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We present a generative AI algorithm for addressing the challenging task of fast, accurate and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on a conditional score-based diffusion model. Through extensive numerical experimentation with both incompressible and compressible fluid flows, we demonstrate that GenCFD provides very accurate approximation of statistical quantities of interest such as mean, variance, point pdfs, higher-order moments, while also generating high quality realistic samples of turbulent fluid flows and ensuring excellent spectral resolution. In contrast, ensembles of operator learning baselines which are trained to minimize mean (absolute) square errors regress to the mean flow. We present rigorous theoretical results uncovering the surprising mechanisms through which diffusion models accurately generate fluid flows. These mechanisms are illustrated with solvable toy models that exhibit the relevant features of turbulent fluid flows while being amenable to explicit analytical formulas., Comment: 71 pages, 30 figures

We introduce Poseidon, a foundation model for learning the solution operators of PDEs. It is based on a multiscale operator transformer, with time-conditioned layer norms that enable continuous-in-time evaluations. A novel training strategy leveraging the semi-group property of time-dependent PDEs to allow for significant scaling-up of the training data is also proposed. Poseidon is pretrained on a diverse, large scale dataset for the governing equations of fluid dynamics. It is then evaluated on a suite of 15 challenging downstream tasks that include a wide variety of PDE types and operators. We show that Poseidon exhibits excellent performance across the board by outperforming baselines significantly, both in terms of sample efficiency and accuracy. Poseidon also generalizes very well to new physics that is not seen during pretraining. Moreover, Poseidon scales with respect to model and data size, both for pretraining and for downstream tasks. Taken together, our results showcase the surprising ability of Poseidon to learn effective representations from a very small set of PDEs during pretraining in order to generalize well to unseen and unrelated PDEs downstream, demonstrating its potential as an effective, general purpose PDE foundation model. Finally, the Poseidon model as well as underlying pretraining and downstream datasets are open sourced, with code being available at https://github.com/camlab-ethz/poseidon and pretrained models and datasets at https://huggingface.co/camlab-ethz.

A new fine grid of nonlinear convective pulsation models for the so-called "bump Cepheids" is presented to investigate the Hertzprung progression (HP) phenomenon shown by their light and radial pulsation velocity curves. The period corresponding to the center of the HP is investigated as a function of various model assumptions, such as the efficiency of super-adiabatic convection, the mass-luminosity relation, and the metal and helium abundances. The assumed mass-luminosity relation is found to significantly affect the phenomenon but variations in the chemical composition as well as in the stellar mass (at fixed mass-luminosity relation) also play a key role in determining the value of the HP center period. Finally, the predictive capability of the presented theoretical scenario is tested against observed light curves of bump Cepheids in the ESA Gaia database, also considering the variation of the pulsation amplitudes and of the Fourier parameters $R_{21}$ and $\Phi_{21}$ with the pulsation period. A qualitative agreement between theory and observations is found for what concerns the evolution of the light curve morphology as the period moves across the HP center, as well for the pattern in period-amplitude, period-$R21$ and period-$\Phi_{21}$ planes. A larger sample of observed Cepheids with accurate light curves and metallicities is required in order to derive more quantitative conclusions., Comment: Accepted for publication on MNRAS

Homogeneous multi-wavelength observations of classical Cepheids from the forthcoming Rubin-LSST have the potential to significantly contribute to our understanding of the evolutionary and pulsation properties of these pulsating stars. Updated pulsation models for Classical Cepheid stars have been computed under various assumptions about chemical compositions, including relatively low metallicity ($Z$ = $0.004$ with $Y$ =$0.25$ and $Z$=$0.008$ with $Y$ =$0.25$), solar metallicity ($Z$=$0.02$ with $Y$=$0.28$), and supersolar metallicity environments ($Z$ = $0.03$ with $Y$ = $0.28$). From the predicted periods, intensity-weighted mean magnitudes, and colors, we have derived the first theoretical pulsation relations in the Rubin-LSST filters (ugrizy), including period-luminosity-color, period-Wesenheit, and period-age-color relations. We find that the coefficients of these relations are almost insensitive to the efficiency of superadiabatic convection but are significantly affected by the assumption of the mass-luminosity relation and the adopted chemical composition. Metal-dependent versions of these relations are also derived, representing valuable tools for individual distance determinations and correction for metallicity effects on the cosmic distance scale., Comment: 23 pages, 6 figures, and 11 tables; accepted for publication in MNRAS

