arXiv subjects

Vaibhav Dixit

Publications and source records attributed to Vaibhav Dixit.

11 recordsLinked to original sources

arXiv2026

Development of ProtoPol: a medium resolution echelle spectro-polarimeter for PRL telescopes, Mt Abu, India -- Part I : the design, development and laboratory characterization

ProtoPol is a medium-resolution echelle spectro-polarimeter developed for Physical Research Laboratory (PRL) 1.2m and 2.5m telescopes, Mt. Abu, India. Though initially conceived to evaluate the development methodology of the echelle spectro-polarimeter, it was subsequently elevated to the level of a full-fledged back-end instrument for PRL telescopes. ProtoPol is developed on the traditional concept of using a half-wave plate with Wollaston prism to achieve the separation of two mutually orthogonal polarized beams. These separated beams are modulated and directed into an echelle spectrometer which is employs an echelle grating and two plane reflection gratings as the cross-dispersers. Therefore, the cross-dispersed spectra for two orthogonal polarized beams are recorded in multiple orders on a CCD detector. ProtoPol is designed to operate in the visible and near IR spectral range, 4000 - 9600 angstrom, with a spectral resolution ($δ$$λ$) around 0.4-0.75 angstrom. The uniqueness of ProtoPol lies in its design which has entirely been developed with commercially available off-the-shelf optical and opto-mechanical components. This feature makes ProtoPol a noteworthy development as it offers a cost-effective way to develop spectro-polarimeters with such resolutions for small-aperture (2-3m) telescopes around the world, in a much shorter development period. ProtoPol has been successfully developed and commissioned on PRL 1.2m and 2.5m telescopes since December 2023, and a variety of observations have been carried out for instrument characterization, performance verification, and scientific purposes. This is the first of the two-part research articles series, wherein we present the design and development methodology of ProtoPol, along with its laboratory characterization and performance.

astro-ph.IM↗

arXiv2026

Development of ProtoPol: a medium resolution echelle spectro-polarimeter for PRL telescopes, Mt Abu, India -- Part II : the data-reduction pipeline, on-sky characterization $\&$ performance verification and first science results

We present the development of ProtoPol - a medium resolution echelle spectro-polarimeter for the PRL 1.2m and 2.5m telescopes at Mt Abu observatory, India. In this second and final part of the paper series, we report on the development of a dedicated data reduction pipeline of ProtoPol along with several characterization, performance evaluation, and scientific observations to quantify the performance of the instrument. ProtoPol provides a spectral resolution in the range of $\sim$0.4 - 0.75 angstrom across various orders in the visible wavelength range of 4000-9600 angstrom. On PRL 2.5m telescope, an SNR of 10 is achieved for $m_V\sim13.2$ source in 1 hour of integration time, and its throughput is estimated to be $\sim$6\% including all the contributing factors such as atmospheric transmission, telescope reflectivity, instrument's optics, CCD efficiency etc. ProtoPol achieved a linear polarization accuracy $δP \approx 0.1-0.2\%$ in 2 hours of integration time for a source with $m_V\approx8$. The instrumental polarization is determined to be around $0.1\%$. We also present the first science results with ProtoPol to demonstrate the capabilities of the instrument. A sample of Herbig Ae/Be stars, classical Herbig stars, Symbiotic stars, and AGB/post-AGB stars were observed over the period of one and half years for their spectro-polarimetry measurements covering various physical mechanisms such as intrinsic line polarization in Herbig and classical Be stars, Raman scattered features in Symbiotic stars, as well as continuum polarization in AGB/post-AGB stars to verify the polarization performance of the instrument.

