Using Surrogate Models to Reduce the Design Complexity of Fiber Amplifiers with Heterogeneous Doping

Identification of design solutions for a built environment that caters to the human needs at all levels, and more specifically, to the needs of the clients and the society, is the main task addressed by architectural design. Architectural design is a prime example of a design task that is characterized by a high degree of complexity. Architectural design problems by definition entail relationships between decisions and objectives that are all but transparent. For the decision-maker to be able to guide design towards fulfilling objectives, a ‘closed-loop’ approach where variations in design solutions are generated and evaluated in an iterative process is employed. Due to the sheer number of alternative solutions to problems of even a moderate scale (due to combinatorial explosion), it is only feasible to iterate over a minuscule fraction of possible solutions. Design intuition of the professionals involved in design is a strong driving force behind the identification of design direction, in which alternatives are explored as part of the preliminary design process. This is an approach that depends on the human cognitive capabilities to navigate the design space and identify potentially promising solutions. Regardless, the complexity associated with architectural design often poses significant challenges to human cognition. Human cognition, while formidable in its ability to flexibly and efficiently navigate challenging environments, is faced with difficulties in addressing the complexity factors outlined previously, namely: the excessive (combinatorially explosive) number of potential solutions to architectural problems, the complex and non-linear relations between objects and their properties and the conflicting nature of design goals that architectural design entails. Thus, design professionals are often faced with the real threat that their decisions may be biased due to the natural limitations of human cognition acting in complex environments.<br/><br/>Due to the reasons highlighted above, a systematic approach to design space exploration must be undertaken, to maximize the potential for discovering optimal solutions to design problems. Due to the nature of such problems that entail multiple conflicting objectives, a single best solution is generally not attainable. Nonetheless, best-tradeoff solutions are distinguished and highly desirable for such multi-objective design problems. The field of Computational Intelligence, and within that in particular Evolutionary Computation-based (EC) intelligent approaches, offer a lucrative option as decision-support tools in design, as they are able to efficiently address the aforementioned proponents of design complexity. EC approaches are able to navigate the design space efficiently and systematically, considering multiple conflicting objectives and hard constraints, and being able to deal with arbitrary relations between design decision variables and design objectives. <br/><br/>In today's setting, products of architecture must lead the way to a sustainable and environmentally friendlier society. As such, the performance of buildings has become the main driving force behind the design process, being referred to as ``performance-driven design''. This initiative emphasizes the quantitative evaluation of a design's function in accordance with established design objectives, related to aspects such as energy performance, visual and thermal comfort, cost and environmental footprint, etc. Simulation-based tools that enable accurate design evaluation are gaining ground and offering valuable insight into the performance of buildings. Nonetheless, making decisions in this multi-objective environment is not trivial, and, as stipulated above, may be challenging to human cognition. Thus, in today’s setting where the quantitative performance of buildings keeps gaining ground, the research on the application of EC in architectural design is high on the scientific agenda.<br/><br/>Recognizing the impact design complexity has on architectural design and the potential that EC-based approaches offer in addressing it, this thesis proposes a comprehensive computational intelligence decision support system that combines components based on intelligence with ones based on cognition, with the ultimate aim of enabling decision-makers manage design complexity and improve decision making. In particular, this thesis adopts the theoretical standpoint that efficient navigation of an unknown environment assumes a fusion of intelligence and cognition. In this sense, and given the already widespread adoption of intelligent approaches (such as EC mentioned above), the main contribution of this thesis is to endow the intelligent approach with cognitive facilities, so as to improve its efficiency to the point that it is readily applicable to the early stages of the architectural design process.<br/><br/>Fusion of intelligent with cognitive approaches, as outlined in the approach proposed by this thesis, offers the unique advantage of a decision support approach that is both powerful, owing to the extensive capabilities of intelligent search algorithms, and flexible, owing to the extensive knowledge modeling capabilities of cognitive approaches. As such, it is uniquely suited to the early conceptual design stage where the need to explore large design spaces, flexibly redefine the design problem, and satisfy preferences that are not included in the primary design goals, are all paramount.<br/><br/>Thus, the word ``comprehensive'' as it appears on this thesis' title obtains a twofold meaning: On one hand comprehension as in the combination of computational intelligence and cognition in a single approach; on the other hand, as in \\textit{comprehension} of the environment, the result of an intelligent and cognitive approach to understanding.<br/><br/>Firstly, it seeks to address the excessive computational burden associated with the use of modern high-fidelity simulation software in architecture, to render computational optimization more approachable. There is a clear trend in modern design practice to employ accurate simulation-based performance assessment tools from the very early stages of design. The use of such tools provides a valuable advantage to the decision-maker, in endowing objective awareness regarding the performance of a design solution. On the other hand, such tools are associated with a heavy computational burden, which may limit their application to the conceptual design stage. There exist methods to alleviate the computational burden through the use of computational cognitive machine learning tools, also known as surrogate modeling. However, training of surrogate models can be time-consuming itself, thus limiting the application. This thesis proposes a surrogate model that is modular in that it considers each space of the building in question as a separate entity, encoded through generic variables, and as such promotes model reuse in different design cases.<br/><br/>Secondly, it seeks to advance the state of the art on post-Pareto decision support by proposing a cognitive machine-learning based approach that enables the decision-maker to combine near-optimality with preferences regarding concrete features of the design solution. Post-Pareto decision making is an important step of the decision-making process, that seeks to identify a best-tradeoff solution among the possible ones that best matches the decision-maker's preferences in terms of performance. Such preferences are termed second-order because they follow design objectives in terms of importance. Nonetheless, it is often in architectural design that preferences are expressed in terms of design properties and not performance. Due to the non-linearity between the objective function space and the decision variable space that dictates object properties, it is challenging to exercise decision making using second-order preferences. Here the contribution of this thesis is a machine cognitive approach that learns the underlying relationships between object properties, distinguishing those that are relevant when the object is optimal with respect to design objectives. In other words, only imposing relations that are relevant to achieve optimality, it enables the expression of preferences by the decision-maker that are minimally constrained.<br/><br/>The main output of this thesis is a comprehensive decision support framework; it is a framework, in the sense that it comprises a set of methods and implemented tools that seek to augment decision making in architectural design; it is termed comprehensive in that it employs computational cognition and machine learning to augment the intelligent decision support capabilities throughout the design decision support process. It is also generic and applicable as-is to a wide spectrum of architectural design problems. In the context of this thesis, validation of the proposed approach is performed mainly in case studies relevant to facade design, recognizing this design topic as a complexity-exhibiting exemplar in architectural design practice.