Type II Cepheids (T2C) are less frequently used counterparts of classical Cepheids which provide the primary calibration of the distance ladder for measuring $H_0$ in the local Universe. In the era of the Hubble Tension, T2C variables with the RR Lyrae stars (RRL) and the tip of the red giant branch (TRGB) can potentially provide classical Cepheid independent calibration of the cosmic distance ladder. Our goal is to provide an absolute calibration of the Period-Luminosity, Period-Luminosity-Color and Period-Wesenheit relations(PL,PLC and PW) of T2Cs in the Large Magellanic Cloud (LMC). We exploited time-series photometry in the near-infrared (NIR) bands for a sample of more than 320 T2Cs in the Magellanic Clouds (MC). These observations were acquired during 2009-2018 in the context of the VMC ESO public survey (The VISTA near-infrared YJKs survey of the Magellanic System). The NIR photometry was supplemented with well-sampled optical light curves and accurate pulsation periods from the OGLE IV survey and the Gaia mission. We used the best-quality NIR light curves to generate custom templates for modelling sparsely sampled light curves in YJKs bands; in turn, we derived accurate and precise intensity-averaged mean magnitudes and pulsation amplitudes of 339 T2Cs in the MC. We used optical and NIR mean magnitudes to derive PL/PLC/PW relations for T2Cs in multiple bands, which were calibrated with the geometric distance to the LMC and with the Gaia parallaxes. We used our new empirical calibrations of PL/PW relations to obtain distances to 22 T2C-host Galactic globular clusters, which were found to be systematically smaller by 0.1 mag and 0.03-0.06 mag compared with the literature. A better agreement is found between our distances and those based on RRLs in globular clusters, providing strong support for using these population II stars with the TRGB for future distance scale studies.

Milky Way Cepheid variables with accurate {\it Hubble Space Telescope} photometry have been established as standards for primary calibration of the cosmic distance ladder to achieve a percent-level determination of the Hubble constant ($H_0$). These 75 Cepheid standards are the fundamental sample for investigation of possible residual systematics in the local $H_0$ determination due to metallicity effects on their period-luminosity relations. We obtained new high-resolution ($R\sim81,000$), high signal-to-noise ($S/N\sim50-150$) multi-epoch spectra of 42 out of 75 Cepheid standards using ESPaDOnS instrument at the 3.6-m Canada-France-Hawaii Telescope. Our spectroscopic metallicity measurements are in good agreement with the literature values with systematic differences up to $0.1$ dex due to different metallicity scales. We homogenized and updated the spectroscopic metallicities of all 75 Milky Way Cepheid standards and derived their multiwavelength ($GVIJHK_s$) period-luminosity-metallicity and period-Wesenheit-metallicity relations using the latest {\it Gaia} parallaxes. The metallicity coefficients of these empirically calibrated relations exhibit large uncertainties due to low statistics and a narrow metallicity range ($\Delta\textrm{[Fe/H]}=0.6$~dex). These metallicity coefficients are up to three times better constrained if we include Cepheids in the Large Magellanic Cloud and range between $-0.21\pm0.07$ and $-0.43\pm0.06$ mag/dex. The updated spectroscopic metallicities of these Milky Way Cepheid standards were used in the Cepheid-Supernovae distance ladder formalism to determine $H_0=72.9~\pm 1.0$\textrm{~km~s$^{-1}$~Mpc$^{-1}$}, suggesting little variation ($\sim 0.1$ ~km~s$^{-1}$~Mpc$^{-1}$) in the local $H_0$ measurements due to different Cepheid metallicity scales., Comment: 14 pages, 4 figures, Accepted for publication in The Astrophysical Journal Letters

Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined on paper, neural operators necessitate discretization in the transition to computer implementations. This step can compromise their integrity, often causing them to deviate from the underlying operators. This research offers a fresh take on neural operators with a framework Representation equivalent Neural Operators (ReNO) designed to address these issues. At its core is the concept of operator aliasing, which measures inconsistency between neural operators and their discrete representations. We explore this for widely-used operator learning techniques. Our findings detail how aliasing introduces errors when handling different discretizations and grids and loss of crucial continuous structures. More generally, this framework not only sheds light on existing challenges but, given its constructive and broad nature, also potentially offers tools for developing new neural operators., Comment: 28 pages

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs. Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. The resulting architecture, termed as convolutional neural operators (CNOs), is designed specifically to preserve its underlying continuous nature, even when implemented in a discretized form on a computer. We prove a universality theorem to show that CNOs can approximate operators arising in PDEs to desired accuracy. CNOs are tested on a novel suite of benchmarks, encompassing a diverse set of PDEs with possibly multi-scale solutions and are observed to significantly outperform baselines, paving the way for an alternative framework for robust and accurate operator learning. Our code is publicly available at https://github.com/bogdanraonic3/ConvolutionalNeuralOperator

A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a novel architecture termed Neural Inverse Operators (NIOs) to solve these PDE inverse problems. Motivated by the underlying mathematical structure, NIO is based on a suitable composition of DeepONets and FNOs to approximate mappings from operators to functions. A variety of experiments are presented to demonstrate that NIOs significantly outperform baselines and solve PDE inverse problems robustly, accurately and are several orders of magnitude faster than existing direct and PDE-constrained optimization methods.

Gaia DR3 contains 1.8 billion sources with G-band photometry, 1.5 billion of which with BP and RP photometry, complemented by positions on the sky, parallax, and proper motion. The median number of field-of-view transits in the three photometric bands is between 40 and 44 measurements per source and covers 34 months of data collection. We pursue a classification of Galactic and extra-galactic objects that are detected as variable by Gaia across the whole sky. Supervised machine learning (eXtreme Gradient Boosting and Random Forest) was employed to generate multi-class, binary, and meta-classifiers that classified variable objects with photometric time series in the G, BP, and RP bands. Classification results comprise 12.4 million sources (selected from a much larger set of potential variable objects) and include about 9 million variable stars classified into 22 variability types in the Milky Way and nearby galaxies such as the Magellanic Clouds and Andromeda, plus thousands of supernova explosions in distant galaxies, 1 million active galactic nuclei, and almost 2.5 million galaxies. The identification of galaxies was made possible by the artificial variability of extended objects as detected by Gaia, so they were published in the galaxy_candidates table of the Gaia DR3 archive, separate from the classifications of genuine variability (in the vari_classifier_result table). The latter contains 24 variability classes or class groups of periodic and non-periodic variables (pulsating, eclipsing, rotating, eruptive, cataclysmic, stochastic, and microlensing), with amplitudes from a few milli-magnitudes to several magnitudes., Comment: 106 pages, 513 figure panels, 4 tables. Accepted by Astronomy & Astrophysics (in press)

A large class of hyperbolic and advection-dominated PDEs can have solutions with discontinuities. This paper investigates, both theoretically and empirically, the operator learning of PDEs with discontinuous solutions. We rigorously prove, in terms of lower approximation bounds, that methods which entail a linear reconstruction step (e.g. DeepONet or PCA-Net) fail to efficiently approximate the solution operator of such PDEs. In contrast, we show that certain methods employing a non-linear reconstruction mechanism can overcome these fundamental lower bounds and approximate the underlying operator efficiently. The latter class includes Fourier Neural Operators and a novel extension of DeepONet termed shift-DeepONet. Our theoretical findings are confirmed by empirical results for advection equation, inviscid Burgers' equation and compressible Euler equations of aerodynamics.

