arXiv subjects

Pavlos Protopapas

Publications and source records attributed to Pavlos Protopapas.

At least 19 recordsLinked to original sources

arXiv2026

Black Hole Love Numbers with Physics-Informed Neural Networks

We develop and validate a physics-informed neural network (PINN) framework for computing the tidal Love numbers of black holes directly from their perturbation equations. We consider static perturbations of the Kerr black hole, whose exact hypergeometric solutions provide a controlled benchmark for both the numerical solver and the extraction of the physical response. The framework combines exact enforcement of the horizon boundary conditions with an $H^2$-Sobolev loss that incorporates derivatives of the differential-equation residual. The Love number is then obtained by extracting the asymptotic coefficients of the learned solution, without using the analytic connection formula. Across the tested scalar, vector, and tensor perturbations, the method recovers the finite dissipative response with relative errors below $10^{-5}$. Controlled comparisons show that the higher-derivative loss terms improve solution accuracy by orders of magnitude, while independent tests of the extraction procedure distinguish solver errors from errors in recovering the response coefficients. The conservative response, which vanishes analytically, is constrained by the numerical error floor. These results demonstrate that PINNs can accurately compute black-hole tidal response and establish a validated framework for future extensions to frequency-dependent and non-separable perturbation problems.

gr-qc↗

arXiv2026

Contrastive Astromer: Two-Stage Contrastive Representation Learning for Astronomical Light Curve Classification

Large astronomical surveys collect abundant light curves, but reliable class labels remain scarce. ASTROMER 2 learns from unlabeled light curves by reconstructing masked observations, yet this objective does not explicitly encourage class separation in a compact representation of each light curve. We introduce Contrastive Astromer, a two-stage approach that makes these representations more useful for classification without changing the ASTROMER 2 encoder architecture. First, unsupervised contrastive learning on single-band MACHO light curves brings together representations of augmented views of the same object. Supervised contrastive learning, supported by an auxiliary classification loss, then uses a separate labeled Alcock sample to strengthen class discrimination. We evaluate the resulting representations by freezing the encoder and training a separate classifier. On a held-out set of 600 objects, this classifier achieves a macro-F1 of 0.7943 with 500 labeled examples per class, exceeding our reproduction of the ASTROMER 2 finetune-and-classify pipeline by 5.10 percentage points. With downstream classifier training budgets of 20 and 100 examples per class, macro-F1 reaches 0.7078 and 0.7704, respectively, also surpassing this baseline. Embedding-space analyses further show that supervised adaptation improves local class consistency and global class separation. These results show that contrastive adaptation makes pretrained light-curve representations more effective for classification and more informative about the structure of variability classes.

astro-ph.IM↗

arXiv2026

Low Residuals, Wrong Value: Learning the Viscosity Solution of Hamilton-Jacobi-Isaacs Equations with PINNs

Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual. For first-order Hamilton-Jacobi equations this is not sufficient: the same equation and boundary data admit Lipschitz almost-everywhere solutions that differ from the viscosity solution by $O(1)$ while violating the equation only on sets of measure zero. We study whether residual minimization selects such solutions in a fixed-horizon pursuit-evasion game whose Hamilton-Jacobi-Isaacs value function is known in closed form on the circle $S^1$ and on the flat tori $\mathbb{T}^{2}$ and $\mathbb{T}^{4}$. We train four neural parameterizations with ten seeds on each geometry, 120 runs in total. A standard network with periodic Fourier features converges to folded almost-everywhere solutions in all 30 runs: small residuals and the expected capture-layer gradient, yet values that are wrong over most of the domain. A network with periodicity imposed through the loss recovers the viscosity solution in one and two dimensions but becomes unreliable in four. Two parameterizations that receive the geodesic distance do substantially better: a single network fed the wrapped displacement and its distance recovers the viscosity solution in all 30 runs, while a minimum over periodic image charts succeeds in 27 of 30 and introduces a wrong-image failure mode. Finally, for the convex Hamiltonian considered here, we use the semiconcavity of the viscosity solution to build a mesh-free finite-difference test that needs only forward network evaluations; it detects the folded solutions and the harmful min-of-charts failures without access to the exact value function. A small sampled residual thus does not by itself validate a learned Hamilton-Jacobi solution; the parameterization and independent structural diagnostics can be essential for selecting the viscosity solution.

