arXiv subjects

Pavlos Protopapas

Publications and source records attributed to Pavlos Protopapas.

At least 73 records · Page 4Linked to original sources

arXiv2021

Unsupervised Reservoir Computing for Solving Ordinary Differential Equations

There is a wave of interest in using unsupervised neural networks for solving differential equations. The existing methods are based on feed-forward networks, {while} recurrent neural network differential equation solvers have not yet been reported. We introduce an unsupervised reservoir computing (RC), an echo-state recurrent neural network capable of discovering approximate solutions that satisfy ordinary differential equations (ODEs). We suggest an approach to calculate time derivatives of recurrent neural network outputs without using backpropagation. The internal weights of an RC are fixed, while only a linear output layer is trained, yielding efficient training. However, RC performance strongly depends on finding the optimal hyper-parameters, which is a computationally expensive process. We use Bayesian optimization to efficiently discover optimal sets in a high-dimensional hyper-parameter space and numerically show that one set is robust and can be used to solve an ODE for different initial conditions and time ranges. A closed-form formula for the optimal output weights is derived to solve first order linear equations in a backpropagation-free learning process. We extend the RC approach by solving nonlinear system of ODEs using a hybrid optimization method consisting of gradient descent and Bayesian optimization. Evaluation of linear and nonlinear systems of equations demonstrates the efficiency of the RC ODE solver.

cs.LG↗

arXiv2021

Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known apriori. Despite this success, many real world dynamical systems are non-autonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such non-autonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed \emph{port-Hamiltonian neural network} can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.

cs.LG↗

arXiv2021

Convolutional Neural Network Models and Interpretability for the Anisotropic Reynolds Stress Tensor in Turbulent One-dimensional Flows

The Reynolds-averaged Navier-Stokes (RANS) equations are widely used in turbulence applications. They require accurately modeling the anisotropic Reynolds stress tensor, for which traditional Reynolds stress closure models only yield reliable results in some flow configurations. In the last few years, there has been a surge of work aiming at using data-driven approaches to tackle this problem. The majority of previous work has focused on the development of fully-connected networks for modeling the anisotropic Reynolds stress tensor. In this paper, we expand upon recent work for turbulent channel flow and develop new convolutional neural network (CNN) models that are able to accurately predict the normalized anisotropic Reynolds stress tensor. We apply the new CNN model to a number of one-dimensional turbulent flows. Additionally, we present interpretability techniques that help drive the model design and provide guidance on the model behavior in relation to the underlying physics.

physics.flu-dyn↗

arXiv2021

StelNet: Hierarchical Neural Network for Automatic Inference in Stellar Characterization

Characterizing the fundamental parameters of stars from observations is crucial for studying the stars themselves, their planets, and the galaxy as a whole. Stellar evolution theory predicting the properties of stars as a function of stellar age and mass enables translating observables into physical stellar parameters by fitting the observed data to synthetic isochrones. However, the complexity of overlapping evolutionary tracks often makes this task numerically challenging, and with a precision that can be highly variable, depending on the area of the parameter space the observation lies in. This work presents StelNet, a Deep Neural Network trained on stellar evolutionary tracks that quickly and accurately predicts mass and age from absolute luminosity and effective temperature for stars with close to solar metallicity. The underlying model makes no assumption on the evolutionary stage and includes the pre-main sequence phase. We use bootstrapping and train many models to quantify the uncertainty of the model. To break the model's intrinsic degeneracy resulting from overlapping evolutionary paths, we also built a hierarchical model that retrieves realistic posterior probability distributions of the stellar mass and age. We further test and train StelNet using a sample of stars with well-determined masses and ages from the literature.

astro-ph.SR↗

arXiv2021

Matching Embeddings for Domain Adaptation

In this work we address the problem of transferring knowledge obtained from a vast annotated source domain to a low labeled target domain. We propose Adversarial Variational Domain Adaptation (AVDA), a semi-supervised domain adaptation method based on deep variational embedded representations. We use approximate inference and domain adversarial methods to map samples from source and target domains into an aligned class-dependent embedding defined as a Gaussian Mixture Model. AVDA works as a classifier and considers a generative model that helps this classification. We used digits dataset for experimentation. Our results show that on a semi-supervised few-shot scenario our model outperforms previous methods in most of the adaptation tasks, even using a fewer number of labeled samples per class on target domain.

