Length Scale Control in Topology Optimization using Fourier Enhanced Neural Networks

Chandrasekhar, Aaditya; Suresh, Krishnan

doi:10.48550/arxiv.2109.01861

Cited by 2 publications

(3 citation statements)

References 32 publications

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“…In the context of inverse problems [313,444,[466][467][468][469][470], the NN acts as regularizer on a spatially varying inverse quantity λ(x) = I N N (x; θ ), providing both smoother and sharper solutions. For topology optimization with a NN parametrization of the density function [471][472][473][474], no regularizing effect was observed. It was however possible to obtain a greater design diversity through different initializations of the NN.…”

Section: Optimizationmentioning

confidence: 99%

“…Another option of introducing NNs to the optimization loop is to use NNs as an ansatz of λ, see, e.g., [313,444,[466][467][468][469][470][471][472][473][474]. In the context of inverse problems [313,444,[466][467][468][469][470], the NN acts as regularizer on a spatially varying inverse quantity λ(x) = I N N (x; θ ), providing both smoother and sharper solutions.…”

Section: Optimizationmentioning

confidence: 99%

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Deep learning in computational mechanics: a review

Herrmann,

Kollmannsberger

2024

Comput Mech

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The rapid growth of deep learning research, including within the field of computational mechanics, has resulted in an extensive and diverse body of literature. To help researchers identify key concepts and promising methodologies within this field, we provide an overview of deep learning in deterministic computational mechanics. Five main categories are identified and explored: simulation substitution, simulation enhancement, discretizations as neural networks, generative approaches, and deep reinforcement learning. This review focuses on deep learning methods rather than applications for computational mechanics, thereby enabling researchers to explore this field more effectively. As such, the review is not necessarily aimed at researchers with extensive knowledge of deep learning—instead, the primary audience is researchers on the verge of entering this field or those attempting to gain an overview of deep learning in computational mechanics. The discussed concepts are, therefore, explained as simple as possible.

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Section: Optimizationmentioning

confidence: 99%

Section: Optimizationmentioning

confidence: 99%

Deep learning in computational mechanics: a review

Herrmann,

Kollmannsberger

2024

Comput Mech

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show abstract

“…Further, deriving analytical expressions for the gradients is extremely challenging. Recently, a number of paradigms have been developed to address this issue through acceleration of the TO engine [31]; another approach directly executes TO by leveraging an machine learning (ML) framework [32][33][34][35]. We leverage recent advances in ML to efficiently predict cracking within the TO using a surrogate model as well as computing gradients using automatic differentiation.…”

Section: Topology Optimization For Manufacturingmentioning

confidence: 99%

PATO: Producibility-Aware Topology Optimization using Deep Learning for Metal Additive Manufacturing

Iyer¹,

Mirzendehdel²,

Raghavan³

et al. 2021

Preprint

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In this paper, we propose PATO-a producibility-aware topology optimization (TO) framework to help efficiently explore the design space of components fabricated using metal additive manufacturing (AM), while ensuring manufacturability with respect to cracking. Specifically, parts fabricated through Laser Powder Bed Fusion (LPBF) are prone to defects such as warpage or cracking due to high residual stress values generated from the steep thermal gradients produced during the build process. Maturing the design for such parts and planning their fabrication can span months to years, often involving multiple handoffs between design and manufacturing engineers. PATO is based on the a priori discovery of crack-free designs, so that the optimized part can be built defect-free at the outset. To ensure that the design is crack free during optimization, producibility is explicitly encoded within the standard formulation of TO, using a crack index. Multiple crack indices are explored and using experimental validation, maximum shear strain index (MSSI) is shown to be an accurate crack index. Simulating the build process, in order to estimate MSSI, is a coupled, multi-physics, time-complex computation and incorporating it in the TO loop can be computationally prohibitive. We leverage the current advances in deep convolutional neural networks (DCNN) and present a high-fidelity surrogate model based on an Attention-based U-Net architecture to predict the MSSI values as a spatially varying field over the part's domain. Further, we employ automatic differentiation to directly compute the gradient of maximum MSSI with respect to the input design variables and augment it with the performance-based sensitivity field to optimize the design while considering the trade-off between weight, manufacturability, and functionality. We demonstrate the effectiveness of the proposed method through benchmark studies in 3D as well as experimental validation.

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Length Scale Control in Topology Optimization using Fourier Enhanced Neural Networks

Cited by 2 publications

References 32 publications

Deep learning in computational mechanics: a review

Deep learning in computational mechanics: a review

PATO: Producibility-Aware Topology Optimization using Deep Learning for Metal Additive Manufacturing

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