math.NA↗

arXiv2026

Local Citation Recommendation Without Graph Signals

Resolving correct citations can be a time-consuming task for research writers. We address local citation recommendation (LCR), where the goal is to retrieve appropriate references for a given sentence. Web tools generally depend on the existing citation graph, which may bias results toward citation count or more recent publications. LCR research using full paper texts has been limited by the lack of publicly available data. We present a new dataset, the Local Citation Recommendation Corpus (LCRC), containing 14,735 scientific statements derived from astrophysics review papers, each with one or more citation targets whose full text is accessible via API. Using this dataset we systematically compare retrieval methods and develop a citation recommendation system that avoids citation graph bias while achieving 8.0% improvement in Recall@25 and 6.9% improvement in NDCG@25 over dense retrieval baselines without model fine-tuning. To support reproducibility, we make our code and dataset publicly available.

cs.IR↗

arXiv2026

Variational Boosting for Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution. However, monolithic PINNs often suffer from ill-conditioning, spectral bias, and optimization instability. We introduce a variational boosting framework in which solutions are constructed additively in function space. Each stage trains a weak learner whose converged correction satisfies a local orthogonality condition, equivalent to a projected functional gradient descent step onto the tangent space of the network's function manifold. Because each correction network is deliberately small, the restricted minimization admits full Newton or conjugate gradient updates, which are typically infeasible in large PINNs. The resulting method separates global nonlinear refinement into a sequence of well-conditioned subproblems while preserving the full variational structure of the operator. This framework provides a geometric interpretation of multi-stage PINNs as projected functional gradient descent and enables stable second-order optimization for nonlinear differential equations.

cs.LG↗

arXiv2026

The Chandra-Gaia Catalog of Counterparts: Resolving ambiguous Gaia matches to X-ray sources in the Chandra Source Catalog using Machine Learning

We present a framework to cross-match sources from the Chandra Source Catalog (CSC v2.1) with optical sources from Gaia Data Release 3. Unlike purely spatial approaches, we use source properties such as magnitudes, colors, and distances to identify true counterparts, detect chance coincidences, and resolve ambiguities when multiple plausible candidates exist. We define a training set of high-confidence matches using NWAY, a Bayesian cross-matching framework that accounts for positional errors and source densities. We train a gradient-boosted classifier (LightGBM) on a variety of features from both catalogs. Of the ~$254$k unique X-ray sources, we find counterparts for ~$113$k sources, of which plausible multiple counterparts are found for ~$7$k. We find no counterparts for ~$20$k sources for which separation-based cross-matching does find a match, and attribute half of these to chance coincidences. We validate the pipeline on the Chandra Orion Ultradeep Project (COUP), where the machine-learning matches reproduce 95% of NWAY cross-matches without using any positional information. We release a catalog of the ~$113$k Chandra-Gaia counterparts, together with ~$7$k alternative matches and ~$20$k ambiguous NWAY associations, supporting future population studies of sources detectable by both Chandra and Gaia. We discuss limitations and provide a generalization of the framework that is applicable in other cross-matching scenarios.

astro-ph.IM↗

arXiv2026

Multivariate time series transformer embeddings for light curves of periodic variable stars

Astronomical surveys produce time series data by observing stellar objects across multiple photometry bands. Foundational transformer-based models, such as Astromer, encode each time series as a sequence of embeddings to classify sources. However, such models operate independently on each band and therefore do not use information across wavelengths or filters. We extend the single-band Astromer framework by introducing a fusion layer that combines single photometry band observations into a unified sequence representation, thus enabling multiband analysis for downstream tasks, namely periodic variable star classification. The challenge in adapting the encoder for multiband data lies in coordinating information across bands observed at asynchronous times. We pre-trained various multiband neural network models on 600 000 high signal-to-noise light curves from the Massive Compact Halo Object (MACHO) survey and fine-tuned them using labeled data from the Alcock catalog (derived from MACHO) and from the Asteroid Terrestrial-impact Last Alert System survey. Our results show that both proposed multiband architectures outperform the single-band models by approximately ten percentage points in the F1-score. Jointly pre-trained multiband encoders further improve the performance compared to a collection of independently pre-trained single-band encoders, reaching an improvement of 23 percentage points in the F1-score. These results demonstrate a trade-off in the training speed and classification accuracy between single-band and multiband encoders, with multiband models improving the F1-score performance by ten percentage points at the cost of increased pretraining time. Our results show the great potential of transformer-based multiband neural network architectures for classification tasks regarding future large-scale time-domain surveys with a greater variety of variable stars.

astro-ph.IM↗

arXiv2026

AGNFormer I: Reconstruction of AGN spectra using a probabilistic transformer model