cs.LG↗

arXiv2021

A New Artificial Neuron Proposal with Trainable Simultaneous Local and Global Activation Function

The activation function plays a fundamental role in the artificial neural network learning process. However, there is no obvious choice or procedure to determine the best activation function, which depends on the problem. This study proposes a new artificial neuron, named global-local neuron, with a trainable activation function composed of two components, a global and a local. The global component term used here is relative to a mathematical function to describe a general feature present in all problem domain. The local component is a function that can represent a localized behavior, like a transient or a perturbation. This new neuron can define the importance of each activation function component in the learning phase. Depending on the problem, it results in a purely global, or purely local, or a mixed global and local activation function after the training phase. Here, the trigonometric sine function was employed for the global component and the hyperbolic tangent for the local component. The proposed neuron was tested for problems where the target was a purely global function, or purely local function, or a composition of two global and local functions. Two classes of test problems were investigated, regression problems and differential equations solving. The experimental tests demonstrated the Global-Local Neuron network's superior performance, compared with simple neural networks with sine or hyperbolic tangent activation function, and with a hybrid network that combines these two simple neural networks.

cs.NE↗

arXiv2020

Learning a Reduced Basis of Dynamical Systems using an Autoencoder

Machine learning models have emerged as powerful tools in physics and engineering. Although flexible, a fundamental challenge remains on how to connect new machine learning models with known physics. In this work, we present an autoencoder with latent space penalization, which discovers finite dimensional manifolds underlying the partial differential equations of physics. We test this method on the Kuramoto-Sivashinsky (K-S), Korteweg-de Vries (KdV), and damped KdV equations. We show that the resulting optimal latent space of the K-S equation is consistent with the dimension of the inertial manifold. The results for the KdV equation imply that there is no reduced latent space, which is consistent with the truly infinite dimensional dynamics of the KdV equation. In the case of the damped KdV equation, we find that the number of active dimensions decreases with increasing damping coefficient. We then uncover a nonlinear basis representing the manifold of the latent space for the K-S equation.

physics.comp-ph↗

arXiv2020

Semi-supervised Neural Networks solve an inverse problem for modeling Covid-19 spread

Studying the dynamics of COVID-19 is of paramount importance to understanding the efficiency of restrictive measures and develop strategies to defend against upcoming contagion waves. In this work, we study the spread of COVID-19 using a semi-supervised neural network and assuming a passive part of the population remains isolated from the virus dynamics. We start with an unsupervised neural network that learns solutions of differential equations for different modeling parameters and initial conditions. A supervised method then solves the inverse problem by estimating the optimal conditions that generate functions to fit the data for those infected by, recovered from, and deceased due to COVID-19. This semi-supervised approach incorporates real data to determine the evolution of the spread, the passive population, and the basic reproduction number for different countries.

cs.LG↗

arXiv2020

Unsupervised Neural Networks for Quantum Eigenvalue Problems

Eigenvalue problems are critical to several fields of science and engineering. We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems with solutions that identically satisfy the boundary conditions. A scanning mechanism is embedded allowing the method to find an arbitrary number of solutions. The network optimization is data-free and depends solely on the predictions. The unsupervised method is used to solve the quantum infinite well and quantum oscillator eigenvalue problems.

physics.comp-ph↗

arXiv2020

MPCC: Matching Priors and Conditionals for Clustering

Clustering is a fundamental task in unsupervised learning that depends heavily on the data representation that is used. Deep generative models have appeared as a promising tool to learn informative low-dimensional data representations. We propose Matching Priors and Conditionals for Clustering (MPCC), a GAN-based model with an encoder to infer latent variables and cluster categories from data, and a flexible decoder to generate samples from a conditional latent space. With MPCC we demonstrate that a deep generative model can be competitive/superior against discriminative methods in clustering tasks surpassing the state of the art over a diverse set of benchmark datasets. Our experiments show that adding a learnable prior and augmenting the number of encoder updates improve the quality of the generated samples, obtaining an inception score of 9.49 $\pm$ 0.15 and improving the Fréchet inception distance over the state of the art by a 46.9% in CIFAR10.

cs.LG↗

arXiv2020

Unsupervised Learning of Solutions to Differential Equations with Generative Adversarial Networks

