arXiv subjects

Disha Hegde

Publications and source records attributed to Disha Hegde.

7 recordsLinked to original sources

arXiv2026

On the interplay between waveform systematics and lensing signatures in gravitational-wave signals

The exceptional gravitational-wave event GW231123 exhibited unusually high total mass and near-extremal spins, while revealing strong waveform-dependent variations in its inferred source properties. Several follow-up studies favored a lensed interpretation, with reduced waveform systematics, raising the question of whether apparent lensing evidence could arise from waveform modeling systematics. Using GW231123-like numerical-relativity injections, we find that lensing degrees of freedom can reduce waveform discrepancies and yield non-negligible lensing support. However, this behavior is not systematic across injections, and cases where all waveform and lens models favor lensing while reducing waveform discrepancies are not found.

gr-qc↗

arXiv2026

GW Microlensing: Degeneracy with Unlensed Precessing and Non-Spinning Gravitational-Wave Signals

With nearly 400 Gravitational Wave (GW) events detected by the LIGO-Virgo-KAGRA network and many more expected, similarities between signals produced by different astrophysical effects can complicate template-based searches and parameter estimation. In particular, GW modulations from spin precession can resemble the beating pattern induced by microlensing from compact objects with masses of $10$-$10^5,M_\odot$. We investigate this degeneracy and assess whether machine learning can distinguish between these effects. We generate 20,000 simulated GW signals for each class with a network optimal signal-to-noise ratio above 20 and train a convolutional neural network on time-frequency (Q-transform) spectrograms. The classifier achieves up to 95% accuracy in Gaussian noise and 82% in real detector noise. We also study classification between microlensed (ML) and unlensed non-spinning (UN) signals, as well as between unlensed non-spinning (UN) and unlensed precessing (UP) signals. While distinguishing UN from UP remains difficult even in Gaussian noise, ML vs. UN classification reaches up to 80% accuracy in real noise. We identify the regions of parameter space where the classifier performs best and evaluate the ML-UN network on real GW events, finding that the model trained on Gaussian noise generalizes better than the one trained on real noise. This work presents the first low-latency machine-learning pipeline for distinguishing microlensed from unlensed non-spinning GW signals.

astro-ph.CO↗

arXiv2026

Extrapolating from Regularised Solutions for Solving Ill-Conditioned Linear Systems in Machine Learning

Rapid prototyping of algorithms is a critical step in modern machine learning. Most algorithms exploit linear algebra, creating a need for lightweight numerical routines which -- while potentially sub-optimal for the task at hand -- can be rapidly implemented. For the numerical solution of ill-conditioned linear systems of equations, the standard solution for prototyping is Tikhonov-regularised inversion using a nugget. However, selection of the size of nugget is often difficult, and the use of data-adaptive procedures precludes automatic differentiation, introducing instabilities into end-to-end training. Further, while data-adaptive procedures perform multiple linear solves to select the size of nugget, only the result of one such solve is returned, which we argue is wasteful. This paper aims to circumvent the above difficulties, presenting autonugget; a Python package for automatic and stable numerical solution of linear systems suitable for rapid prototyping, and fully compatible with automatic differentiation using JAX. autonugget combines multiple linear solves using Richardson extrapolation to determine the solution of the ill-conditioned system, improving in accuracy over approximations based on a single nugget.

stat.ML↗

arXiv2026

Affine Tracing: A New Paradigm for Probabilistic Linear Solvers

Probabilistic linear solvers (PLSs) return probability distributions that quantify uncertainty due to limited computation in the solution of linear systems. The literature has traditionally distinguished between Bayesian PLSs, which condition a prior on information obtained from projections of the linear system, and probabilistic iterative methods (PIMs), which lift classical iterative solvers to probability space. In this work we show this dichotomy to be false: Bayesian PLSs are a special case of non-stationary affine PIMs. In addition, we prove that any realistic affine PIM is calibrated. These results motivate a focus on (non-stationary) affine PIMs, but their practical adoption has been limited by the significant manual effort required to implement them. To address this, we introduce affine tracing, an algorithmic framework that automatically constructs a PIM from a standard implementation of an affine iterative method by passing symbolic tracers through the computation to build an affine computational graph. We show how this graph can be transformed to compute posterior covariances, and how equality saturation can be used to perform algebraic simplifications required for computation under specific prior choices. We demonstrate the framework by automatically generating a probabilistic multigrid solver and evaluate its performance in the context of Gaussian process approximation.

stat.ML↗

arXiv2025

Randomised Postiterations for Calibrated BayesCG

The Bayesian conjugate gradient method offers probabilistic solutions to linear systems but suffers from poor calibration, limiting its utility in uncertainty quantification tasks. Recent approaches leveraging postiterations to construct priors have improved computational properties but failed to correct calibration issues. In this work, we propose a novel randomised postiteration strategy that enhances the calibration of the BayesCG posterior while preserving its favourable convergence characteristics. We present theoretical guarantees for the improved calibration, supported by results on the distribution of posterior errors. Numerical experiments demonstrate the efficacy of the method in both synthetic and inverse problem settings, showing enhanced uncertainty quantification and better propagation of uncertainties through computational pipelines.

stat.ML↗

arXiv2025

Learning to Solve Related Linear Systems

Solving multiple parametrised related systems is an essential component of many numerical tasks, and learning from the already solved systems will make this process faster. In this work, we propose a novel probabilistic linear solver over the parameter space. This leverages information from the solved linear systems in a regression setting to provide an efficient posterior mean and covariance. We advocate using this as companion regression model for the preconditioned conjugate gradient method, and discuss the favourable properties of the posterior mean and covariance as the initial guess and preconditioner. We also provide several design choices for this companion solver. Numerical experiments showcase the benefits of using our novel solver in a hyperparameter optimisation problem.

stat.ML↗

arXiv2024

Calibrated Computation-Aware Gaussian Processes

Gaussian processes are notorious for scaling cubically with the size of the training set, preventing application to very large regression problems. Computation-aware Gaussian processes (CAGPs) tackle this scaling issue by exploiting probabilistic linear solvers to reduce complexity, widening the posterior with additional computational uncertainty due to reduced computation. However, the most commonly used CAGP framework results in (sometimes dramatically) conservative uncertainty quantification, making the posterior unrealistic in practice. In this work, we prove that if the utilised probabilistic linear solver is calibrated, in a rigorous statistical sense, then so too is the induced CAGP. We thus propose a new CAGP framework, CAGP-GS, based on using Gauss-Seidel iterations for the underlying probabilistic linear solver. CAGP-GS performs favourably compared to existing approaches when the test set is low-dimensional and few iterations are performed. We test the calibratedness on a synthetic problem, and compare the performance to existing approaches on a large-scale global temperature regression problem.

stat.ML↗