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Register a new userGalaxy Morphology Classification using Neural Ordinary Differential Equations
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We use a continuous depth version of the Residual Network (ResNet) model known as Neural ordinary differential equations (NODE) for the purpose of galaxy morphology classification. We applied this method to carry out supervised classification of galaxy images from the Galaxy Zoo 2 dataset, into five distinct classes, and obtained an accuracy of about 92% for most of the classes. Through our experiments, we show that NODE not only performs as well as other deep neural networks, but has additional advantages over them, which can prove very useful for next generation surveys. We also compare our result against ResNet. While ResNet and its variants suffer problems, such as time consuming architecture selection (e.g. the number of layers) and the requirement of large data for training, NODE does not have these requirements. Through various metrics, we conclude that the performance of NODE matches that of other models, despite using only one-third of the total number of parameters as compared to these other models.
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We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.
Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems. We first show the challenges of learning neural ODE in the classical stiff ODE systems of Robertsons problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems. We then present successful demonstrations in stiff systems of Robertsons problem and an air pollution problem. The demonstrations show that the usage of deep networks with rectified activations, proper scaling of the network outputs as well as loss functions, and stabilized gradient calculations are the key techniques enabling the learning of stiff neural ODE. The success of learning stiff neural ODE opens up possibilities of using neural ODEs in applications with widely varying time-scales, like chemical dynamics in energy conversion, environmental engineering, and the life sciences.
Optical satellite sensors cannot see the Earths surface through clouds. Despite the periodic revisit cycle, image sequences acquired by Earth observation satellites are therefore irregularly sampled in time. State-of-the-art methods for crop classification (and other time series analysis tasks) rely on techniques that implicitly assume regular temporal spacing between observations, such as recurrent neural networks (RNNs). We propose to use neural ordinary differential equations (NODEs) in combination with RNNs to classify crop types in irregularly spaced image sequences. The resulting ODE-RNN models consist of two steps: an update step, where a recurrent unit assimilates new input data into the models hidden state; and a prediction step, in which NODE propagates the hidden state until the next observation arrives. The prediction step is based on a continuous representation of the latent dynamics, which has several advantages. At the conceptual level, it is a more natural way to describe the mechanisms that govern the phenological cycle. From a practical point of view, it makes it possible to sample the system state at arbitrary points in time, such that one can integrate observations whenever they are available, and extrapolate beyond the last observation. Our experiments show that ODE-RNN indeed improves classification accuracy over common baselines such as LSTM, GRU, and temporal convolution. The gains are most prominent in the challenging scenario where only few observations are available (i.e., frequent cloud cover). Moreover, we show that the ability to extrapolate translates to better classification performance early in the season, which is important for forecasting.
Understanding morphological types of galaxies is a key parameter for studying their formation and evolution. Neural networks that have been used previously for galaxy morphology classification have some disadvantages, such as not being invariant under rotation. In this work, we studied the performance of Capsule Network, a recently introduced neural network architecture that is rotationally invariant and spatially aware, on the task of galaxy morphology classification. We designed two evaluation scenarios based on the answers from the question tree in the Galaxy Zoo project. In the first scenario, we used Capsule Network for regression and predicted probabilities for all of the questions. In the second scenario, we chose the answer to the first morphology question that had the highest user agreement as the class of the object and trained a Capsule Network classifier, where we also reconstructed galaxy images. We achieved promising results in both of these scenarios. Automated approaches such as the one introduced here will greatly decrease the workload of astronomers and will play a critical role in the upcoming large sky surveys.
Combinations of neural ODEs with recurrent neural networks (RNN), like GRU-ODE-Bayes or ODE-RNN are well suited to model irregularly observed time series. While those models outperform existing discrete-time approaches, no theoretical guarantees for their predictive capabilities are available. Assuming that the irregularly-sampled time series data originates from a continuous stochastic process, the $L^2$-optimal online prediction is the conditional expectation given the currently available information. We introduce the Neural Jump ODE (NJ-ODE) that provides a data-driven approach to learn, continuously in time, the conditional expectation of a stochastic process. Our approach models the conditional expectation between two observations with a neural ODE and jumps whenever a new observation is made. We define a novel training framework, which allows us to prove theoretical guarantees for the first time. In particular, we show that the output of our model converges to the $L^2$-optimal prediction. This can be interpreted as solution to a special filtering problem. We provide experiments showing that the theoretical results also hold empirically. Moreover, we experimentally show that our model outperforms the baselines in more complex learning tasks and give comparisons on real-world datasets.
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