using 45 nm CMOS technology: a differential amplifier, a two-stage OTA, and a folded cascode OTA, and its performance, measured in terms of figure-of-merit (FoM), is compared against the Quantum-Inspired Genetic Algorithm (QIGA), which simulates quantum behavior through mathematical modeling. Experimental results show that, relative to QIGA, the proposed EA-QGA achieves FoM improvements of 0.62%, 3.33%, and 14.10% across the three evaluated circuits, while converging 4.6×, 5.8×, and 5.6× faster in generations and reducing runtime by 2.8×, 2.8×, and 2.4×, respectively. These results demonstrate that the proposed EA QGA consistently achieves globally optimal solutions with substantially improved computational efficiency, making it a promising candidate for high-performance analog IC design.

An improved adaptive sampling and experiment design method for aerodynamic optimization

A process-structure-property model via physics-based/data-driven hybrid methods for freeze-cast porous ceramics in Si3N4-Si2N2O case system

Metamodel has been widely used to solve computationally expensive engineering problems, and there have been many studies on how to efficiently and accurately generate metamodels with limited number of samples. However, applications of these methods could be limited in high-dimensional problems since it is still challenging due to curse of dimensionality to generate accurate metamodels in high-dimensional design space. In this paper, recursive decomposition coupled with a sequential sampling method is proposed to identify latent decomposability and efficiently generate high-dimensional metamodels. Whenever a new sample is inserted, variable decomposition is repeatedly performed using interaction estimation from a full-dimension Kriging metamodel. The sampling strategy of the proposed method consists of two units: decomposition unit and accuracy improvement unit. Using the proposed method, latent decomposability of a function can be identified using reasonable number of samples, and a high-dimensional metamodel can be generated very efficiently and accurately using the identified decomposability. Numerical examples using both decomposable and indecomposable problems show that the proposed method shows reasonable decomposition results, and thus improves metamodel accuracy using similar number of samples compared with conventional methods.

This study investigates the process of hazard identification in complex manufacturing environments during the design phase, emphasizing the significance of the design process in developing designs that effectively mitigate hazards in contexts with numerous variables, such as a variety of machines, sensors, actuators, and agents. Through a mixed-methods approach, the objective of this work is to understand how the evolution of design outcomes across various stages might influence a designer’s ability to recognize both standard and novel hazards. To achieve this understanding, an experimental design task was conducted with six designers from a national lab specializing in manufacturing technologies. This approach combined qualitative and quantitative data analysis from a one-hour virtual session with participants. Findings suggest that the complexity of identifying hazards in a high-dimensional design space is challenging within a limited time frame and that the identification of hazards is significantly influenced by the stage of the design task and the initial design decisions, indicating the need for extended time and strategic initial planning in the design process to enhance hazard identification.

Objective: The objective of this work is to investigate the mapping relationship between transcranial ultrasound image quality and transcranial acoustic metamaterial parameters using inverse design methods. Impact Statement: Our study provides insights into inverse design methods and opens the route to guide the preparation of transcranial acoustic metamaterials. Introduction: The development of acoustic metamaterials has enabled the exploration of cranial ultrasound, and it has been found that the influence of the skull distortion layer on acoustic waves can be effectively eliminated by adjusting the parameters of the acoustic metamaterial. However, the interaction mechanism between transcranial ultrasound images and transcranial acoustic metamaterial parameters is unknown. Methods: In this study, 1,456 transcranial ultrasound image datasets were used to explore the mapping relationship between the quality of transcranial ultrasound images and the parameters of transcranial acoustic metamaterials. Results: The multioutput parameter prediction model of transcranial metamaterials based on deep back-propagation neural network was built, and metamaterial parameters under transcranial image evaluation indices are predicted using the prediction model. Conclusion: This inverse big data design approach paves the way for guiding the preparation of transcranial metamaterials.