The Vera C. Rubin Legacy Survey of Space and Time holds the potential to revolutionize time domain astrophysics, reaching completely unexplored areas of the Universe and mapping variability time scales from minutes to a decade. To prepare to maximize the potential of the Rubin LSST data for the exploration of the transient and variable Universe, one of the four pillars of Rubin LSST science, the Transient and Variable Stars Science Collaboration, one of the eight Rubin LSST Science Collaborations, has identified research areas of interest and requirements, and paths to enable them. While our roadmap is ever-evolving, this document represents a snapshot of our plans and preparatory work in the final years and months leading up to the survey's first light., Comment: 202 pages (in book format) 34 figures plus chapter heading figures (13)

Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation. Consequently, they may fail at approximating discontinuous solutions of PDEs such as nonlinear hyperbolic equations. To ameliorate this, we propose a novel variant of PINNs, termed as weak PINNs (wPINNs) for accurate approximation of entropy solutions of scalar conservation laws. wPINNs are based on approximating the solution of a min-max optimization problem for a residual, defined in terms of Kruzkhov entropies, to determine parameters for the neural networks approximating the entropy solution as well as test functions. We prove rigorous bounds on the error incurred by wPINNs and illustrate their performance through numerical experiments to demonstrate that wPINNs can approximate entropy solutions accurately.

To properly quantify possible residual systematic errors affecting the Classical Cepheid distance scale, a detailed theoretical scenario is recommended. By extending the set of nonlinear convective pulsation models published for $Z=0.02$ \citep[][]{Desomma2020a} to $Z=0.004$, $Z=0.008$ and $Z=0.03$, we provide a detailed homogeneous nonlinear model grid taking into account simultaneous variations of the mass-luminosity relation, the efficiency of super-adiabatic convection and the chemical composition. The dependence of the inferred Period-Radius, Period-Mass-Radius, and Period-Mass-Luminosity-Temperature relations on the input parameters is discussed for both the Fundamental and First Overtone modes. The trend of the instability strip getting redder as the metallicity increases is confirmed for the additional ML assumptions and mixing length values. From the obtained multi-filter light curves, we derive mean magnitudes and colors and in turn Period-Luminosity-Color and Period-Wesenheit relations for each assumed chemical composition, mass-luminosity relation and efficiency of super-adiabatic convection. Application to a well-studied sample of Cepheids in the Large Magellanic Cloud allows us to constrain the dependence of the inferred distance modulus on the assumed mass-luminosity relation, and the inclusion of the metallicity term in the derivation of Period-Wesenheit relations allows us, for each assumed mass-luminosity relation, to predict the metallicity dependence of the Cepheid distance scale. The obtained metal-dependent Period-Wesenheit relations are compared with recent results in the literature and applied to a sample of Gaia Early Data Release 3 Galactic Cepheids with known metal abundances to derive individual parallaxes. The comparison of these predictions with Gaia results is finally discussed., Comment: 78 pages, 35 tables, 25 figures. Accepted for publication on ApJ Supplement

The revolutionary power of future Rubin-LSST observations will allow us to significantly improve the physics of pulsating stars, including RR Lyrae. In this context, an updated theoretical scenario predicting all the relevant pulsation observables in the corresponding photometric filters is mandatory. The bolometric light curves based on a recently computed extensive set of nonlinear convective pulsation models for RR Lyrae stars, covering a broad range in metal content and transformed into the Rubin-LSST photometric system. Predicted Rubin-LSST mean magnitudes and pulsation amplitudes have been adopted to built the Bailey diagrams (luminosity amplitude vs period) and the color-color diagrams in these bands. The current findings indicate that the gLSST-rLSST, rLSST-iLSST colors obey to a well defined linear relation with the metal content. Moreover, the Period Luminosity relations display in the reddest filters (rLSST,iLSST,zLSST,yLSST) a significant dependence on the assumed metal abundance. In particular, more metal-rich RR Lyrae are predicted to be fainter at fixed period. Metal-dependent Period-Wesenheit relations for different combinations of optical and NIR filters are also provided. These represent powerful tools to infer individual distances independently of reddening uncertainties, once the metal abundance is known and no relevant deviations from the adopted extinction law occur. Finally, we also derived new linear and quadratic absolute magnitude metallicity relations (gLSST vs [Fe/H]) and the metallicity coefficient is consistent with previous findings concerning the B and the V band., Comment: Accepted for publication on ApJ