We explore how an uncertainty-aware transformer-based architecture can leverage information embedded across the entire observed optical spectra of AGN, focusing on the algorithm's ability to predict unseen or masked parts of luminous AGN spectra. This provides a direct probe of the learnable correlations between AGN continua and broad lines. We introduce AGNFormer, a transformer model trained to predict the mean expected flux and variance in masked spectral regions (major broad lines to ${\pm}10^{4}$kms$^{-1}$; missing halves), inputting rest-frame spectral fluxes and uncertainties across the entire redshift range of the SDSS DR16 Quasar Catalogue. We evaluate the performance of the model on both full (no S/N limit) and high-quality (S/N > 10) spectral samples using the negative-log likelihood, and via comparisons with existing C IV and ly-a reconstruction algorithms. The model successfully reconstructs unseen AGN broad lines to better than 10-16% (4-8%) of the flux for the full (S/N > 10) test sets, up to an error floor of $\approx$2-6% of the flux at S/N $\approx$ 40, while predictions for larger unseen halves grow to 12-25% (5-15%) of the flux the further away they are from the cut-off wavelength of the seen input spectrum. Predictions faithfully reproduce the broad AGN spectral diversity across the entire optical and UV QSO main sequence parameter spaces, including both Gaussian and Lorentzian profile regimes, Feii complexes, and narrow emission lines. Performance is similar or better compared to previous spectral reconstruction algorithms. The high precision of the broad-line region reconstruction demonstrates that the method successfully aggregates information across the spectrum and highlights how the AGN continuum and weaker lines/complexes have the potential to assist astronomers in the extraction of the entire wealth of information embedded in AGN spectra.

astro-ph.GA↗

arXiv2026

Physics-Informed Neural Embeddings of PDE Solution Families

We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations. The method uses a multihead Physics-Informed Neural Network in which a shared body learns a latent manifold representing the solution space, while linear heads reconstruct individual solutions associated with different initial conditions. A head-orthogonalization penalty removes degeneracies in the latent representation and stabilizes the principal-component spectrum across training realizations. Because the initial condition is built into the network output by construction, these principal components measure the additional variability the network learns on top of the initial profile, not the full solution itself. We apply the method to the one-dimensional viscous Burgers equation, with the heat and wave equations as robustness checks. For a latent dimension $n_b=20$, the learned manifolds exhibit pronounced effective dimensional reduction: for Burgers dynamics, only $2$-$4$ principal components capture about $95\%$ of the latent-space variance, while $4$-$7$ capture about $99\%$, depending on the initial-condition family; the same qualitative compression holds for the heat and wave equations. We also split the wavenumber axis into bands (``Fourier shells'') and measure how much each band contributes to every principal component. The resulting frequency profile is invariant under the change-of-basis freedom that the orthogonalization penalty leaves in the latent space, and is therefore reproducible across independent training runs. More broadly, this establishes the learned spectral profiles and principal components as robust observables of solution-manifold geometry.

cs.LG↗

arXiv2026

ABC-SN: Attention Based Classifier for Supernova Spectra

While significant advances have been made in photometric classification ahead of the millions of transient events and hundreds of supernovae (SNe) each night that the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) will discover, classifying SNe spectroscopically remains the best way to determine most subtypes of SNe. Traditional spectrum classification tools use template matching techniques (eg., SNID, SuperFit) and require significant human supervision. Two deep learning spectral classifiers, DASH and SNIascore, define the state of the art, but SNIascore is a binary classifier devoted to maximizing the purity of the SN Ia-norm sample, while DASH is no longer maintained and the original work suffers from contamination of multi-epoch spectra in the training and test sets. We have explored several neural network architectures in order to create a new automated method for classifying SN subtypes, settling on an attention-based model we call ABC-SN. We benchmark our results against an updated version of DASH, thus providing the community with an up-to-date general-purpose SN classifier. Our dataset is comprised of ten different SN subtypes, including subtypes of SN Ia, core collapse, and interacting SNe. We find that ABC-SN outperforms DASH for nearly all classes, including an improvement of $26\%$ in SN Ia completeness ($\sim88\%$) and $2.4\%$ in SN Ia purity ($\sim95\%$) when unthresholded (improvements for each class can further be obtained by tuned thresholds), and we discuss the limitations of current SN datasets for benchmarking performance.

astro-ph.IM↗

arXiv2026

Gravitational Duals from Equations of State II: Large Hierarchies and False Vacua