astro-ph.IM↗

arXiv2025

Disciplined Geodesically Convex Programming

Convex programming plays a fundamental role in machine learning, data science, and engineering. Testing convexity structure in nonlinear programs relies on verifying the convexity of objectives and constraints. Grant et al. (2006) introduced a framework, Disciplined Convex Programming (DCP), for automating this verification task for a wide range of convex functions that can be decomposed into basic convex functions (atoms) using convexity-preserving compositions and transformations (rules). Here, we extend this framework to functions defined on manifolds with non-positive curvature (Hadamard manifolds) by introducing Disciplined Geodesically Convex Programming (DGCP). In particular, this allows for verifying a broader range of convexity notions. For instance, many notable instances of statistical estimators and matrix-valued (sub)routines in machine learning applications are Euclidean non-convex, but exhibit geodesic convexity through a more general Riemannian lens. To define the DGCP framework, we determine convexity-preserving compositions and transformations for geodesically convex functions on general Hadamard manifolds, as well as for the special case of symmetric positive definite matrices, a common setting in matrix-valued optimization. For the latter, we also define a basic set of atoms. Our paper is accompanied by a Julia package SymbolicAnalysis.jl, which provides functionality for testing and certifying DGCP-compliant expressions. Our library interfaces with manifold optimization software, which allows for directly solving verified geodesically convex programs.

math.OC↗

arXiv2025

Scientific Machine Learning of Chaotic Systems Learns Reduced-Order Equations for Neural Populations

Extracting interpretable mathematical models from complex dynamical systems is difficult, especially for chaotic dynamics observed with noisy experimental data. We present PEM-UDE, a method that combines prediction-error methodology with universal differential equations to discover governing equations from limited, noise-corrupted observations. Prediction-error feedback smooths the chaotic optimization problem; for noise-free data generated within the model class, it preserves the data-consistent zero-loss set, whereas noise and model misspecification introduce a gain-dependent stability-bias trade-off. Preservation of the zero-loss set is not a guarantee of unique structural identifiability. We test the method on two benchmark chaotic systems, the Rossler attractor and a real electrical circuit, and recover the correct functional forms even when one observed dimension contains noise of five times the signal magnitude. The method also accepts prior knowledge of the system as an initial functional form, which we use to learn neural circuit equations that account for sparse connectivity, a feature missing from conventional neural mass models. Applied to a population of Izhikevich neurons, PEM-UDE yields a multi-scale neural mass model that ties single-neuron parameters to macroscopic network dynamics and predicts a relationship between connection density, dominant oscillation frequency, and synchrony. We test these predictions against three intracranial recording datasets from rat and human cortices. For the neuroscience application, the learned equations are a reduced-order closure for a specified simulated Izhikevich network family; the experimental recordings provide an indirect consistency check of predicted frequency and synchrony trends, not a direct fit of the equations to recordings.

cs.LG↗

arXiv2022

Bayesian Neural Ordinary Differential Equations

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the question: "Can Bayesian learning frameworks be integrated with Neural ODE's to robustly quantify the uncertainty in the weights of a Neural ODE?" remains unanswered. In an effort to address this question, we primarily evaluate the following categories of inference methods: (a) The No-U-Turn MCMC sampler (NUTS), (b) Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) and (c) Stochastic Langevin Gradient Descent (SGLD). We demonstrate the successful integration of Neural ODEs with the above Bayesian inference frameworks on classical physical systems, as well as on standard machine learning datasets like MNIST, using GPU acceleration. On the MNIST dataset, we achieve a posterior sample accuracy of 98.5% on the test ensemble of 10,000 images. Subsequently, for the first time, we demonstrate the successful integration of variational inference with normalizing flows and Neural ODEs, leading to a powerful Bayesian Neural ODE object. Finally, considering a predator-prey model and an epidemiological system, we demonstrate the probabilistic identification of model specification in partially-described dynamical systems using universal ordinary differential equations. Together, this gives a scientific machine learning tool for probabilistic estimation of epistemic uncertainties.

cs.LG↗

arXiv2021

Design and Development of Mt. Abu Faint Object Spectrograph and Camera -- Pathfinder (MFOSC-P) for PRL 1.2m Mt. Abu Telescope