Adaptive modeling strategy for constrained global optimization with application to aerodynamic wing design

The management of technologies remains a challenging and risky constituent of gas turbine component design. The performance impact of a single new technology on a gas turbine component is often uncertain, requiring statistical methods to fully quantify. The inclusion of multiple new technologies further complicates gas turbine component performance prediction because there may be significant non-linear technology interactions. When designing gas turbine components to operate within the context of a fully specified gas turbine engine, each component introduces its own mix of new technologies. Because gas turbine components are linked thermodynamically, a new technology in one component may induce secondary impacts in other engine components. Thus, technology portfolio analysis for gas turbines is further complicated by the dynamics of component interaction. In this paper, a new technology portfolio planning methodology is presented that directly addresses these three inherent complexities of gas turbine component design. This methodology includes Technology Impact Matrices to quantify component level technology impacts as well as Technology Compatibility Matrices and Technology Synergy Matrices to account for non-linear component level technology interactions. Through surrogate modeling, a physicsbased dynamic engine model is formed that quickly translates component technology impacts into total-system thermodynamic performance. Real Options analysis is used to translate engine performance metrics to net engine economic performance. Finally, a probabilistic multi-objective genetic algorithm is used to discover a robust Pareto front of optimal technology combinations with respect to system level thermodynamic and economic performance metrics. This paper first describes the proposed methodology in detail. Next, a benchmark gas turbine technology portfolio problem is outlined. Finally, a baseline technology portfolio planning methodology and the newly proposed methodology are both executed upon the benchmark problem, allowing for the benefits of the new methodology to be quantified.