Solutions to differential equations are of significant scientific and engineering relevance. Recently, there has been a growing interest in solving differential equations with neural networks. This work develops a novel method for solving differential equations with unsupervised neural networks that applies Generative Adversarial Networks (GANs) to \emph{learn the loss function} for optimizing the neural network. We present empirical results showing that our method, which we call Differential Equation GAN (DEQGAN), can obtain multiple orders of magnitude lower mean squared errors than an alternative unsupervised neural network method based on (squared) $L_2$, $L_1$, and Huber loss functions. Moreover, we show that DEQGAN achieves solution accuracy that is competitive with traditional numerical methods. Finally, we analyze the stability of our approach and find it to be sensitive to the selection of hyperparameters, which we provide in the appendix. Code available at https://github.com/dylanrandle/denn. Please address any electronic correspondence to dylanrandle@alumni.harvard.edu.

cs.LG↗

arXiv2020

Solving Differential Equations Using Neural Network Solution Bundles

The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution whose values are computed at discrete times. When many varied solutions with different initial conditions to the ODE are required, the computational cost can become significant. We propose that a neural network be used as a solution bundle, a collection of solutions to an ODE for various initial states and system parameters. The neural network solution bundle is trained with an unsupervised loss that does not require any prior knowledge of the sought solutions, and the resulting object is differentiable in initial conditions and system parameters. The solution bundle exhibits fast, parallelizable evaluation of the system state, facilitating the use of Bayesian inference for parameter estimation in real dynamical systems.

cs.LG↗

arXiv2020

Application of Machine Learning to Predict the Risk of Alzheimer's Disease: An Accurate and Practical Solution for Early Diagnostics

Alzheimer's Disease (AD) ravages the cognitive ability of more than 5 million Americans and creates an enormous strain on the health care system. This paper proposes a machine learning predictive model for AD development without medical imaging and with fewer clinical visits and tests, in hopes of earlier and cheaper diagnoses. That earlier diagnoses could be critical in the effectiveness of any drug or medical treatment to cure this disease. Our model is trained and validated using demographic, biomarker and cognitive test data from two prominent research studies: Alzheimer's Disease Neuroimaging Initiative (ADNI) and Australian Imaging, Biomarker Lifestyle Flagship Study of Aging (AIBL). We systematically explore different machine learning models, pre-processing methods and feature selection techniques. The most performant model demonstrates greater than 90% accuracy and recall in predicting AD, and the results generalize across sub-studies of ADNI and to the independent AIBL study. We also demonstrate that these results are robust to reducing the number of clinical visits or tests per visit. Using a metaclassification algorithm and longitudinal data analysis we are able to produce a "lean" diagnostic protocol with only 3 tests and 4 clinical visits that can predict Alzheimer's development with 87% accuracy and 79% recall. This novel work can be adapted into a practical early diagnostic tool for predicting the development of Alzheimer's that maximizes accuracy while minimizing the number of necessary diagnostic tests and clinical visits.

q-bio.QM↗

arXiv2020

An Automated Pipeline for Character and Relationship Extraction from Readers' Literary Book Reviews on Goodreads.com

Reader reviews of literary fiction on social media, especially those in persistent, dedicated forums, create and are in turn driven by underlying narrative frameworks. In their comments about a novel, readers generally include only a subset of characters and their relationships, thus offering a limited perspective on that work. Yet in aggregate, these reviews capture an underlying narrative framework comprised of different actants (people, places, things), their roles, and interactions that we label the "consensus narrative framework". We represent this framework in the form of an actant-relationship story graph. Extracting this graph is a challenging computational problem, which we pose as a latent graphical model estimation problem. Posts and reviews are viewed as samples of sub graphs/networks of the hidden narrative framework. Inspired by the qualitative narrative theory of Greimas, we formulate a graphical generative Machine Learning (ML) model where nodes represent actants, and multi-edges and self-loops among nodes capture context-specific relationships. We develop a pipeline of interlocking automated methods to extract key actants and their relationships, and apply it to thousands of reviews and comments posted on Goodreads.com. We manually derive the ground truth narrative framework from SparkNotes, and then use word embedding tools to compare relationships in ground truth networks with our extracted networks. We find that our automated methodology generates highly accurate consensus narrative frameworks: for our four target novels, with approximately 2900 reviews per novel, we report average coverage/recall of important relationships of > 80% and an average edge detection rate of >89\%. These extracted narrative frameworks can generate insight into how people (or classes of people) read and how they recount what they have read to others.