Mt. Abu Faint Object Spectrograph and Camera - Pathfinder (MFOSC-P) is an imager-spectrograph developed for the Physical Research Laboratory (PRL) 1.2m telescope at Gurushikhar, Mt. Abu, India. MFOSC-P is based on a focal reducer concept and provides seeing limited imaging (with a sampling of 3.3 pixels per arc-second) in Bessell's B, V, R, I and narrow-band H-$α$ filters. The instrument uses three plane reflection gratings, covering the spectral range of 4500-8500$Å$, with three different resolutions of 500, 1000, and 2000 around their central wavelengths. MFOSC-P was conceived as a pathfinder instrument for a next-generation instrument on the PRL's 2.5m telescope which is coming up at Mt. Abu. The instrument was developed during 2015-2019 and successfully commissioned on the PRL 1.2m telescope in February 2019. The designed performance has been verified with laboratory characterization tests and on-sky commissioning observations. Different science programs covering a range of objects are being executed with MFOSC-P since then, e.g., spectroscopy of M-dwarfs, novae $\&$ symbiotic systems, and detection of H-$α$ emission in star-forming regions. MFOSC-P presents a novel design and cost-effective way to develop a FOSC (Faint Object Spectrograph and Camera) type of instrument on a shorter time-scale of development. The design and development methodology presented here is most suitable in helping the small aperture telescope community develop such a versatile instrument, thereby diversifying the science programs of such observatories.

astro-ph.IM↗

arXiv2020

First Results from MFOSC-P : Low Resolution Optical Spectroscopy of a Sample of M dwarfs within 100 parsecs

Mt. Abu Faint Object Spectrograph and Camera (MFOSC-P) is an in-house developed instrument for Physical Research Laboratory (PRL) 1.2m telescope at Mt. Abu India, commissioned in February 2019. Here we present the first science results derived from the low resolution spectroscopy program of a sample of M Dwarfs carried out during the commissioning run of MFOSC-P between February-June 2019. M dwarfs carry great significance for exoplanets searches in habitable zone and are among the promising candidates for the observatory's several ongoing observational campaigns. Determination of their accurate atmospheric properties and fundamental parameters is essential to constrain both their atmospheric and evolutionary models. In this study, we provide a low resolution (R$\sim$500) spectroscopic catalogue of 80 bright M dwarfs (J$<$10) and classify them using their optical spectra. We have also performed the spectral synthesis and $χ^2$ minimisation techniques to determine their fundamental parameters viz. effective temperature and surface gravity by comparing the observed spectra with the most recent BT-Settl synthetic spectra. Spectral type of M dwarfs in our sample ranges from M0 to M5. The derived effective temperature and surface gravity are ranging from 4000 K to 3000 K and 4.5 to 5.5 dex, respectively. In most of the cases, the derived spectral types are in good agreement with previously assigned photometric classification.

astro-ph.SR↗

arXiv2019

DiffEqFlux.jl - A Julia Library for Neural Differential Equations

DiffEqFlux.jl is a library for fusing neural networks and differential equations. In this work we describe differential equations from the viewpoint of data science and discuss the complementary nature between machine learning models and differential equations. We demonstrate the ability to incorporate DifferentialEquations.jl-defined differential equation problems into a Flux-defined neural network, and vice versa. The advantages of being able to use the entire DifferentialEquations.jl suite for this purpose is demonstrated by counter examples where simple integration strategies fail, but the sophisticated integration strategies provided by the DifferentialEquations.jl library succeed. This is followed by a demonstration of delay differential equations and stochastic differential equations inside of neural networks. We show high-level functionality for defining neural ordinary differential equations (neural networks embedded into the differential equation) and describe the extra models in the Flux model zoo which includes neural stochastic differential equations. We conclude by discussing the various adjoint methods used for backpropogation of the differential equation solvers. DiffEqFlux.jl is an important contribution to the area, as it allows the full weight of the differential equation solvers developed from decades of research in the scientific computing field to be readily applied to the challenges posed by machine learning and data science.

