Research

I build contrastive learning methods for gravitational-wave science: models that learn what gravitational-wave data mean by learning what belongs together and what does not.

Contrastive learning trains a network to tell matched pairs from mismatched ones. That one principle covers much of what gravitational-wave science needs. Pair data with data, and you learn representations of detector strain that transfer across tasks. Pair data with physical parameters, and you get inference: calibrated posteriors, learned directly from simulations. Next-generation detectors such as LISA and the Einstein Telescope will record far more signals than today’s instruments, many of them long and overlapping, and I develop contrastive methods that scale to that regime.

Contrastive representation learning

An encoder learns a representation of detector strain by pulling together different views of the same signal and pushing apart unrelated signals and noise. A good representation captures the physics of the data, so one encoder can serve many tasks.

Views of the same signal are mapped close together in representation space, while other signals and noise are pushed apart. The learned encoder is shared across downstream tasks.

Contrastive inference

A classifier is trained to distinguish matched pairs (θ, x) drawn together from the simulator from pairs where θ and x have been shuffled. The optimal classifier encodes the posterior-to-prior ratio, so the likelihood is never evaluated. Because θ can be any subset of parameters, each marginal posterior can be learned on its own.

For inference, the contrastive objective pairs data with physical parameters. This is neural ratio estimation (NRE). Two features make it powerful for gravitational waves. It is marginal: a network can target only the parameters you care about, such as the chirp mass and mass ratio, without sampling the full 15-dimensional posterior. It is targeted: after each round, regions of the prior that are ruled out for the observed signal are truncated, so later simulations concentrate where the posterior actually is. Together these give truncated marginal neural ratio estimation (TMNRE).

Targeted marginal inference for transient signals

Four-step TMNRE loop: simulate, train ratio estimators, infer, truncate the prior, repeat. — The TMNRE loop as implemented in *peregrine*: simulate, estimate ratios for each marginal, infer for the target observation, truncate the prior, and repeat until converged.

With peregrine we showed that TMNRE recovers marginal posteriors for precessing binary black hole mergers that match a standard nested-sampling analysis, while using only about 2% of the waveform evaluations. Because each marginal is learned directly, cost goes into the parameters of interest rather than the full joint space.

1D marginal posteriors for all 15 binary black hole parameters, peregrine versus dynesty. — 1D marginals for all 15 parameters of a high-SNR binary black hole: *peregrine* (orange) against the likelihood-based *dynesty* result (purple). Dashed lines mark injected values.

Paper: Bhardwaj et al., PRD 108, 042004 (2023) · Code: peregrine

Overlapping transient signals

Einstein Telescope and Cosmic Explorer will regularly record several signals in the same stretch of data. A joint likelihood analysis of overlapping sources scales badly with the number of parameters. Marginal NRE sidesteps this: we inferred all 30 parameters of two overlapping binary black holes, using only about 15% of the waveform evaluations a traditional method needs for a single signal.

Two binary black hole signals overlapping in detector strain, merging 0.05 seconds apart. — Two binary black hole signals merging 0.05 s apart, individually (top) and as observed (bottom).

Chirp mass posteriors of both signals for three different merger-time separations. — Chirp masses of both signals are recovered for all three time separations, consistent with single-signal analyses (dashed).

Paper: Bhardwaj & Alvey et al. (2023) · Code: peregrine

Persistent and transient signals in LISA

LISA data will contain a stochastic gravitational-wave background on top of instrumental noise and a population of transient signals. With saqqara, we use marginalisation to infer the background in simulated LISA data in the presence of overlapping transients. A standard analysis that ignores the transients is biased; the marginal NRE analysis is not.

Corner plot of background and noise parameters with and without transients, comparing saqqara and MCMC. — Background amplitude and slope (α, γ) and noise parameters (A, P). Without transients, *saqqara* (solid) and MCMC (dashed) agree (black). With transients added (orange), MCMC is pulled away from the truth, while *saqqara* still recovers it. Inset: excess power from the transients.

Paper: Alvey, Bhardwaj et al., PRD 109, 083008 (2024) · Code: saqqara

Flexible representations: time-varying noise

Real LISA noise will drift over the mission. Likelihood-based methods have to model this explicitly, but a neural ratio estimator can learn a data representation that absorbs it. We showed that this representation flexibility turns time-varying noise from a nuisance into an advantage: constraints on the background come close to the Fisher-matrix forecast, and are tighter than when the noise is assumed fixed.

Histograms of sensitivity to background amplitude and slope for time-dependent versus time-independent noise. — Sensitivity to the background amplitude σ(α) and slope σ(γ). SBI with time-dependent noise (blue) approaches the Fisher forecast (black) and outperforms the time-independent case (orange).

Paper: Alvey, Bhardwaj et al., PRD 111, 102006 (2025)

Extreme mass ratio inspirals

EMRIs produce long, intricate waveforms with a highly multimodal likelihood, which makes them a hard case for stochastic samplers. Sequential truncation with TMNRE reliably narrows an initially broad prior to the true source parameters over a few rounds.

Prior bounds for each EMRI parameter shrinking over seven rounds of TMNRE, compared with differential evolution. — Prior region retained by TMNRE (shaded) over seven rounds, for each EMRI parameter, compared with points found by differential evolution (red). Dashed lines mark injected values.

Paper: Cole et al., PRD 113, 063030 (2026)

Multi-messenger astronomy

How binary neutron star ejecta models affect kilonova parameter estimation (Henkel et al. 2025).

AI for scientific discovery

praxis configures a large language model as a small research lab that follows the scientific method explicitly; the reference setup and examples use Claude. It frames a falsifiable question, reads the literature, computes on real data, then tries to break its own result, with every number traceable to its source. Domain packs make it an expert co-scientist in a given field; the first cover ground-based gravitational waves and pulsar timing arrays. Built at the Anthropic–ETH AI Sprint.

Student projects

I supervise BSc and MSc thesis projects in gravitational-wave data analysis and machine learning. I am especially keen to hear from students interested in:

gravitational-wave inference with simulation-based inference,
contrastive learning across multiple data representations,
interpretable machine-learning models for gravitational-wave science.

If you are interested, email me with a short, informal motivation statement and your CV.