28 research outputs found
Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics
Three recent breakthroughs due to AI in arts and science serve as motivation:
An award winning digital image, protein folding, fast matrix multiplication.
Many recent developments in artificial neural networks, particularly deep
learning (DL), applied and relevant to computational mechanics (solid, fluids,
finite-element technology) are reviewed in detail. Both hybrid and pure machine
learning (ML) methods are discussed. Hybrid methods combine traditional PDE
discretizations with ML methods either (1) to help model complex nonlinear
constitutive relations, (2) to nonlinearly reduce the model order for efficient
simulation (turbulence), or (3) to accelerate the simulation by predicting
certain components in the traditional integration methods. Here, methods (1)
and (2) relied on Long-Short-Term Memory (LSTM) architecture, with method (3)
relying on convolutional neural networks. Pure ML methods to solve (nonlinear)
PDEs are represented by Physics-Informed Neural network (PINN) methods, which
could be combined with attention mechanism to address discontinuous solutions.
Both LSTM and attention architectures, together with modern and generalized
classic optimizers to include stochasticity for DL networks, are extensively
reviewed. Kernel machines, including Gaussian processes, are provided to
sufficient depth for more advanced works such as shallow networks with infinite
width. Not only addressing experts, readers are assumed familiar with
computational mechanics, but not with DL, whose concepts and applications are
built up from the basics, aiming at bringing first-time learners quickly to the
forefront of research. History and limitations of AI are recounted and
discussed, with particular attention at pointing out misstatements or
misconceptions of the classics, even in well-known references. Positioning and
pointing control of a large-deformable beam is given as an example.Comment: 275 pages, 158 figures. Appeared online on 2023.03.01 at
CMES-Computer Modeling in Engineering & Science
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A Perturbation Method for Dynamic Analysis of Under-Integrated Shell Elements
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Formulation of a Basic Building-Block Model for Interaction of High-Speed Vehicles on Flexible Structures
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Interaction Between High-Speed Moving Vehicles and Flexible Structures: An Analysis without Assumption of Known Vehicle Nominal Motion
Efficient simulation of coupled circuit-field problems: Generalized falk method
Abstract—The proposed generalized Falk (GF) method offers an extremely simple and convenient way to solve coupled circuit-field problems in circuit simulators by transforming the discretized governing-field equations into guaranteed stable-and-passive one-dimensional (1-D) equivalent-circuit systems, which are then combined with the circuit part of the overall coupled problem. More efficient than the traditional Lanczos-type methods, the GF method transforms a general finite-element system represented by a system of full matrices into an identity capacitance (mass) matrix and a tridiagonal conductance (stiffness) matrix. No positive poles are produced; all transformed matrices remain positive definite. The resulting 1-D equivalent-circuit system contains only resistors, capacitors, inductors, and current sources. Several numerical examples are provided. Index Terms—Converters, coordinate transformation, coupled circuit-field problems, electrothermal simulation, insulated gate bipolar transistor (IGBT) device, power electronics, reorthogonalization, stable and passive one-dimensional (1-D) equivalent thermal circuit. I