AuTO: a framework for Automatic differentiation in Topology Optimization

Chandrasekhar, Aaditya; Sridhara, Saketh; Suresh, Krishnan

doi:10.1007/s00158-021-03025-8

Cited by 38 publications

(7 citation statements)

References 51 publications

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“…This can be laborious and error-prone, especially for non-trivial objectives. Here, by expressing all our computations including computing the permeability tensors, stiffness matrix, FEA, objectives and constraints in PyTorch [76], we use the NN's automatic differentiation (AD) capabilities to completely automate this step [77]. In other words, only the forward expressions need to be defined, and all required derivatives are computed to machine precision by PyTorch computing library.…”

Section: Sensitivity Analysismentioning

confidence: 99%

TOMAS: Topology Optimization of Multiscale Fluid-Flow Devices using Variational Autoencoders and Super-Shapes

Padhy,

Suresh,

Chandrasekhar

2023

Preprint

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In this paper, we present a framework for multiscale topology optimization of fluid-flow devices. The objective is to minimize dissipated power, subject to a desired contact-area. The proposed strategy is to design optimal microstructures in individual finite element cells, while simultaneously optimizing the overall fluid flow. In particular, parameterized super-shapes are chosen here to represent microstructures since they exhibit a wide range of permeability and contact area. To avoid repeated homogenization, a finite set of these super-shapes are analyzed a priori, and a variational autoencoder (VAE) is trained on their fluid constitutive properties (permeability), contact area and shape parameters. The resulting differentiable latent space is integrated with a coordinate neural network to carry out a global multi-scale fluid flow optimization. The latent space enables the use of new microstructures that were not present in the original data-set. The proposed method is illustrated using numerous examples in 2D Overview of the proposed method: A dataset of shape parameters of super-shapes, contact areas, and homogenized permeability tensors is used to train a variational autoencoder (VAE). The resulting latent space is then used for global multiscale optimization of fluid flow.

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Section: Sensitivity Analysismentioning

confidence: 99%

TOMAS: Topology Optimization of Multiscale Fluid-Flow Devices using Variational Autoencoders and Super-Shapes

Padhy,

Suresh,

Chandrasekhar

2023

Preprint

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“…( 9)) with respect to the design variable (weights of the NN w). Fortunately, one can exploit modern automatic differentiation frameworks ( [58]) to avoid manual sensitivity calculations. In particular, expressing all our computation, including FEA within JAX ( [59]), results in an end-to-end differentiable framework, as illustrated in fig.…”

Section: Sensitivity Analysismentioning

confidence: 99%

GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks

Chandrasekhar¹,

Sridhara²,

Suresh³

2022

Preprint

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Multiscale topology optimization (M-TO) entails generating an optimal global topology, and an optimal set of microstructures at a smaller scale, for a physics-constrained problem. With the advent of additive manufacturing, M-TO has gained significant prominence. However, generating optimal microstructures at various locations can be computationally very expensive. As an alternate, graded multiscale topology optimization (GM-TO) has been proposed where one or more pre-selected and graded (parameterized) microstructural topologies are used to fill the domain optimally. This leads to a significant reduction in computation while retaining many of the benefits of M-TO. A successful GM-TO framework must: (1) be capable of efficiently handling numerous pre-selected microstructures, (2) be able to continuously switch between these microstructures during optimization, (3) ensure that the partition of unity is satisfied, and (4) discourage microstructure mixing at termination. In this paper, we propose to meet these requirements by exploiting the unique classification capacity of neural networks. Specifically, we propose a graded multiscale topology optimization using neural-network (GM-TOuNN) framework with the following features: (1) the number of design variables is only weakly dependent on the number of pre-selected microstructures, (2) it guarantees partition of unity while discouraging microstructure mixing, and (3) it supports automatic differentiation, thereby eliminating manual sensitivity analysis. The proposed framework is illustrated through several examples.

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“…The symbolic approach is limited to simple expressions, while manual derivation and implementation are arduous and error-prone, especially with the involvement of non-trivial objectives and/or constraints. Researchers have recently used automatic differentiation to quantify the sensitivities for TO problems [15].…”

Section: Introductionmentioning

confidence: 99%

“…Although using AD in TO stays limited to a few studies in the literature, it has been recently proven successful for several applications [15]. Dilgen et al [19] presented an approach for TO of turbulent flow systems, where the gradients are computed using automatic differentiation.…”

Section: Introductionmentioning

confidence: 99%

Multiphysics Topology Optimization Using Automatic Differentiation and Adjoint Method

He¹,

Abueidda²

2022

Preprint

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An essential step in solving any topology optimization problem is determining the sensitivities of the objective function and optimization constraints. Unfortunately, these sensitivities are usually derived and implemented manually. Nontrivial objective functions and constraints, especially with the involvement of material and geometric nonlinearities, need strenuous mathematical derivation, leading to error-prone implementation. Another intriguing approach to finding sensitivities is automatic differentiation. This paper uses the automatic differentiation and adjoint method to find the sensitivities for two multiphysics topology optimization problems: 1) thermoelasticity and 2) piezoelectricity. This approach is not limited to these examples and can be easily extended to other single- or multi-physics topology optimization problems.

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AuTO: a framework for Automatic differentiation in Topology Optimization

Cited by 38 publications

References 51 publications

TOMAS: Topology Optimization of Multiscale Fluid-Flow Devices using Variational Autoencoders and Super-Shapes

TOMAS: Topology Optimization of Multiscale Fluid-Flow Devices using Variational Autoencoders and Super-Shapes

GM-TOuNN: Graded Multiscale Topology Optimization using Neural Networks

Multiphysics Topology Optimization Using Automatic Differentiation and Adjoint Method

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