Based on updated pulsation models for Classical Cepheids, computed for various assumptions about the metallicity and helium abundance, roughly representative of pulsators in the Small Magellanic Cloud ($Z$=$0.004$ and $Y$=$0.25$), Large Magellanic Cloud ($Z$=$0.008$ and $Y$=$0.25$), and M31 ($Z$=$0.03$ and $Y$=$0.28$), and self-consistent updated evolutionary predictions, we derived Period-Age and multi-band Period-Age-Color relations that also take into account variations in the Mass-Luminosity relation. These results, combined with those previously derived for Galactic Cepheids, were used to investigate the metallicity effect when using these variables as age indicators. In particular, we found that a variation in the metal abundance affects both the slope and the zero point of the above-mentioned relations. The new relations were applied to a sample of Gaia Early Data Release 3 Classical Cepheids. The retrieved distribution of the individual ages confirms that a brighter Mass-Luminosity relation produces older ages and that First Overtone pulsators are found to be concentrated towards older ages with respect to the Fundamental ones at a fixed Mass-Luminosity relation. Moreover, the inclusion of a metallicity term in the Period-Age and Period-Age-Color relations slightly modifies the predicted ages. In particular, the age distribution of the selected sample of Galactic Cepheids is found to be shifted towards slightly older values, when the F-mode canonical relations are considered, with respect to the case at a fixed solar chemical composition. A marginally opposite dependence can be found in the noncanonical F-mode and canonical FO-mode cases., Comment: 21 pages, 15 figures and 13 tables. Accepted for publication in MNRAS

We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-Holm and Benjamin-Ono equations. The stability of solutions of these dispersive PDEs is leveraged to prove rigorous bounds on the resulting error. We present several numerical experiments to demonstrate that PINNs can approximate solutions of these dispersive PDEs very accurately, Comment: arXiv admin note: text overlap with arXiv:2006.16144

Ultra Long Period Cepheids (ULPs) are pulsating variable stars with a period longer than 80d and have been hypothesized to be the extension of the Classical Cepheids (CCs) at higher masses and luminosities. If confirmed as standard candles, their intrinsic luminosities, 1 to 3 mag brighter than typical CCs, would allow to reach the Hubble flow and, in turn, to determine the Hubble constant, H_0, in one step, avoiding the uncertainties associated with the calibration of primary and secondary indicators. To investigate the accuracy of ULPs as cosmological standard candles, we first collect all the ULPs known in the literature. The resulting sample includes 63 objects with a very large metallicity spread with 12 + log([O/H]) ranging from 7.2 to 9.2 dex. The analysis of their properties in the VI period-Wesenheit plane and in the color-magnitude diagram (CMD) supports the hypothesis that the ULPs are the extension of CCs at longer periods, higher masses and luminosities, even if, additional accurate and homogeneous data and a devoted theoretical scenario are needed to get firm conclusions. Finally, the three M31 ULPs, 8-0326, 8-1498 and H42, are investigated in more detail. For 8-1498 and H42, we cannot confirm their nature as ULPs, due to the inconsistency between their position in the CMD and the measured periods. For 8-0326, the light curve model fitting technique applied to the available time-series data allows us to constrain its intrinsic stellar parameters, distance and reddening., Comment: MNRAS - Accepted 2020 November 19. Received 2020 November 19; in original form 2020 July 15 - 9 pages and 8 figures

