Microstructure Representation and Reconstruction of Heterogeneous Materials Via Deep Belief Network for Computational Material Design

Cang, Ruijin; Xu, Yaopengxiao; Chen, Shaohua; Liu, Yongming; Jiao, Yang; Ren, Max Yi

doi:10.1115/1.4036649

Cited by 158 publications

(75 citation statements)

References 67 publications

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“…Reference design represented as * x is a binary matrix with entries from the Boolean domain since it is black-and-white design. Hence, sensitivity analysis for additional similarity term can be expressed as (13) The above expression means that if a specific element in reference design is solid, then the sensitivity is set to   , and 0 otherwise to avoid providing the positive sensitivity to the OC optimizer. In other words, the purpose of Eq.…”

Section: Fig 2 Design Domain and Boundary Conditions Of A 2d Wheel mentioning

confidence: 99%

“…The generative model is an algorithm for constructing a generator that learns the probability distribution of training data and generates new data based on learned probability distribution. In particular, variational autoencoder (VAE) and generative adversarial network (GAN) are popular generative models used in design optimization, where high-dimensional design variables are encoded in low-dimensional design space [13,14]. In addition, these models are utilized in the design exploration and shape parameterization [8,9].The use of generative model to produce engineering designs directly is limited [23].…”

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Deep Generative Design: Integration of Topology Optimization and Generative Models

Jung

Kim

et al. 2019

Journal of Mechanical Design

282

124

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Deep learning has recently been applied to various research areas of design optimization. This study presents the need and effectiveness of adopting deep learning for generative design (or design exploration) research area. This work proposes an artificial intelligent (AI)-based deep generative design framework that is capable of generating numerous design options which are not only aesthetic but also optimized for engineering performance. The proposed framework integrates topology optimization and generative models (e.g., generative adversarial networks (GANs)) in an iterative manner to explore new design options, thus generating a large number of designs starting from limited previous design data. In addition, anomaly detection can evaluate the novelty of generated designs, thus helping designers choose among design options. The 2D wheel design problem is applied as a case study for validation of the proposed framework. The framework manifests better aesthetics, diversity, and robustness of generated designs than previous generative design methods. Nomenclature: expectation : differentiable function of discriminator : differentiable function of generator : noise variable ℒ: loss function of autoencoder c: compliance : density variable ̃: filtered density variable ̃̅ : projected density variable : penalization factor Generative Models for Generative DesignGenerative models, one of the promising deep learning areas, can enhance research on generative design. The generative model is an algorithm for constructing a generator that learns the probability distribution of training data and generates new data based on learned probability distribution. In particular, variational autoencoder (VAE) and generative adversarial network (GAN) are popular generative models used in design optimization, where high-dimensional design variables are encoded in low-dimensional design space [13,14]. In addition, these models are utilized in the design exploration and shape parameterization [8,9].The use of generative model to produce engineering designs directly is limited [23]. However, this study claims that the limitations can be overcome by integrating with topology optimization. First, the generative model requires a number of training data, but accumulated training data for various designs in the industry are confidential and difficult to access. A number of designs obtained from topology optimization are expected to serve as training data. Second, the generative model cannot guarantee feasible engineering. In this case,

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Section: Fig 2 Design Domain and Boundary Conditions Of A 2d Wheel mentioning

confidence: 99%

mentioning

confidence: 99%

Deep Generative Design: Integration of Topology Optimization and Generative Models

Jung

Kim

et al. 2019

Journal of Mechanical Design

282

124

View full text Add to dashboard Cite

show abstract

“…And based on these two, (3) how do we search for a good design? Challenges in answering these questions include high-dimensional or ill-defined design spaces such as for topologies [10,11], material microstructures [12,13,14], or complex geometries [15,16], expensive evaluations of designs and their sensitivities, e.g., due to model nonlinearity [17,18], coupled materials or physics [19,20,21], or subjective goodness measures [22,23], or search inefficiency due to the absence of sensitivities [24,25,26] or the existence of random variables [27].…”