cs.CL↗

arXiv2020

Gravitational Wave Detection and Information Extraction via Neural Networks

Laser Interferometer Gravitational-Wave Observatory (LIGO) was the first laboratory to measure the gravitational waves. It was needed an exceptional experimental design to measure distance changes much less than a radius of a proton. In the same way, the data analyses to confirm and extract information is a tremendously hard task. Here, it is shown a computational procedure base on artificial neural networks to detect a gravitation wave event and extract the knowledge of its ring-down time from the LIGO data. With this proposal, it is possible to make a probabilistic thermometer for gravitational wave detection and obtain physical information about the astronomical body system that created the phenomenon. Here, the ring-down time is determined with a direct data measure, without the need to use numerical relativity techniques and high computational power.

gr-qc↗

arXiv2020

Scalable End-to-end Recurrent Neural Network for Variable star classification

During the last decade, considerable effort has been made to perform automatic classification of variable stars using machine learning techniques. Traditionally, light curves are represented as a vector of descriptors or features used as input for many algorithms. Some features are computationally expensive, cannot be updated quickly and hence for large datasets such as the LSST cannot be applied. Previous work has been done to develop alternative unsupervised feature extraction algorithms for light curves, but the cost of doing so still remains high. In this work, we propose an end-to-end algorithm that automatically learns the representation of light curves that allows an accurate automatic classification. We study a series of deep learning architectures based on Recurrent Neural Networks and test them in automated classification scenarios. Our method uses minimal data preprocessing, can be updated with a low computational cost for new observations and light curves, and can scale up to massive datasets. We transform each light curve into an input matrix representation whose elements are the differences in time and magnitude, and the outputs are classification probabilities. We test our method in three surveys: OGLE-III, Gaia and WISE. We obtain accuracies of about $95\%$ in the main classes and $75\%$ in the majority of subclasses. We compare our results with the Random Forest classifier and obtain competitive accuracies while being faster and scalable. The analysis shows that the computational complexity of our approach grows up linearly with the light curve size, while the traditional approach cost grows as $N\log{(N)}$.

astro-ph.IM↗

arXiv2019

Streaming Classification of Variable Stars

In the last years, automatic classification of variable stars has received substantial attention. Using machine learning techniques for this task has proven to be quite useful. Typically, machine learning classifiers used for this task require to have a fixed training set, and the training process is performed offline. Upcoming surveys such as the Large Synoptic Survey Telescope (LSST) will generate new observations daily, where an automatic classification system able to create alerts online will be mandatory. A system with those characteristics must be able to update itself incrementally. Unfortunately, after training, most machine learning classifiers do not support the inclusion of new observations in light curves, they need to re-train from scratch. Naively re-training from scratch is not an option in streaming settings, mainly because of the expensive pre-processing routines required to obtain a vector representation of light curves (features) each time we include new observations. In this work, we propose a streaming probabilistic classification model; it uses a set of newly designed features that work incrementally. With this model, we can have a machine learning classifier that updates itself in real time with new observations. To test our approach, we simulate a streaming scenario with light curves from CoRot, OGLE and MACHO catalogs. Results show that our model achieves high classification performance, staying an order of magnitude faster than traditional classification approaches.

astro-ph.IM↗

arXiv2019

An Information Theory Approach on Deciding Spectroscopic Follow Ups

Classification and characterization of variable phenomena and transient phenomena are critical for astrophysics and cosmology. These objects are commonly studied using photometric time series or spectroscopic data. Given that many ongoing and future surveys are in time-domain and given that adding spectra provide further insights but requires more observational resources, it would be valuable to know which objects should we prioritize to have spectrum in addition to time series. We propose a methodology in a probabilistic setting that determines a-priory which objects are worth taking spectrum to obtain better insights, where we focus 'insight' as the type of the object (classification). Objects for which we query its spectrum are reclassified using their full spectrum information. We first train two classifiers, one that uses photometric data and another that uses photometric and spectroscopic data together. Then for each photometric object we estimate the probability of each possible spectrum outcome. We combine these models in various probabilistic frameworks (strategies) which are used to guide the selection of follow up observations. The best strategy depends on the intended use, whether it is getting more confidence or accuracy. For a given number of candidate objects (127, equal to 5% of the dataset) for taking spectra, we improve 37% class prediction accuracy as opposed to 20% of a non-naive (non-random) best base-line strategy. Our approach provides a general framework for follow-up strategies and can be extended beyond classification and to include other forms of follow-ups beyond spectroscopy.

astro-ph.IM↗