On the basis of an extended set of nonlinear convective RR Lyrae pulsation models we derive the first theoretical light curves in the Gaia bands and the corresponding intensity-weighted mean magnitudes and pulsation amplitudes. The effects of chemical com-position on the derived Bailey diagrams in the Gaia filters are discussed for both Fundamental and First Overtone mode pulsators. The inferred mean magnitudes and colors are used to derive the first theoretical Period-Wesenheit relations for RR Lyrae in the Gaia filters. The application of the theoretical Period-Wesenheit relations for both the Fundamental and FirstOvertone mode to Galactic RR Lyrae in the Gaia Data Release 2 database and complementary information on individual metal abundances, allows us to derive theoretical estimates of their individual parallaxes. These results are compared with the astrometric solutions to conclude that a very small offset, consistent with zero, is required in order to reconcile the predicted distances with Gaia results., Comment: Accepted for publication on MNRAS

We propose a novel machine learning algorithm for simulating radiative transfer. Our algorithm is based on physics informed neural networks (PINNs), which are trained by minimizing the residual of the underlying radiative tranfer equations. We present extensive experiments and theoretical error estimates to demonstrate that PINNs provide a very easy to implement, fast, robust and accurate method for simulating radiative transfer. We also present a PINN based algorithm for simulating inverse problems for radiative transfer efficiently.

On the basis of recently computed nonlinear convective pulsation models of Galactic Cepheids, spanning wide ranges of input stellar parameters, we derive theoretical mass-dependent Period-Wesenheit relations in the Gaia bands, namely $G$, $G_{BP}$ and $G_{RP}$, that are found to be almost independent of the assumed efficiency of super-adiabatic convection. The application to a selected sub-sample of Gaia Data Release 2 Galactic Cepheids database allows us to derive mass-dependent estimates of their individual distances. By imposing their match with the astrometric values inferred from Gaia, we are able to evaluate the individual mass of each pulsator. The inferred mass distribution is peaked around 5.6$M_{\odot}$ and 5.4$M_{\odot}$ for the F and FO pulsators, respectively. If the estimated Gaia parallax offset $<\Delta\varpi>$=0.046 mas is applied to Gaia parallaxes before imposing their coincidence with the theoretical ones, the inferred mass distribution is found to shift towards lower masses, namely $\sim$5.2$M_{\odot}$ and 5.1$M_{\odot}$ for the F and FO pulsators, respectively. The comparison with independent evaluations of the stellar masses, for a subset of binary Cepheids in our sample, seems to support the predictive capability of current theoretical scenario. By forcing the coincidence of our mass determinations with these literature values we derive an independent estimate of the mean offset to be applied to Gaia DR2 parallaxes, $<\Delta\varpi>$=0.053 $\pm$ 0.029 mas, slightly higher but in agreement within the errors with Riess2018 value., Comment: 6 pages, 3 figures, 2 tables. Accepted for publication in ApJ Letters

Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique continuation problems, and prove rigorous estimates on the generalization error of PINNs approximating them. An abstract framework is presented and conditional stability estimates for the underlying inverse problem are employed to derive the estimate on the PINN generalization error, providing rigorous justification for the use of PINNs in this context. The abstract framework is illustrated with examples of four prototypical linear PDEs. Numerical experiments, validating the proposed theory, are also presented.

Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for PDEs. An abstract formalism is introduced and stability properties of the underlying PDE are leveraged to derive an estimate for the generalization error in terms of the training error and number of training samples. This abstract framework is illustrated with several examples of nonlinear PDEs. Numerical experiments, validating the proposed theory, are also presented.

