We introduce a theory-driven mechanism for learning a neural network model that performs generative topology design in one shot given a problem setting, circumventing the conventional iterative process that computational design tasks usually entail. The proposed mechanism can lead to machines that quickly response to new design requirements based on its knowledge accumulated through past experiences of design generation. Achieving such a mechanism through supervised learning would require an impractically large amount of problem-solution pairs for training, due to the known limitation of deep neural networks in knowledge generalization. To this end, we introduce an interaction between a student (the neural network) and a teacher (the optimality conditions underlying topology optimization): The student learns from existing data and is tested on unseen problems. Deviation of the student's solutions from the optimality conditions is quantified, and used for choosing new data points to learn from. We call this learning mechanism "theory-driven", as it explicitly uses domain-specific theories to guide the learning, thus distinguishing itself from purely data-driven supervised learning. We show through a compliance minimization problem that the proposed learning mechanism leads to topology generation with near-optimal structural compliance, much improved from standard supervised learning under the same computational budget.
Existing research on generative design answer three types of questions: (1) What is the design ? (2) What is the measure of a design? And based on these two, (3) how do we for a good design? Challenges in answering these questions include such as for topologies @cite_14 @cite_7 , material microstructures @cite_11 @cite_30 @cite_3 , or complex geometries @cite_8 @cite_0 , of designs and their sensitivities, e.g., due to model nonlinearity @cite_6 @cite_15 , coupled materials or physics @cite_13 @cite_31 @cite_47 , or subjective goodness measures @cite_32 @cite_33 , or due to the absence of sensitivities @cite_42 @cite_22 @cite_36 or the existence of random variables @cite_45 .
@cite_30 @cite_31 @cite_14 @cite_47 @cite_33 @cite_7 @cite_8 @cite_22 @cite_36 @cite_42 @cite_32 @cite_3 @cite_6 @cite_0 @cite_45 @cite_15 @cite_13 @cite_11
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Abstract Direct prediction of material properties from microstructures through statistical models has shown to be a potential approach to accelerating computational material design with large design spaces. However, statistical modeling of highly nonlinear mappings defined on high-dimensional microstructure spaces is known to be data-demanding. Thus, the added value of such predictive models diminishes in common cases where material samples (in forms of 2D or 3D microstructures) become costly to acquire either experimentally or computationally. To this end, we propose a generative machine learning model that creates an arbitrary amount of artificial material samples with negligible computation cost, when trained on only a limited amount of authentic samples. The key contribution of this work is the introduction of a morphology constraint to the training of the generative model, that enforces the resultant artificial material samples to have the same morphology distribution as the authentic ones. We show empirically that the proposed model creates artificial samples that better match with the authentic ones in material property distributions than those generated from a state-of-the-art Markov Random Field model, and thus is more effective at improving the prediction performance of a predictive structure-property model. In this paper we address the problem of structural shape and topology optimization in a multi-material domain. A level-set method is employed as an alternative approach to the popular homogenization-based methods of rule of mixtures for multi-material modeling. A multi-phase level-set model is adapted for material and topology representation. This model eliminates the need for a material interpolation or phase mixing scheme. It only requires m level-set functions to represent a structure of n=2m different material phases, in a principle similar to combining colors from the three primary colors. Therefore, this multi-phase model may be referred to as a “color” level-set representation which has its unique benefits: it is flexible to handle complex topologies; it substantially reduces the number of model functions when n>3; it automatically avoids the problem of overlap between material phases of a conventional partitioning approach. We describe numerical techniques for efficient and robust implementation of the method, by embedding a rectilinear grid in a fixed finite element mesh defined on a reference design domain. This would separate the issues of accuracy in numerical calculations of the physical equation and in the level-set model propagation. A gradient projection method is described for incorporating multiple constraints in the problem. Finally, the benefits and the advantages of the developed method are illustrated with several 2D examples of mean compliance minimization of multi-material structures. In this article, we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks of the object. We start by precomputing the material property gamut—the set of bulk material properties that can be achieved with all material microstructures of a given size. We represent the boundary of this material property gamut using a level set field. Next, we propose an efficient and general topology optimization algorithm that simultaneously computes an optimal object topology and spatially varying material properties constrained by the precomputed gamut. Finally, we map the optimal spatially varying material properties onto the microstructures with the corresponding properties to generate a high-resolution printable structure. We demonstrate the efficacy of our framework by designing, optimizing, and fabricating objects in different material property spaces on the level of a trillion voxels, that is, several orders of magnitude higher than what can be achieved with current systems. Describes development work to combine the basic ESO with the additive evolutionary structural optimisation (AESO) to produce bidirectional ESO whereby material can be added and can be removed. It will be shown that this provides the same results as the traditional ESO. This has two benefits, it validates the whole ESO concept and there is a significant time saving since the structure grows from a small initial one rather than contracting from a sometimes huge initial one where 90 per cent of the material gets removed over many hundreds of finite element analysis (FEA) evolutionary cycles. Presents a brief background to the current state of Structural Optimisation research. This is followed by a discussion of the strategies for the bidirectional ESO (BESO) algorithm and two examples are presented. A new efficient optimization method, called 'Teaching-Learning-Based Optimization (TLBO)', is proposed in this paper for the optimization of mechanical design problems. This method works on the effect of influence of a teacher on learners. Like other nature-inspired algorithms, TLBO is also a population-based method and uses a population of solutions to proceed to the global solution. The population is considered as a group of learners or a class of learners. The process of TLBO is divided into two parts: the first part consists of the 'Teacher Phase' and the second part consists of the 'Learner Phase'. 