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Register a new userConvolutional Autoencoders for Reduced-Order Modeling
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Added by
Sreeram Venkat
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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In the construction of reduced-order models for dynamical systems, linear projection methods, such as proper orthogonal decompositions, are commonly employed. However, for many dynamical systems, the lower dimensional representation of the state space can most accurately be described by a textit{nonlinear} manifold. Previous research has shown that deep learning can provide an efficient method for performing nonlinear dimension reduction, though they are dependent on the availability of training data and are often problem-specific citep[see][]{carlberg_ca}. Here, we utilize randomized training data to create and train convolutional autoencoders that perform nonlinear dimension reduction for the wave and Kuramoto-Shivasinsky equations. Moreover, we present training methods that are independent of full-order model samples and use the manifold least-squares Petrov-Galerkin projection method to define a reduced-order model for the heat, wave, and Kuramoto-Shivasinsky equations using the same autoencoder.
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Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as a non-intrusive method for propagating the latent-space dynamics in reduced order models. Here, we investigate employing deep autoencoders for discovering the reduced basis representation, the dynamics of which are then approximated by NODE. The ability of deep autoencoders to represent the latent-space is compared to the traditional proper orthogonal decomposition (POD) approach, again in conjunction with NODE for capturing the dynamics. Additionally, we compare their behavior with two classical non-intrusive methods based on POD and radial basis function interpolation as well as dynamic mode decomposition. The test problems we consider include incompressible flow around a cylinder as well as a real-world application of shallow water hydrodynamics in an estuarine system. Our findings indicate that deep autoencoders can leverage nonlinear manifold learning to achieve a highly efficient compression of spatial information and define a latent-space that appears to be more suitable for capturing the temporal dynamics through the NODE framework.
This paper reports a reduced-order modeling framework of bladed disks on a rotating shaft to simulate the vibration signature of faults like cracks in different components aiming towards simulated data-driven machine learning. We have employed lumped and one-dimensional analytical models of the subcomponents for better insight into the complex dynamic response. The framework seeks to address some of the challenges encountered in analyzing and optimizing fault detection and identification schemes for health monitoring of rotating turbomachinery, including aero-engines. We model the bladed disks and shafts by combining lumped elements and one-dimensional finite elements, leading to a coupled system. The simulation results are in good agreement with previously published data. We model the cracks in a blade analytically with their effective reduced stiffness approximation. Multiple types of faults are modeled, including cracks in the blades of single and two-stage bladed disks, Fan Blade Off (FBO), and Foreign Object Damage (FOD). We have applied aero-engine operational loading conditions to simulate realistic scenarios of online health monitoring. The proposed reduced-order simulation framework will have applications in probabilistic signal modeling, machine learning toward fault signature identification, and parameter estimation with measured vibration signals.
In this paper, we present a novel neuroevolutionary method to identify the architecture and hyperparameters of convolutional autoencoders. Remarkably, we used a hypervolume indicator in the context of neural architecture search for autoencoders, for the first time to our current knowledge. Results show that images were compressed by a factor of more than 10, while still retaining enough information to achieve image classification for the majority of the tasks. Thus, this new approach can be used to speed up the AutoML pipeline for image compression.
In this paper we propose a convolutional autoencoder to address the problem of motion infilling for 3D human motion data. Given a start and end sequence, motion infilling aims to complete the missing gap in between, such that the filled in poses plausibly forecast the start sequence and naturally transition into the end sequence. To this end, we propose a single, end-to-end trainable convolutional autoencoder. We show that a single model can be used to create natural transitions between different types of activities. Furthermore, our method is not only able to fill in entire missing frames, but it can also be used to complete gaps where partial poses are available (e.g. from end effectors), or to clean up other forms of noise (e.g. Gaussian). Also, the model can fill in an arbitrary number of gaps that potentially vary in length. In addition, no further post-processing on the models outputs is necessary such as smoothing or closing discontinuities at the end of the gap. At the heart of our approach lies the idea to cast motion infilling as an inpainting problem and to train a convolutional de-noising autoencoder on image-like representations of motion sequences. At training time, blocks of columns are removed from such images and we ask the model to fill in the gaps. We demonstrate the versatility of the approach via a number of complex motion sequences and report on thorough evaluations performed to better understand the capabilities and limitations of the proposed approach.
Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics, which pose challenges to network management and operation. This chapter provides an overview of reduced-order modeling techniques that are developed recently for simplifying complex dynamical networks. In the first part, clustering-based approaches are reviewed, which aim to reduce the network scale, i.e., find a simplified network with a fewer number of nodes. The second part presents structure-preserving methods based on generalized balanced truncation, which can reduce the dynamics of each subsystem.
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