Updated evolutionary and pulsational model predictions are combined in order to interpret the properties of Galactic Classical Cepheids in the Gaia Data Release 2. In particular, the location of the instability strip boundaries and the analytical relations connecting pulsation periods to the intrinsic stellar parameters are combined with evolutionary tracks to derive reliable and accurate period-age, and the first theoretical period-age-color relations in the Gaia bands for a solar chemical abundance pattern ($Z$=$0.02$, $Y$=$0.28$). The adopted theoretical framework takes into account possible variations in the mass-luminosity relation for the core helium-burning stage as due to changes in the core convective overshooting and/or mass loss efficiency, as well as the impact on the instability strip boundaries due to different assumptions for superadiabatic convection efficiency. The inferred period-age and period-age-color relations are applied to a selected sample of both fundamental and first overtone Gaia Cepheids, and individual ages for the various adopted theoretical scenarios are derived. The retrieved age distributions confirm that a variation in the efficiency of superadiabatic convection in the pulsational model computations has a negligible effect, whereas a brighter Mass-Luminosity relation, as produced by mild overshooting, rotation or mass loss, implies significantly older age predictions. Moreover, older Cepheids are found at larger Galactocentric distances, while first overtone Cepheids are found to be systematically older than the fundamental ones. The comparison with independent age distribution analysis in literature supports the predictive capability of current theoretical framework., Comment: 14 pages, 11 figures, 8 tables, accepted for publication in MNRAS

We present the results of the light curve model fitting technique applied to optical and near-infrared photometric data for a sample of 18 Classical Cepheids (11 fundamentals and 7 first overtones) in the Large Magellanic Cloud (LMC). We use optical photometry from the OGLE III database and near--infrared photometry obtained by the European Southern bservatory public survey "VISTA near--infrared survey of the Magellanic Clouds system". Iso--periodic nonlinear convective model sequences have been computed for each selected Cepheid in order to reproduce the multi--filter light curve amplitudes and shape details. The inferred individual distances provide an intrinsic weighted mean value for the LMC distance modulus of $\mu_0=18.56$ mag with a standard deviation of 0.13 mag. We derive also the Period--Radius, the Period--Luminosity and the Period--Wesenheit relations that are consistent with similar relations in the literature. The intrinsic masses and luminosities of the best--fitting models show that all the investigated pulsators are brighter than the redictions of the canonical evolutionary mass--luminosity relation, suggesting a significant efficiency of non--canonical phenomena, such as overshooting, mass loss and/or rotation., Comment: 14 pages, 10 figures, MNRAS accepted

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies on judiciously combining a large number of computationally cheap training data on coarse resolutions with a few expensive training samples on fine grid resolutions. Theoretical arguments for lowering the generalization error, based on reducing the variance of the underlying maps, are provided and numerical evidence, indicating significant gains over underlying single-level machine learning algorithms, are presented. Moreover, we also apply the multi-level algorithm in the context of forward uncertainty quantification and observe a considerable speed-up over competing algorithms.

The second Gaia data release is expected to contain data products from about 22 months of observation. Based on these data, we aim to provide an advance publication of a full-sky Gaia map of RR Lyrae stars. Although comprehensive, these data still contain a significant fraction of sources which are insufficiently sampled for Fourier series decomposition of the periodic light variations. The challenges in the identification of RR Lyrae candidates with (much) fewer than 20 field-of-view transits are described. General considerations of the results, their limitations, and interpretation are presented together with prospects for improvement in subsequent Gaia data releases., Comment: 5 pages, 1 figure, Proceedings of the RR Lyrae 2017 Conference (Revival of the Classical Pulsators: from Galactic Structure to Stellar Interior Diagnostics), to be published in the Proceedings of the Polish Astronomical Society

The "VISTA near-infrared YJKs survey of the Magellanic System" (VMC) is collecting deep Ks-band time-series photometry of pulsating stars hosted by the two Magellanic Clouds and their connecting Bridge. Here we present YJKs light curves for a sample of 717 Small Magellanic Cloud (SMC) Classical Cepheids (CCs). These data, complemented with our previous results and V magnitude from literature, allowed us to construct a variety of period-luminosity and period-Wesenheit relationships, valid for Fundamental, First and Second Overtone pulsators. These relations provide accurate individual distances to CCs in the SMC over an area of more than 40 sq. deg. Adopting literature relations, we estimated ages and metallicities for the majority of the investigated pulsators, finding that: i) the age distribution is bimodal, with two peaks at 120+-10 and 220+-10 Myr; ii) the more metal-rich CCs appear to be located closer to the centre of the galaxy. Our results show that the three-dimensional distribution of the CCs in the SMC, is not planar but heavily elongated for more than 25-30 kpc approximately in the east/north-east towards south-west direction. The young and old CCs in the SMC show a different geometric distribution. Our data support the current theoretical scenario predicting a close encounter or a direct collision between the Clouds some 200 Myr ago and confirm the presence of a Counter-Bridge predicted by some models. The high precision three-dimensional distribution of young stars presented in this paper provides a new testbed for future models exploring the formation and evolution of the Magellanic System., Comment: 21 Pages. Accepted for publication in MNRAS. Minor changes with respect to previous version