We investigate the reconstruction of holographic duals for strongly coupled quantum field theories in regimes characterized by large hierarchies and the presence of false vacua. Within the gauge/gravity duality, these features translate into non-trivial thermodynamic behaviour and exotic renormalization group flows, including skipping flows between non-adjacent fixed points. Building on previous work based on Physics-Informed Neural Networks (PINNs), we extend the holographic inverse problem of reconstructing the bulk scalar potential from boundary thermodynamic data into this new regime. This setting presents a variety of conceptual and numerical challenges, such as near-degenerate states, large hierarchies of energy scales, and regions of the potential that are not directly probed by the input data. We develop a set of methodological advances that overcome these obstacles, thereby improving the established PINNs-based methodology and extending it to new physical regimes of interest that were previously out of reach. Applying the developed framework, we demonstrate accurate reconstruction of scalar potentials deep into the false vacuum regime, achieving robust agreement with the physical features of the underlying thermodynamics despite significant numerical stiffness. Our results extend the bridge between holography and machine learning, and suggest that data-driven approaches can provide new insights into the structure of strongly coupled systems.

hep-th↗

arXiv2026

Identifying Observational Signatures of Flux Eruption Events in Supermassive Black Hole Accretion Flows with Machine Learning

Simulated black hole accretion flows with strong magnetic fields often exhibit "flux eruption events" (FEEs), transient and localized expulsions of matter near the event horizon due to magnetic reconnection. It may now be possible to image them with the Event Horizon Telescope (EHT), a global network of millimeter-wave observatories that images black holes. Here we use machine learning as an interpretable inference tool to identify observational signatures of FEEs that could be accessible to the EHT. First, we train a convolutional neural network to learn task-relevant representations of FEEs in uncorrupted simulated images. After using this network to label a larger set of images, we then train interpretable models (random forest and logistic regression) to determine observational signatures. We find that during a FEE, images in the millimeter tend toward more diffuse emission, higher linear polarization, and lower total fluxes, but these signatures are weak for most FEEs compared to the usual time variability of these features. Moreover, the Q-U loop rotation rate decreases during FEEs, contrary to a picture in which FEEs could jointly cause both millimeter Q-U loops and flares. Our random forest trained on observable summary statistics achieves ~80% class-weighted accuracy, suggesting that the CNN learns FEE structure not fully mapped onto these traditional summary statistics. Our results imply that image size and polarization fraction can be used to flag candidate FEEs, but high-resolution, high-dynamic range images will still be important to confirm FEEs and test accretion flows for this phenomenon.

astro-ph.HE↗

arXiv2026

Gradient Scaling Effects in Adaptive Spectral PINNs for Stiff Nonlinear ODEs

Physics-Informed Neural Networks (PINNs) often struggle to train reliably on stiff and oscillatory dynamical systems due to poor optimization conditioning. While prior work has emphasized representational remedies such as spectral parameterizations, the optimization implications of initial-condition (IC) embeddings in adaptive spectral PINNs have not been well characterized. In this work, we show that the choice of IC gating function induces explicit time-dependent gradient scaling, which interacts with spectral representations during training. Using a nonlinear stiff spring-pendulum ODE as a controlled benchmark, we compare exponential and linear IC gates in combination with fixed and adaptive Fourier spectral trunks. We observe stiffness-dependent changes in relative dominance for adaptive PINNs: at moderate stiffness ($k=20$), exponential gating often yields lower error but exhibits heterogeneous behavior across random seeds, whereas at higher stiffness ($k=60$), linear gating becomes preferable, with additional reversals observed at larger $k$. These trends hold for both relative $L^2$ error and maximum pointwise error and are confirmed by paired Wilcoxon signed-rank tests with Holm correction. Overall, our results demonstrate that IC embeddings are not a neutral design choice in PINNs: the induced gradient scaling materially shapes optimization conditioning in stiff regimes, with distinct sensitivity patterns in baseline and adaptive spectral models.

cs.LG↗

arXiv2026

Chebyshev-Augmented One-Shot Transfer Learning for PINNs on Nonlinear Differential Equations

Physics-Informed Neural Networks (PINNs) offer a flexible paradigm for solving differential equations by embedding governing laws into the training objective. A persistent limitation is instance specificity: standard PINNs typically require retraining for each new forcing term, boundary/initial condition, or parameter setting. One-shot transfer learning (OTL) addresses this bottleneck for linear operators by freezing a pretrained latent representation and computing optimal output weights in closed form, but for nonlinear problems closed-form adaptation is generally unavailable because the loss is nonconvex in the output layer. In this paper we substantially broaden the class of nonlinearities amenable to one-shot PINN transfer by combining OTL with Chebyshev polynomial surrogates. We approximate general smooth weakly nonlinear terms by truncated Chebyshev expansions over a prescribed solution range, yielding a polynomial nonlinearity that can be handled by a perturbative decomposition into linear subproblems. A multi-head PINN learns a reusable latent space associated with the dominant linear operator; at test time, solutions to new instances are obtained via a sequence of closed-form linear solves in the output layer, without retraining the network body. We provide a unified derivation of the framework for ODEs and PDEs and demonstrate accuracy and fast online adaptation on nonlinear benchmarks, including non-polynomial and singular ODE nonlinearities as well as a reaction-diffusion PDE with saturating kinetics, demonstrating the method's utility in many-query regimes.