Section: Related Workmentioning

confidence: 99%

“…10 Derive x * for s * by solving (TO); 11 Record δB as the number of Ku = s solved in solving (TO) and computing Eq. (6); 12 Update the budget B = B − δB;…”

Section: The Heuristic Of Benchmark IImentioning

confidence: 99%

One-shot generation of near-optimal topology through theory-driven machine learning

Cang

Yao

Ren

2019

Computer-Aided Design

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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. example, the design of vehicle body-in-white is often done by experienced structure engineers, since topology optimization (TO) on full-scale crash simulation is not yet fast enough to respond to requests from higher-level design tasks, e.g., geometry design with style and aerodynamic considerations, and thus may slow down the entire design process 1 .Research exists in developing deep neural network models that learn to create structured solutions in a one-shot fashion, circumventing the need of iterations (e.g., in solving systems of equations [1], simulating dynamical systems [2], or searching for optimal solutions [3,4,5]). Learning of such models through data, however, is often criticized to have limited generalization capability, especially when highly nonlinear input-output relations or highdimensional output spaces exist [6,7,8]. In the context of TO, this means that the network may create structures with unreasonably poor physical properties when it responds to new problem settings. More concretely, consider a topology with a tiny crack in one of its trusses. This design would be far from optimal if the goal is to lower compliance, yet standard datadriven learning mechanisms do not prevent this from happening, i.e., they don't know that they don't know (physics).Our goal is to create a learning mechanism that knows what it does not know, and thus can self-improve in an effective way. Specifically, we are curious about how physicsbased knowledge, e.g., in the forms of dynamical models, theoretical bounds, and optimality conditions, can be directly injected into the learning of networks that ...

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“…The idle pace of development and deployment of new/improved materials has been deemed as the main bottleneck in the innovation cycles of most emerging technologies [26]. Exploring and harnessing the association between processing, structure, properties, and performance is a critical aspect of new materials exploration [27]- [30]. Data-driven techniques provide faster methods to know the important properties of materials and to predict feasibility to synthesize materials experimentally.…”

Section: Related Workmentioning

confidence: 99%

A Real-Time Iterative Machine Learning Approach for Temperature Profile Prediction in Additive Manufacturing Processes

Paul¹,

Mozaffar²,

Yang³

et al. 2019

2019 IEEE International Conference on Data Science and Advanced Analytics (DSAA)

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Additive Manufacturing (AM) is a manufacturing paradigm that builds three-dimensional objects from a computeraided design model by successively adding material layer by layer. AM has become very popular in the past decade due to its utility for fast prototyping such as 3D printing as well as manufacturing functional parts with complex geometries using processes such as laser metal deposition that would be difficult to create using traditional machining. As the process for creating an intricate part for an expensive metal such as Titanium is prohibitive with respect to cost, computational models are used to simulate the behavior of AM processes before the experimental run. However, as the simulations are computationally costly and timeconsuming for predicting multiscale multi-physics phenomena in AM, physics-informed data-driven machine-learning systems for predicting the behavior of AM processes are immensely beneficial. Such models accelerate not only multiscale simulation tools but also empower real-time control systems using in-situ data. In this paper, we design and develop essential components of a scientific framework for developing a data-driven model-based real-time control system. Finite element methods are employed for solving time-dependent heat equations and developing the database. The proposed framework uses extremely randomized trees -an ensemble of bagged decision trees as the regression algorithm iteratively using temperatures of prior voxels and laser information as inputs to predict temperatures of subsequent voxels. The models achieve mean absolute percentage errors below 1% for predicting temperature profiles for AM processes. The code is made available for the research community at https://github.com/paularindam/ml-iter-additive.

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Microstructure Representation and Reconstruction of Heterogeneous Materials Via Deep Belief Network for Computational Material Design

Cited by 158 publications

References 67 publications

Deep Generative Design: Integration of Topology Optimization and Generative Models

Deep Generative Design: Integration of Topology Optimization and Generative Models

One-shot generation of near-optimal topology through theory-driven machine learning

A Real-Time Iterative Machine Learning Approach for Temperature Profile Prediction in Additive Manufacturing Processes

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