Gaia Data Release 1 contains parallaxes for more than 700 Galactic Cepheids and RR Lyrae stars, computed as part of the Tycho-Gaia Astrometric Solution (TGAS). We have used TGAS parallaxes, along with literature ($V, I, J, {K_\mathrm{s}}, W_1$) photometry and spectroscopy, to calibrate the zero point of the Period-Luminosity and Period-Wesenheit relations of classical and type II Cepheids, and the near-infrared Period-Luminosity, Period-Luminosity-Metallicity and optical Luminosity-Metallicity relations of RR Lyrae stars. In this contribution we briefly summarise results obtained by fitting these basic relations adopting different techniques that operate either in parallax or distance (absolute magnitude) space., Comment: 5 pages, 4 figures, proceedings for the 22nd Los Alamos Stellar Pulsation Conference Series Meeting "Wide field variability surveys: a 21st-century perspective", held in San Pedro de Atacama, Chile, Nov. 28 - Dec. 2, 2016

We present the results of the chi2 minimization model fitting technique applied to optical and near-infrared photometric and radial velocity data for a sample of 9 fundamental and 3 first overtone classical Cepheids in the Small Magellanic Cloud (SMC). The near- infrared photometry (JK filters) was obtained by the European Southern Observatory (ESO) public survey "VISTA near-infrared Y; J;Ks survey of the Magellanic Clouds system"(VMC). For each pulsator isoperiodic model sequences have been computed by adopting a nonlinear convective hydrodynamical code in order to reproduce the multi- filter light and (when available) radial velocity curve amplitudes and morphological details. The inferred individual distances provide an intrinsic mean value for the SMC distance modulus of 19.01 mag and a standard deviation of 0.08 mag, in agreement with the literature. Moreover the instrinsic masses and luminosities of the best fitting model show that all these pulsators are brighter than the canonical evolutionary Mass- Luminosity relation (MLR), suggesting a significant efficiency of core overshooting and/or mass loss. Assuming that the inferred deviation from the canonical MLR is only due to mass loss, we derive the expected distribution of percentage mass loss as a function of both the pulsation period and of the canonical stellar mass. Finally, a good agreement is found between the predicted mean radii and current Period-Radius (PR) relations in the SMC available in the literature. The results of this investigation support the predictive capabilities of the adopted theoretical scenario and pave the way to the application to other extensive databases at various chemical compositions, including the VMC Large Magellanic Cloud pulsators and Galactic Cepheids with Gaia parallaxes., Comment: 14 pages, 11 figures, accepted for publication on MNRAS

We present a theoretical investigation of multifilter (U,B,V, I and K) light and radial velocity curves of five Classical Cepheids in NGC 1866, a young massive cluster of the Large Magellanic Cloud. The best fit models accounting for the luminosity and radial velocity variations of the five selected variables, four pulsating in the fundamental mode and one in the first overtone, provide direct estimates of their intrinsic stellar parameters and individual distances. The resulting stellar properties indicate a slightly brighter Mass Luminosity relation than the canonical one, possibly due to mild overshooting and/or mass loss. As for the inferred distances, the individual values are consistent within the uncertainties. Moreover, their weighted mean value corresponds to a distance modulus of 18.56 + - 0.03 (stat) + - 0.1 (syst) mag, in agreement with several independent results in the literature., Comment: 14 pages, 10 figures, accepted for publication on MNRAS