arXiv subjects

Pavlos Protopapas

Publications and source records attributed to Pavlos Protopapas.

At least 55 records · Page 3Linked to original sources

arXiv2023

Positional Encodings for Light Curve Transformers: Playing with Positions and Attention

We conducted empirical experiments to assess the transferability of a light curve transformer to datasets with different cadences and magnitude distributions using various positional encodings (PEs). We proposed a new approach to incorporate the temporal information directly to the output of the last attention layer. Our results indicated that using trainable PEs lead to significant improvements in the transformer performances and training times. Our proposed PE on attention can be trained faster than the traditional non-trainable PE transformer while achieving competitive results when transfered to other datasets.

astro-ph.IM↗

arXiv2023

Residual-based error bound for physics-informed neural networks

Neural networks are universal approximators and are studied for their use in solving differential equations. However, a major criticism is the lack of error bounds for obtained solutions. This paper proposes a technique to rigorously evaluate the error bound of Physics-Informed Neural Networks (PINNs) on most linear ordinary differential equations (ODEs), certain nonlinear ODEs, and first-order linear partial differential equations (PDEs). The error bound is based purely on equation structure and residual information and does not depend on assumptions of how well the networks are trained. We propose algorithms that bound the error efficiently. Some proposed algorithms provide tighter bounds than others at the cost of longer run time.

cs.CE↗

arXiv2023

Cosmology-informed neural networks to solve the background dynamics of the Universe

The field of machine learning has drawn increasing interest from various other fields due to the success of its methods at solving a plethora of different problems. An application of these has been to train artificial neural networks to solve differential equations without the need of a numerical solver. This particular application offers an alternative to conventional numerical methods, with advantages such as lower memory required to store solutions, parallelization, and, in some cases, a lower overall computational cost than its numerical counterparts. In this work, we train artificial neural networks to represent a bundle of solutions of the differential equations that govern the background dynamics of the Universe for four different models. The models we have chosen are $Λ\mathrm{CDM}$, the Chevallier-Polarski-Linder parametric dark energy model, a quintessence model with an exponential potential, and the Hu-Sawicki $f(R)$ model. We use the solutions that the networks provide to perform statistical analyses to estimate the values of each model's parameters with observational data; namely, estimates of the Hubble parameter from cosmic chronometers, type Ia supernovae data from the Pantheon compilation, and measurements from baryon acoustic oscillations. The results we obtain for all models match similar estimations done in the literature using numerical solvers. In addition, we estimate the error of the solutions that the trained networks provide by comparing them with the analytical solution when there is one, or to a high-precision numerical solution when there is not. Through these estimations we find that the error of the solutions is at most $\sim1\%$ in the region of the parameter space that concerns the $95\%$ confidence regions that we find using the data, for all models and all statistical analyses performed in this work.

astro-ph.CO↗

arXiv2022

Error-Aware B-PINNs: Improving Uncertainty Quantification in Bayesian Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) are gaining popularity as a method for solving differential equations. While being more feasible in some contexts than the classical numerical techniques, PINNs still lack credibility. A remedy for that can be found in Uncertainty Quantification (UQ) which is just beginning to emerge in the context of PINNs. Assessing how well the trained PINN complies with imposed differential equation is the key to tackling uncertainty, yet there is lack of comprehensive methodology for this task. We propose a framework for UQ in Bayesian PINNs (B-PINNs) that incorporates the discrepancy between the B-PINN solution and the unknown true solution. We exploit recent results on error bounds for PINNs on linear dynamical systems and demonstrate the predictive uncertainty on a class of linear ODEs.

cs.LG↗

arXiv2022

Improving astroBERT using Semantic Textual Similarity

The NASA Astrophysics Data System (ADS) is an essential tool for researchers that allows them to explore the astronomy and astrophysics scientific literature, but it has yet to exploit recent advances in natural language processing. At ADASS 2021, we introduced astroBERT, a machine learning language model tailored to the text used in astronomy papers in ADS. In this work we: - announce the first public release of the astroBERT language model; - show how astroBERT improves over existing public language models on astrophysics specific tasks; - and detail how ADS plans to harness the unique structure of scientific papers, the citation graph and citation context, to further improve astroBERT.

cs.CL↗

arXiv2022

Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning approach for PINNs and introduce a multi-head model to efficiently obtain accurate solutions to nonlinear systems of ordinary differential equations with random potentials. In particular, we apply the method to simulate stochastic branched flows, a universal phenomenon in random wave dynamics. Finally, we compare the results achieved by feed forward and GAN-based PINNs on two physically relevant transfer learning tasks and show that our methods provide significant computational speedups in comparison to standard PINNs trained from scratch.

cs.LG↗

arXiv2022

DEQGAN: Learning the Loss Function for PINNs with Generative Adversarial Networks