'Teacher Phase' means learning from the teacher and 'Learner Phase' means learning by the interaction between learners. The basic philosophy of the TLBO method is explained in detail. To check the effectiveness of the method it is tested on five different constrained benchmark test functions with different characteristics, four different benchmark mechanical design problems and six mechanical design optimization problems which have real world applications. The effectiveness of the TLBO method is compared with the other population-based optimization algorithms based on the best solution, average solution, convergence rate and computational effort. Results show that TLBO is more effective and efficient than the other optimization methods for the mechanical design optimization problems considered. This novel optimization method can be easily extended to other engineering design optimization problems. Abstract A simple evolutionary procedure is proposed for shape and layout optimization of structures. During the evolution process low stressed material is progressively eliminated from the structure. Various examples are presented to illustrate the optimum structural shapes and layouts achieved by such a procedure. We seek to elicit individual design preferences through human-computer interaction. During an iteration of the interactive session, the computer queries the subject by presenting a set of designs from which the subject must make a choice. The computer uses this choice feedback and creates the next set of designs using knowledge accumulated from previous choices. Under the hypothesis that human responses are deterministic, we discuss how query schemes in the elicitation task can be viewed mathematically as learning or optimization algorithms. Two query schemes are defined. Query type 1 considers the subject’s binary choices as definite preferences, i.e., only preferred designs are chosen, while others are skipped; query type 2 treats choices as comparisons among a set, i.e., preferred designs are chosen relative to those in the current set but may be dropped in future iterations. We show that query type 1 can be considered as an active learning problem, while type 2 as a “black-box” optimization problem. This paper concentrates on query type 2. Two algorithms based on support vector machine and efficient global optimization search are presented and discussed. Early user tests for vehicle exterior styling preference elicitation are also presented. [DOI: 10.1115 1.4005104] Abstract Building sensible processing-structure-property (PSP) links to gain fundamental insights and understanding of materials behavior has been the focus of many works in computational materials science. Microstructure characterization and reconstruction (MCR), coupled with machine learning techniques and materials modeling and simulation, is an important component of discovering PSP relations and inverse material design in the era of high-throughput computational materials science. In this article, we provide a comprehensive review of representative approaches for MCR and elaborate on their algorithmic details, computational costs, and how they fit into the PSP mapping problems. Multiple categories of MCR methods relying on statistical functions (such as n-point correlation functions), physical descriptors, spectral density function, texture synthesis, and supervised unsupervised learning are reviewed. As no MCR method is applicable to the analysis and (inverse) design of all material systems, our goal is to provide the scientific community with a close examination of the state-of-the-art techniques for MCR, as well as useful guidance on which MCR method to choose and how to systematically apply it to a problem at hand. We illustrate applications of MCR on materials modeling and building structure-property relations via two examples: One on learning the materials law of a class of composite microstructures, and the second on relating the permittivity and dielectric loss to a structural parameter in nanodielectrics. In the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level-set method for front propagation. We implement this method in two and three space dimensions for a model of linear or nonlinear elasticity. We consider various objective functions with weight and perimeter constraints. The shape derivative is computed by an adjoint method. The cost of our numerical algorithm is moderate since the shape is captured on a fixed Eulerian mesh. Although this method is not specifically designed for topology optimization, it can easily handle topology changes. However, the resulting optimal shape is strongly dependent on the initial guess. Abstract A semantic recognition and rule-oriented approach for developing a product design is proposed. The development of an office chair is used to describe the design procedures. A number of referential products are used to quantify partial correlation coefficients, which represent individual contributions of constituent components to the impression of a whole product with respect to an image, by using the ‘quantification theory type I’ and ‘semantic differential method’. The results are then built as an image database. A computer program is constructed by integrating the techniques of constructing B-splines, shape grammars and fuzzy operations to provide a CAD environment in which 3D basic models of a product can be constructed by starting with inputting an image word(s) and the corresponding membership functions for describing the image of the required product. After a basic product model has been constructed, new product forms can further be generated by regulating the shapes of the component(s) using shape rule(s). The objective of this work is to integrate reliability analysis into topology optimization problems. The new model, in which we introduce reliability constraints into a deterministic topology optimization formulation, is called Reliability-Based Topology Optimization (RBTO). Several applications show the importance of this integration. The application of the RBTO model gives a different topology relative to deterministic topology optimization. We also find that the RBTO model yields structures that are more reliable than those produced by deterministic topology optimization (for the same weight). In this paper, topology optimization of both geometrically and materially nonlinear structure is studied using a general displacement functional as the objective function. In order to consider large deformation, effective stress and strain are expressed in terms of 2nd Piolar-Kirchhoff stress tensor and Green-Lagrange strain tensor, and constitutive equation is derived from the relation between the effective stress and strain. Sensitivity analysis of the general displacement functional is derived using the adjoint method. Numerical results of mean compliance design are compared under linear analysis, geometrical nonlinear analysis, material nonlinear analysis, and combined nonlinear analysis.