In this paper, an airfoil aerodynamic prediction model based on neural network is proposed. In the traditional prediction method based on surrogate model, there are some shortcomings, such as over dependence on airfoil parameters, limited dimension of design variables, and complexity of strong nonlinear engineering design. As an alternative method, convolutional neural network (CNN) has been proved to have good ability of complex image classification, and is widely used in aerodynamic element modeling task. So in this paper, based on enough data sets, a convolutional neural network framework is constructed to replace the traditional CFD solver to predict large-scale nonlinear aerodynamic parameters. Using CNN, the aerodynamic parameters of airfoil at different angles of attack can be predicted（α)，The results of CFD solver are compared. The results show that the proposed method can maintain a high level of accuracy, and its efficiency is far better than CFD method.

Simulation-based problems involving mixed-variable inputs frequently feature domains that are hierarchical, conditional, heterogeneous, or tree-structured. These characteristics pose challenges for data representation, modeling, and optimization. This paper reviews extensive literature on these structured input spaces and proposes a unified framework that generalizes existing approaches. In this framework, input variables may be continuous, integer, or categorical. A variable is described as meta if its value governs the presence of other decreed variables , enabling the modeling of conditional and hierarchical structures. We further introduce the concept of partially decreed variables , whose activation depends on contextual conditions. To capture these inter-variable hierarchical relationships, we introduce design space graphs , combining principles from feature modeling and graph theory. This allows the definition of general hierarchical domains suitable for describing complex system architectures. Our framework defines hierarchical distances and kernels to enable surrogate modeling and optimization on hierarchical domains. We demonstrate its effectiveness on complex system design problems, including a neural network and a green-aircraft case study. Our methods are available in the open-source Surrogate Modeling Toolbox (SMT 2.0).

Abstract. Synergies between neural networks and traditional surrogate modelling techniques have emerged as the forefront of data-driven engineering. Neural network-based surrogate models, trained on carefully selected experimental data or high-fidelity simulations, can predict behaviours of complex systems with remarkable speed and accuracy. This review examines the current state and recent developments in neural surrogate technologies, highlighting their expanding roles in engineering design optimisation and generation. It also covers various feature engineering methods for representing 3D geometries, the principles of neural surrogate modelling, and the potential of emerging AI-driven design tools. While feature engineering remains a challenge, especially in parameterising complex designs for machine learning, recent advancements in code/language-based representations offer promising solutions for digitalising various design scenarios. Moreover, the emergence of AI-driven design tools, including text-to-CAD models powered by large language models, enables engineers to rapidly generate and evaluate innovative design concepts. Neural surrogate modelling has the potential to transform engineering workflows. Continued research into geometric feature engineering, along with the integration of AI-driven design tools, will speed up the use of neural surrogate models in engineering designs.

In post-amputation rehabilitation, a common goal is to return to ambulation using a prosthetic limb, suspended by a customised socket. Prosthetic socket design aims to optimise load transfer between the residual limb and mechanical limb, by customisation to the user. This is a time-consuming process, and with the increase in people requiring these prosthetics, it is vital that these personalised devices can be produced rapidly while maintaining excellent fit, to maximise function and comfort. Prosthetic sockets are designed by capturing the residual limb’s shape and applying a series of geometrical modifications, called rectifications. Expert knowledge is required to achieve a comfortable fit in this iterative process. A variety of rectifications can be made, grouped into established strategies [e.g. in transtibial sockets: patellar tendon bearing (PTB) and total surface bearing (TSB)], creating a complex design space. To date, adoption of advanced engineering solutions to support fitting has been limited. One method is numerical optimisation, which allows the designer a number of likely candidate solutions to start the design process. Numerical optimisation is commonly used in many industries but not prevalent in the design of prosthetic sockets. This paper therefore presents candidate shape optimisation methods which might benefit the prosthetist and the limb user, by blending the state of the art from prosthetic mechanical design, surrogate modelling and evolutionary computation. The result of the analysis is a series of prosthetic socket designs that preferentially load and unload the pressure tolerant and intolerant regions of the residual limb. This spectrum is bounded by the general forms of the PTB and TSB designs, with a series of variations in between that represent a compromise between these accepted approaches. This results in a difference in pressure of up to 31 kPa over the fibula head and 14 kPa over the residuum tip. The presented methods would allow a trained prosthetist to rapidly assess these likely candidates and then to make final detailed modifications and fine-tuning. Importantly, insights gained about the design should be seen as a compliment, not a replacement, for the prosthetist’s skill and experience. We propose instead that this method might reduce the time spent on the early stages of socket design and allow prosthetists to focus on the most skilled and creative tasks of fine-tuning the design, in face-to-face consultation with their client.

