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Targeted Use of Deep Learning for Physics and Engineering
Published in Anuj Karpatne, Ramakrishnan Kannan, Vipin Kumar, Knowledge-Guided Machine Learning, 2023
Steven L. Brunton, J. Nathan Kutz
In addition to learning dynamics, deep learning provides a tremendous opportunity to uncover effective coordinate systems in which to represent the dynamics. Figure 2.3 shows two competing neural network architectures for learning coordinates. In the first approach, a deep autoencoder is used to uncover a low-dimensional latent space, where the dynamics are simplified. In many cases, simplified dynamics may mean linear, as in Koopman operator theory. In other cases, simplified dynamics will be sparse, having as few nonlinear terms as possible, as in the SINDy modeling procedure. In the second approach, the measured variables are lifted to a higher-dimensional space. This approach is consistent with many fields of machine learning, such as support vector machines (SVMs), where lifting to a higher dimensional space often makes tasks simpler; for example, in SVM, nonlinear classification problems often become linearly separable in higher dimensions.
Transfer Learning to Enhance Amenorrhea Status Prediction in Cancer and Fertility Data with Missing Values
Published in Sandeep Reddy, Artificial Intelligence, 2020
Xuetong Wu, Hadi Akbarzadeh Khorshidi, Uwe Aickelin, Zobaida Edib, Michelle Peate
The deep neural network is used to learn a common latent space where the correlation between two views is as high as possible. The neural network shown in Figure 13.3 is defined as ωs and ωT in both views. We denote the neural network models of source and target views as fs(⋅) and fT(⋅), and then, we aim to find the optimal wS* and wT*, where (wS*,wT*)=argmax(wS,wT)corr(fS(X^S;wS),fT(X^T;wT))
Deep Learning
Published in Seyedeh Leili Mirtaheri, Reza Shahbazian, Machine Learning Theory to Applications, 2022
Seyedeh Leili Mirtaheri, Reza Shahbazian
The autoecoders compress the input into a lower dimensional features and then reconstruct the output from this representation. The feature is a compact summary or compression of the input, also called the latent-space representation. An autoencoder consists of 3 components which are encoder, code and decoder. The encoder compresses the input and produces the code, the decoder then reconstructs the input only using this code. Therefore, to build an autoencoder you need an encoding method, a decoding method, and a loss function to compare the output with the target. Autoencoders are mainly a dimensionality reduction or compression algorithm with a couple of important properties. The first property is that they are data specific. In other words, the autoencoders are only able to meaningfully compress data similar to what they have been trained on. Since they learn features specific for the given training data, they are different than a standard data compression algorithm like gzip. Therefore, you cannot expect an autoencoder trained on handwritten digits to compress landscape photos. The second property of autoencoders is that they are lossy. The output of the autoencoder will not be exactly the same as the input, it will be a close but degraded representation. If you want lossless compression they are not the way to go. Remember that these networks are classify to unsupervised category of machine learning algorithm. To train an autoencoder you do not need to do anything fancy and just throw the raw input data at it. Autoencoders are considered an unsupervised learning technique since they don’t need explicit labels to train on. But to be more precise they are self-supervised because they generate their own labels from the training data.
DETONATE: Nonlinear Dynamic Evolution Modeling of Time-dependent 3-dimensional Point Cloud Profiles
Published in IISE Transactions, 2023
Michael Biehler, Daniel Lin, Jianjun Shi
To tackle this challenging problem, we take inspiration from the existing work in physics and dynamic control on Koopman-based models (Durbin and Kooperman, 2012; Otto and Rowley, 2019; Azencot et al., 2020; Han et al., 2020; Surana, 2020; Bevanda et al., 2021; Brunton et al. 2021; Lange et al., 2021; Wang et al., 2022). On a high level, Koopman theory is based on the insight that a nonlinear dynamic system can be fully described using an operator that describes how scalar functions propagate over time. The Koopman operator is linear, and thus, preferable in practice. However, the Koopman operator maps between function spaces, and it is infinite-dimensional. When the Koopman theory was discovered a century ago, this property limited its applications (Koopman 1931). However, advancements in computation and operator theory has led to a revived interest. Nowadays, machine learning can be utilized to learn a data transformation under which an approximate finite-dimensional Koopman operator is available. This data mapping can be represented by an autoencoder network, which embeds the high-dimensional input onto a low-dimensional latent space. In this latent space, the Koopman operator is approximated using a linear layer that encodes the dynamics (Takeishi et al., 2017).
PAEDID: Patch Autoencoder-based Deep Image Decomposition for pixel-level defective region segmentation
Published in IISE Transactions, 2023
Shancong Mou, Meng Cao, Haoping Bai, Ping Huang, Jianjun Shi, Jiulong Shan
AEs are widely used as an unsupervised nonlinear dimensional reduction tool in the context of deep learning (Hinton and Salakhutdinov, 2006). An AE consists of two components, an encoder network ), and a decoder network where and are the parameters of the encoder () and decoder (). The encoder learns a mapping from the high-dimensional input space to a low-dimensional latent space; the decoder learns to reconstruct the input from its latent representation. Given normal images with channels, i.e., where the AE learns the parameters and simultaneously by solving the following optimization problem: where is vectorization.
Computer-aided identification of stroke-associated motor impairments using a virtual reality augmented robotic system
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2022
Faranak Akbarifar, Sean P. Dukelow, Parvin Mousavi, Stephen H. Scott
We chose a simple deep architecture, namely an autoencoder, for capturing the non-linear relationship between movement parameters of Kinarm and a subject’s stroke/control status. Autoencoders produce a concise representation of data in their latent space while trying to reconstruct the input as precisely as possible. Hence, the latent space can be a reduced and efficient representation of the input data. In order to examine this non-linearity hypothesis, we also performed linear transformation and classification of the data using PCA/LDA. We developed a symmetric 3-layer autoencoder with latent dimension of 5. We used the latent layer as input to a classifier represented by a dense layer and a single-neuron sigmoid stroke predictor. We used mean squared error for reconstruction loss and binary cross entropy for classification loss. ReLU activation function and L2 regularisation were used for each autoencoder layer. The networks were simultaneously trained and optimised on two constraints, the reconstructed input and the class label, using the Adam optimisation function.