cs.LG↗

arXiv2018

A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions

Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of choices and a Cartesian product of potential methods, it can be difficult for practitioners to understand which method is likely to be the most effective on their particular application. In this manuscript we investigate the performance characteristics of Discrete Local Sensitivity Analysis implemented via Automatic Differentiation (DSAAD) against continuous adjoint sensitivity analysis. Non-stiff and stiff biological and pharmacometric models, including a PDE discretization, are used to quantify the performance of sensitivity analysis methods. Our benchmarks show that on small systems of ODEs (approximately $<100$ parameters+ODEs), forward-mode DSAAD is more efficient than both reverse-mode and continuous forward/adjoint sensitivity analysis. The scalability of continuous adjoint methods is shown to be more efficient than discrete adjoints and forward methods after crossing this size range. These comparative studies demonstrate a trade-off between memory usage and performance in the continuous adjoint methods that should be considered when choosing the technique, while numerically unstable backsolve techniques from the machine learning literature are demonstrated as unsuitable for most scientific models. The performance of adjoint methods is shown to be heavily tied to the reverse-mode AD method, with tape-based AD methods shown to be 2 orders of magnitude slower on nonlinear partial differential equations than static AD techniques. These results also demonstrate the applicability of DSAAD to differential-algebraic equations, delay differential equations, and hybrid differential equation systems, showcasing an ease of implementation advantage for DSAAD approaches.

math.NA↗

arXiv2014

Determination of mass and orbital parameters of a low-mass star HD 213597B

HD 213597 is an eclipsing binary system which was detected by the STEREO spacecraft and was speculated to host a low-mass stellar companion. We used high-resolution spectroscopy with the 10-m Hobby-Eberly Telescope and the 1.2-m telescope in Mt Abu for radial velocity (RV) measurements of this source. We performed aperture photometry for this star on the STEREO archival data and thereby confirm the transit signature. We also did follow-up ground-based photometry with a 10-inch telescope from Mt Abu. The spectroscopic RV semi-amplitude of the primary (33.39 km s^-1) indicates that the secondary is an M dwarf making the system a short period F+M eclipsing binary. These RVs along with the inclination derived from our combined photometric analysis (i=84.9 degree), enable us to estimate the mass of the secondary as M_B ~ 0.286 M_sun and radius as R_B ~ 0.344 R_sun using an estimated mass M_A ~ 1.3 M_sun and radius R_B ~ 1.97 R_sun of the primary. Our spectral analysis returned the following parameters: T_eff = 6625 +/-121 K, [Fe/H] = -0.095 +\-0.08 and log(g) = 3.72 +/-0.22 for the primary. When log(g) is constrained to a value of 3.96, we derive T_eff = 6753 +/-52 K and [Fe/H] = -0.025+\-0.05.

astro-ph.SR↗

arXiv2013

The PRL Stabilized High Resolution Echelle Fiber-fed Spectrograph: Instrument Description & First Radial Velocity Results

We present spectrograph design details and initial radial velocity results from the PRL optical fiber-fed high-resolution cross-dispersed echelle spectrograph (PARAS), which has recently been commissioned at the Mt Abu 1.2 m telescope, in India. Data obtained as part of the post-commissioning tests with PARAS show velocity precision better than 2m/s over a period of several months on bright RV standard stars. For observations of sigma-Dra we report 1.7m/s precision for a period of seven months and 2.1m/s for HD 9407 over a period of 2 months. PARAS is capable of a single-shot spectral coverage of 3800A - 9500A at a resolution of about 67,000. The RV results were obtained between 3800A and 6900A using simultaneous wavelength calibration with a Thorium-Argon (ThAr) hollow cathode lamp. The spectrograph is maintained under stable conditions of temperature with a precision of 0.01 - 0.02C (rms) at 25.55C, and enclosed in a vacuum vessel at pressure of 0.1 +/-0.03 mbar. The blaze peak efficiency of the spectrograph between 5000A and 6500A, including the detector, is 30%; and about 25% with the fiber transmission. The total efficiency, including spectrograph, fiber transmission, focal ratio degradation (FRD), and telescope (with 81% reflectivity) is about 7% in the same wavelength region on a clear night with good seeing conditions.

astro-ph.IM↗