The optimization of functional materials is important to enhance their properties, but their complex geometries pose great challenges to optimization. Data‐driven algorithms efficiently navigate such complex design spaces by learning relationships between material structures and performance metrics to discover high‐performance functional materials. Surrogate‐based active learning, continually improving its surrogate model by iteratively including high‐quality data points, has emerged as a cost‐effective data‐driven approach. Furthermore, it can be coupled with quantum computing to enhance optimization processes, especially when paired with a special form of surrogate model (i.e., quadratic unconstrained binary optimization), formulated by factorization machine (FM). However, current practices often overlook the variability in design space sizes when determining the initial data size for optimization. In this work, we investigate the optimal initial data sizes required for efficient convergence across various design space sizes. By employing averaged piecewise linear regression, we identify initiation points where convergence begins, highlighting the crucial role of employing adequate initial data in achieving efficient optimization. These results contribute to the efficient optimization of functional materials by ensuring faster convergence and reducing computational costs in FM‐based active learning.

All engineering design problems can be characterized by the underlying assumptions around which the problem is formulated. The effect of these assumptions - including everything from general assumptions defining an operating environment to detailed assumptions regarding material properties - is variability in system performance, and resulting deviations from expected performance. Assumptions are made to eliminate uncertainties that would prevent the quantification of design performance. Probabilistic methods have been developed in recent decades to convert such deterministic problem formulations into probabilistic formulations to model and assess the effects of these known uncertainties and thus relax restrictive assumptions. Until very recently, however, the computational expense of probabilistic analysis of a single design has made its application impractical for all but very simplistic design problems. Consequently, probabilistic optimization has been considered prohibitively expensive, particularly for complex multidisciplinary systems. Today a number of enabling technologies are available to support probabilistic design analysis and optimization for complex engineering design problems, including: flexible software frameworks that allow integration and automation of a complex multidisciplinary process; probabilistic analysis and optimization tools that allow uncertainty to be modeled and performance variation to be measured and reduced; large scale parallel processing capabilities leading to greatly increased efficiency; and advanced surrogate modeling capabilities to replace complex nonlinear analyses with computationally efficient approximation models. Along with steady increases in computing power, the combination of these enabling technologies can facilitate effective probabilistic analysis and optimization for complex design problems. In this paper we focus primarily on two of these enabling technologies. We present a comprehensive probabilistic design optimization formulation, a six sigma based approach that incorporates variability within all elements of the formulation - input design variable bound formulation, output constraint formulation, and robust objective formulation. We discuss the applicability of kriging, one surrogate modeling approach that supports the approximation of complex nonlinear analyses, for facilitating probabilistic multidisciplinary design optimization. These enabling technologies, as implemented within the commercial software framework provided by iSIGHT, including capability to facilitate parallel processing, are demonstrated for a multidisciplinary conceptual ship design problem.

