Computational Mechanics with Deep Learning

Yagawa, Genki; Oishi, Atsuya

doi:10.1007/978-3-031-11847-0_3

Cited by 2 publications

(3 citation statements)

References 156 publications

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“…1 Number of publications concerning artificial intelligence and some of its subtopics since 1999 showing the exponential growth of literature within the field. Illustration inspired by [40] the data, but to generate statistically similar data. This is useful in diversifying the design space or enhancing a data set to train surrogate models.…”

Section: Taxonomy Of Deep Learning Techniques In Computational Mechanicsmentioning

confidence: 99%

“…Further applications of RNNs are full waveform inversion [188][189][190], high-dimensional chaotic systems [191], fluid flow [40,192], fracture propagation [116], sensor signals in non-linear dynamic systems [193,194], and settlement field predictions induced by tunneling [195], which was extended to damage prediction in affected structures [196,197]. RNNs are often combined with reduced order model encodings [198], where the dynamics are predicted on the reduced latent space, as demonstrated in [199][200][201][202][203][204][205].…”

Section: Recurrent Neural Networkmentioning

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: Taxonomy Of Deep Learning Techniques In Computational Mechanicsmentioning

confidence: 99%

Section: Recurrent Neural Networkmentioning

confidence: 99%

Deep learning in computational mechanics: a review

Herrmann,

Kollmannsberger

2024

Comput Mech

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“…Examples comprise virtually any problem where approximation of functions is required, but also efficient reduced order modelling e.g. in fluid mechanics, the deep Ritz method, or more specific numerical tasks such as optimisation of the quadrature rule for the computation of the finite element stiffness matrix, acceleration of simulations on coarser meshes by learning appropriate collocation points, and replacing expensive numerical computations with data-driven predictions [9,12,[25][26][27]. This recent literature is evidence that neural networks can be used successfully as surrogate models for the solution operators of various differential equations.…”

Section: Introductionmentioning

confidence: 99%

Neural networks for the approximation of Euler's elastica

Celledoni,

Çokaj,

Leone

et al. 2023

Preprint

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Euler's elastica is a classical model of flexible slender structures, relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions of this problem can be challenging due to nonlinearity and constraints. We here present two neural network based approaches for the simulation of this Euler's elastica. Starting from a data set of solutions of the discretised static equilibria, we train the neural networks to produce solutions for unseen boundary conditions. We present a \textit{discrete} approach learning discrete solutions from the discrete data. We then consider a \textit{continuous} approach using the same training data set, but learning continuous solutions to the problem. We present numerical evidence that the proposed neural networks can effectively approximate configurations of the planar Euler's elastica for a range of different boundary conditions.

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Computational Mechanics with Deep Learning

Cited by 2 publications

References 156 publications

Deep learning in computational mechanics: a review

Deep learning in computational mechanics: a review

Neural networks for the approximation of Euler's elastica

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