Solutions to differential equations are of significant scientific and engineering relevance. Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving differential equations, but they lack a theoretical justification for the use of any particular loss function. This work presents Differential Equation GAN (DEQGAN), a novel method for solving differential equations using generative adversarial networks to "learn the loss function" for optimizing the neural network. Presenting results on a suite of twelve ordinary and partial differential equations, including the nonlinear Burgers', Allen-Cahn, Hamilton, and modified Einstein's gravity equations, we show that DEQGAN can obtain multiple orders of magnitude lower mean squared errors than PINNs that use $L_2$, $L_1$, and Huber loss functions. We also show that DEQGAN achieves solution accuracies that are competitive with popular numerical methods. Finally, we present two methods to improve the robustness of DEQGAN to different hyperparameter settings.

cs.LG↗

arXiv2022

RcTorch: a PyTorch Reservoir Computing Package with Automated Hyper-Parameter Optimization

Reservoir computers (RCs) are among the fastest to train of all neural networks, especially when they are compared to other recurrent neural networks. RC has this advantage while still handling sequential data exceptionally well. However, RC adoption has lagged other neural network models because of the model's sensitivity to its hyper-parameters (HPs). A modern unified software package that automatically tunes these parameters is missing from the literature. Manually tuning these numbers is very difficult, and the cost of traditional grid search methods grows exponentially with the number of HPs considered, discouraging the use of the RC and limiting the complexity of the RC models which can be devised. We address these problems by introducing RcTorch, a PyTorch based RC neural network package with automated HP tuning. Herein, we demonstrate the utility of RcTorch by using it to predict the complex dynamics of a driven pendulum being acted upon by varying forces. This work includes coding examples. Example Python Jupyter notebooks can be found on our GitHub repository https://github.com/blindedjoy/RcTorch and documentation can be found at https://rctorch.readthedocs.io/.

cs.LG↗

arXiv2022

One-Shot Transfer Learning of Physics-Informed Neural Networks

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed Neural Networks (PINNs) to tackle such problems as they provide numerous benefits over traditional numerical approaches. Despite their potential benefits for solving differential equations, transfer learning has been under explored. In this study, we present a general framework for transfer learning PINNs that results in one-shot inference for linear systems of both ordinary and partial differential equations. This means that highly accurate solutions to many unknown differential equations can be obtained instantaneously without retraining an entire network. We demonstrate the efficacy of the proposed deep learning approach by solving several real-world problems, such as first- and second-order linear ordinary equations, the Poisson equation, and the time-dependent Schrodinger complex-value partial differential equation.

cs.LG↗

arXiv2022

Evaluating Error Bound for Physics-Informed Neural Networks on Linear Dynamical Systems

There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore, it is less credible than its traditional counterparts, such as the finite difference method. This paper shows that one can mathematically derive explicit error bounds for physics-informed neural networks trained on a class of linear systems of differential equations. More importantly, evaluating such error bounds only requires evaluating the differential equation residual infinity norm over the domain of interest. Our work shows a link between network residuals, which is known and used as loss function, and the absolute error of solution, which is generally unknown. Our approach is semi-phenomonological and independent of knowledge of the actual solution or the complexity or architecture of the network. Using the method of manufactured solution on linear ODEs and system of linear ODEs, we empirically verify the error evaluation algorithm and demonstrate that the actual error strictly lies within our derived bound.

cs.NE↗

arXiv2022

Improving Astronomical Time-series Classification via Data Augmentation with Generative Adversarial Networks

Due to the latest advances in technology, telescopes with significant sky coverage will produce millions of astronomical alerts per night that must be classified both rapidly and automatically. Currently, classification consists of supervised machine learning algorithms whose performance is limited by the number of existing annotations of astronomical objects and their highly imbalanced class distributions. In this work, we propose a data augmentation methodology based on Generative Adversarial Networks (GANs) to generate a variety of synthetic light curves from variable stars. Our novel contributions, consisting of a resampling technique and an evaluation metric, can assess the quality of generative models in unbalanced datasets and identify GAN-overfitting cases that the Fréchet Inception Distance does not reveal. We applied our proposed model to two datasets taken from the Catalina and Zwicky Transient Facility surveys. The classification accuracy of variable stars is improved significantly when training with synthetic data and testing with real data with respect to the case of using only real data.

astro-ph.IM↗

arXiv2022

Encoding Involutory Invariances in Neural Networks

In certain situations, neural networks are trained upon data that obey underlying symmetries. However, the predictions do not respect the symmetries exactly unless embedded in the network structure. In this work, we introduce architectures that embed a special kind of symmetry namely, invariance with respect to involutory linear/affine transformations up to parity $p=\pm 1$. We provide rigorous theorems to show that the proposed network ensures such an invariance and present qualitative arguments for a special universal approximation theorem. An adaption of our techniques to CNN tasks for datasets with inherent horizontal/vertical reflection symmetry is demonstrated. Extensive experiments indicate that the proposed model outperforms baseline feed-forward and physics-informed neural networks while identically respecting the underlying symmetry.