cs.LG↗

arXiv2026

Learning embeddings of non-linear PDEs: the Burgers' equation

Embeddings provide low-dimensional representations that organize complex function spaces and support generalization. They provide a geometric representation that supports efficient retrieval, comparison, and generalization. In this work we generalize the concept to Physics Informed Neural Networks. We present a method to construct solution embedding spaces of nonlinear partial differential equations using a multi-head setup, and extract non-degenerate information from them using principal component analysis (PCA). We test this method by applying it to viscous Burgers' equation, which is solved simultaneously for a family of initial conditions and values of the viscosity. A shared network body learns a latent embedding of the solution space, while linear heads map this embedding to individual realizations. By enforcing orthogonality constraints on the heads, we obtain a principal-component decomposition of the latent space that is robust to training degeneracies and admits a direct physical interpretation. The obtained components for Burgers' equation exhibit rapid saturation, indicating that a small number of latent modes captures the dominant features of the dynamics.

math.AP↗

arXiv2026

PTL-PINNs: Perturbation-Guided Transfer Learning with Physics- Informed Neural Networks for Nonlinear Systems

Accurately and efficiently solving nonlinear differential equations is crucial for modeling dynamic behavior across science and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful solution that embeds physical laws in training by enforcing equation residuals. However, these struggle to model nonlinear dynamics, suffering from limited generalization across problems and long training times. To address these limitations, we propose a perturbation-guided transfer learning framework for PINNs (PTL-PINN), which integrates perturbation theory with transfer learning to efficiently solve nonlinear equations. Unlike gradient-based transfer learning, PTL-PINNs solve an approximate linear perturbative system using closed-form expressions, enabling rapid generalization with the time complexity of matrix-vector multiplication. We show that PTL-PINNs achieve accuracy comparable to various Runge-Kutta methods, with computational speeds up to one order of magnitude faster. To benchmark performance, we solve a broad set of problems, including nonlinear oscillators across various damping regimes, the equilibrium-centered Lotka-Volterra system, the KPP-Fisher and the Wave equation. Since perturbation theory sets the accuracy bound of PTL-PINNs, we systematically evaluate its practical applicability. This work connects long-standing perturbation methods with PINNs, demonstrating how perturbation theory can guide foundational models to solve nonlinear systems with speeds comparable to those of classical solvers.

cs.LG↗

arXiv2026

Improving Router Security using BERT

Previous work on home router security has shown that using system calls to train a transformer-based language model built on a BERT-style encoder using contrastive learning is effective in detecting several types of malware, but the performance remains limited at low false positive rates. In this work, we demonstrate that using a high-fidelity eBPF-based system call sensor, together with contrastive augmented learning (which introduces controlled mutations of negative samples), improves detection performance at a low false positive rate. In addition, we introduce a network packet abstraction language that enables the creation of a pipeline similar to network packet data, and we show that network behavior provides complementary detection signals-yielding improved performance for network-focused malware at low false positive rates. Lastly, we implement these methods in an online router anomaly detection framework to validate the approach in an Internet of Things (IoT) deployment environment.

cs.CR↗

arXiv2025

One-Shot Transfer Learning for Nonlinear PDEs with Perturbative PINNs

We propose a framework for solving nonlinear partial differential equations (PDEs) by combining perturbation theory with one-shot transfer learning in Physics-Informed Neural Networks (PINNs). Nonlinear PDEs with polynomial terms are decomposed into a sequence of linear subproblems, which are efficiently solved using a Multi-Head PINN. Once the latent representation of the linear operator is learned, solutions to new PDE instances with varying perturbations, forcing terms, or boundary/initial conditions can be obtained in closed form without retraining. We validate the method on KPP-Fisher and wave equations, achieving errors on the order of 1e-3 while adapting to new problem instances in under 0.2 seconds; comparable accuracy to classical solvers but with faster transfer. Sensitivity analyses show predictable error growth with epsilon and polynomial degree, clarifying the method's effective regime. Our contributions are: (i) extending one-shot transfer learning from nonlinear ODEs to PDEs, (ii) deriving a closed-form solution for adapting to new PDE instances, and (iii) demonstrating accuracy and efficiency on canonical nonlinear PDEs. We conclude by outlining extensions to derivative-dependent nonlinearities and higher-dimensional PDEs.

math.NA↗