As modern buildings face increasing sustainability and performance demands, simulation‐based optimization and machine learning have become essential tools in the design process. This article highlights the limitations of traditional design methods and explores how multi‐objective optimization and surrogate modeling enable scalable, efficient, and data‐driven evaluation of building performance. The design paradigm has shifted from rule‐based approaches to intelligent, algorithm‐driven processes that balance energy, comfort, cost, and emissions. Simulation‐based optimization integrates dynamic simulation with advanced algorithms to explore complex design spaces and identify optimal trade‐offs. To this end, a case study of a low‐rise residential building in Patras, Greece, is presented using the Non‐dominated Sorting Genetic Algorithm II. The model evaluated 12 envelope‐related design variables and generated a well‐distributed Pareto front of 65 non‐dominated solutions, highlighting trade‐offs between heating energy demand and construction cost. The sensitivity patterns observed across the Pareto set showed that insulation thickness and glazing performance were the most influential drivers of heating demand. Machine learning–based surrogate modeling enhances optimization further by approximating computationally expensive simulations with fast, predictive models. Trained on sampled simulation data, these surrogates enable rapid optimization and sensitivity analysis. A second case study, referring to a school retrofit in Portugal, demonstrated that an Artificial Neural Network surrogate reduced computation time from approximately 75 days to just 3 days while maintaining high predictive accuracy. Sensitivity analysis indicated that window upgrades, HVAC efficiency, and solar thermal integration had the strongest influence on energy use and thermal discomfort. These quantitative and sensitivity‐based insights demonstrate how combining simulation‐based and machine learning methodologies supports high‐performance, cost‐effective, and environmentally responsible building design and retrofit. This article is categorized under: Sustainable Energy > Energy Efficiency Cities and Transportation > Buildings

A Repetitively Enhanced Neural Networks (RENN) method is developed and presented for complex and implicit engineering design problems. The enhanced neural networks module constructs an accurate surrogate model and avoids over-fitting during neural networks training from supervised learning data. The optimiser is executed by the enhanced neural networks models to seek a tentative optimum point. It is repetitively added into the supervised learning data set to refine the surfaces until the RENN tolerance is reached. The RENN method demonstrates the effectiveness and feasibility for a 2D highly non-linear numerical example and the structure design of a two-member frame reaching a convergent solution at 10 and 15 iterations at the maximum error of 1% when compared with the exact solution. Then, the RENN method is applied for a long endurance unmanned aerial vehicle (UAV) aerofoil design optimisation. A Class/Shape function transformation (CST) geometry parameterisation method represents an accurate UAV aerofoil with ten geometry design variables. The high-fidelity analysis solver with structured mesh is used for a UAV aerofoil design problem. Using the RENN method, an optimal UAV aerofoil is obtained using 88 high fidelity evaluations at an error of 1·24%. The process reduces the computational time by 81·2% compared with the full high fidelity model. The optimal aerofoil shows a drag reduction of 10·8% in the cruise condition and an improvement in the maximum lift coefficient and stall angle-of-attack when compared with the baseline AG24 aerofoil.

The global expansion of 5G and the approaching 6G era are pushing conventional single-mode fibers toward their fundamental capacity limits, necessitating a paradigm shift in optical network infrastructure. This study introduces a novel, AI-optimized tri-concentric-core fiber with an optimized grading profile (TCC-OGP) to overcome this capacity crunch through spatial-division multiplexing (SDM). The fiber design was realized through an integrated artificial intelligence framework, combining a neural network surrogate model with particle swarm optimization to efficiently navigate a complex multi-objective design space. The resultant TCC-OGP fiber supports six spatial-division-multiplexed LP modes, achieving a breakthrough in the traditional capacity–nonlinearity trade-off. A comprehensive numerical analysis demonstrates that the proposed structure achieves 92% of the theoretical Shannon capacity while simultaneously suppressing nonlinear impairments by 65% compared to the standard single-core fiber. Furthermore, the fiber exhibits low differential mode delay, a flattened dispersion of approximately 16 ps/(nm·km) at 1550 nm, strong bend tolerance (<0.01 dB/m at a 30 mm radius), and excellent inter-modal crosstalk below −25 dB over 20 km. These performance metrics confirm the TCC-OGP fiber’s suitability for terabit-scale transmission in metro networks, dense 5G back-haul, and future 6G infrastructures, establishing a scalable and intelligent platform for next-generation optical networks.