cs.LG↗

arXiv2022

Hamiltonian neural networks for solving equations of motion

There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine learning method where the optimization process of the network depends solely on the predicted functions without using any ground truth data. The model learns solutions that satisfy, up to an arbitrarily small error, Hamilton's equations and, therefore, conserve the Hamiltonian invariants. The choice of an appropriate activation function drastically improves the predictability of the network. Moreover, an error analysis is derived and states that the numerical errors depend on the overall network performance. The Hamiltonian network is then employed to solve the equations for the nonlinear oscillator and the chaotic Henon-Heiles dynamical system. In both systems, a symplectic Euler integrator requires two orders more evaluation points than the Hamiltonian network in order to achieve the same order of the numerical error in the predicted phase space trajectories.

physics.comp-ph↗

arXiv2022

Physics-Informed Neural Networks for Quantum Eigenvalue Problems

Eigenvalue problems are critical to several fields of science and engineering. We expand on the method of using unsupervised neural networks for discovering eigenfunctions and eigenvalues for differential eigenvalue problems. The obtained solutions are given in an analytical and differentiable form that identically satisfies the desired boundary conditions. The network optimization is data-free and depends solely on the predictions of the neural network. We introduce two physics-informed loss functions. The first, called ortho-loss, motivates the network to discover pair-wise orthogonal eigenfunctions. The second loss term, called norm-loss, requests the discovery of normalized eigenfunctions and is used to avoid trivial solutions. We find that embedding even or odd symmetries to the neural network architecture further improves the convergence for relevant problems. Lastly, a patience condition can be used to automatically recognize eigenfunction solutions. This proposed unsupervised learning method is used to solve the finite well, multiple finite wells, and hydrogen atom eigenvalue quantum problems.

cs.LG↗

arXiv2022

Multi-Task Learning based Convolutional Models with Curriculum Learning for the Anisotropic Reynolds Stress Tensor in Turbulent Duct Flow

The Reynolds-averaged Navier-Stokes (RANS) equations require accurate modeling of the anisotropic Reynolds stress tensor. Traditional closure models, while sophisticated, often only apply to restricted flow configurations. Researchers have started using machine learning approaches to tackle this problem by developing more general closure models informed by data. In this work we build upon recent convolutional neural network architectures used for turbulence modeling and propose a multi-task learning-based fully convolutional neural network that is able to accurately predict the normalized anisotropic Reynolds stress tensor for turbulent duct flows. Furthermore, we also explore the application of curriculum learning to data-driven turbulence modeling.

physics.flu-dyn↗

arXiv2021

Building astroBERT, a language model for Astronomy & Astrophysics

The existing search tools for exploring the NASA Astrophysics Data System (ADS) can be quite rich and empowering (e.g., similar and trending operators), but researchers are not yet allowed to fully leverage semantic search. For example, a query for "results from the Planck mission" should be able to distinguish between all the various meanings of Planck (person, mission, constant, institutions and more) without further clarification from the user. At ADS, we are applying modern machine learning and natural language processing techniques to our dataset of recent astronomy publications to train astroBERT, a deeply contextual language model based on research at Google. Using astroBERT, we aim to enrich the ADS dataset and improve its discoverability, and in particular we are developing our own named entity recognition tool. We present here our preliminary results and lessons learned.

cs.CL↗

arXiv2021

Adversarial Sampling for Solving Differential Equations with Neural Networks

Neural network-based methods for solving differential equations have been gaining traction. They work by improving the differential equation residuals of a neural network on a sample of points in each iteration. However, most of them employ standard sampling schemes like uniform or perturbing equally spaced points. We present a novel sampling scheme which samples points adversarially to maximize the loss of the current solution estimate. A sampler architecture is described along with the loss terms used for training. Finally, we demonstrate that this scheme outperforms pre-existing schemes by comparing both on a number of problems.

cs.LG↗

arXiv2021

Uncertainty Quantification in Neural Differential Equations

Uncertainty quantification (UQ) helps to make trustworthy predictions based on collected observations and uncertain domain knowledge. With increased usage of deep learning in various applications, the need for efficient UQ methods that can make deep models more reliable has increased as well. Among applications that can benefit from effective handling of uncertainty are the deep learning based differential equation (DE) solvers. We adapt several state-of-the-art UQ methods to get the predictive uncertainty for DE solutions and show the results on four different DE types.

cs.LG↗