We present posterior-landscape, a Python framework to identify and characterize morphological features in two-dimensional probability densities. The framework combines concepts from topological data analysis, statistical density-ridge estimation, and scale-space image analysis. It extracts localized concentrations, valleys, ridges, and changes of slope; for Bayesian reconstructions, it propagates uncertainty in feature recovery, geometry, and correspondence across posteriors. The framework also connects two-dimensional structures to features in one-dimensional marginals, and quantifies their correlation with other inferred parameters. We validate the method on controlled densities, and demonstrate its use on gravitational-wave population reconstructions, where it provides a systematic way to identify and interpret population features and assess which ones carry information relevant for cosmology. The resulting catalogues also offer a common morphological representation for future comparisons between predictions and population reconstructions.
Machine learning (ML) techniques are increasingly explored to analyse gravitational wave (GW) data expected from the Laser Interferometer Space Antenna (LISA). At the same time, advances in quantum computing have stimulated interest in quantum machine learning as a potential alternative to conventional approaches. We investigate the applicability of quantum, hybrid quantum-classical, and classical ML models to two tasks relevant for LISA observations of massive black hole binaries: GW signal detection and merger prediction. Using the Sangria dataset from the LISA Data Challenge, we benchmark several quantum architectures, including variational quantum classifiers (VQCs), post VQC hybrid models, quantum kernel methods, data reuploading classifiers, and quantum long short-term memory (QLSTM) networks, against classical support vector machines, multilayer perceptrons, recurrent neural networks, and LSTM networks. The models are trained on labelled data derived from the Sangria training dataset and evaluated on the corresponding blind dataset. For signal detection, several quantum models match or outperform classical baselines. In particular, the best performing hybrid post VQC architecture correctly identifies all signal samples in the blind dataset, while the standard VQC and data reuploading classifier achieve competitive detection rates. For merger detection and coalescence time estimation, however, the standard VQC emerges as the most reliable model, successfully localising all detected merger events with the lowest localisation errors. We further analyse the trade-offs between predictive performance, model complexity, and quantum circuit resources. Our results indicate that, although no universal quantum advantage is observed, selected quantum models can provide practical benefits for specific GW analysis tasks and represent promising candidates for future LISA data analysis pipelines.
How many latent variables are needed to fit the cosmic microwave background (CMB) temperature and polarisation power spectra when a neural network is given no cosmological model, and to what extent do they map onto the standard cosmological parameters? We use multi-task learning with variational autoencoders trained on CLASS-generated spectra (TT, TE, EE) over $2\le\ell\le2500$. No cosmological model is built into the network, and the number of latent variables, $L$, is varied over $L=5$, $6$ and $7$. Their fits are compared to the Planck 2018 data using $\hatχ^2$, AIC, BIC and Bayesian evidence. Their correspondence with cosmological parameters is measured with normalised mutual information post-training. The loss weights are set within a single training run by uncertainty weighting, with the weight of the disentanglement term either fixed (semi-automated, SA) or learned (completely automated, CA). The reconstruction loss is split over multipole ranges in three configurations that separate the roles of temperature and polarisation and of the low- and high-$\ell$ ranges. In four of the six combinations of configuration and strategy, the fit improves from $L=5$ to $L=6$ and not beyond, and $L=6$ is the best, or close to the best, in five of the six cases. So, six latent variables are needed, as many as the free parameters of the standard, model-dependent approach. SA gives clearer disentanglement, while CA needs no a priori choice of the disentanglement weight and has the higher evidence at $L=5$ and $6$: the two strategies are points on a trade-off between interpretability and fit to the data. Notably, the latent variables for $τ$ and $A_s$ share almost no information in any model, consistent with large-scale polarisation separating the two, as in standard analyses. A deep-learning approach can thus give a compact, data-driven parametrisation of the CMB spectra.
As spectroscopic surveys grow, estimating galaxy properties such as metallicity, star formation rate, and redshift becomes computationally cumbersome. Methods of estimating such properties rely on template spectra or curated redshift catalogs, which fail to represent the diversity of objects seen in large-scale surveys. We present UnEZ, a fully unsupervised, physics-informed machine learning model that can predict spectroscopic redshifts and line strengths with no prior redshift or line strength labels. An encoder predicts emission and absorption line amplitudes/widths, and a fixed deterministic decoder constructs a unique template, estimated redshift, redshift confidence curve, and spectral model. UnEZ was tested on the Sloan Digital Sky Survey (SDSS) Data Release 18 due to its large dataset and thoroughly vetted redshift catalog which serves as an independent benchmark. Despite the lack of templates, line strength labels, or redshift labels, UnEZ's performance competes with modern redshift estimation algorithms. At SNR > 10, UnEZ achieves an outlier fraction of 0.459% and a normalized median absolute deviation (NMAD) of $1.237 \times 10^{-4}$. At SNR > 3, UnEZ achieves an outlier fraction of 3.89% and an NMAD of $1.471 \times 10^{-4}$. Furthermore, we demonstrate how UnEZ's line strength and redshift predictions can be utilized for various purposes such as constructing template spectra required in traditional redshift estimation algorithms. UnEZ illustrates how a fully unsupervised neural network can allow redshift, among other galaxy properties, to emerge naturally from the spectra themselves, providing a template-free, label-free approach that scales to the demands of future surveys.
The next-generation Very Large Array (ngVLA) intends to use 22 GHz water vapor radiometry (WVR) to correct for tropospheric phase fluctuations in its high-frequency bands. However, current delay-retrieval methods do not reach the required accuracy and reliability. As a remedy, we propose a machine-learning based retrieval concept and a preliminary architecture, framed as heterogeneous, multi-rate sensor fusion. Atmospheric reanalysis profiles and surface weather set the context in which per-antenna WVR spectra are used to estimate excess path by a Kalman filter whose parameters are learned from high-cadence calibrator phases. The method is being developed, with planned first validation on the 183 GHz WVR system of the Atacama Large Millimeter/submillimeter Array (ALMA).
Anomaly detectors rank unfamiliar examples for expert confirmation, and the confirmed examples teach a classifier to recognise a new class. Across five benchmarks from physics, medicine and computer vision, the members flagged by the detector are those the classifier learns first. In three systems, confirming the highest-ranked members of a new class gives lower recognition than confirming the same number of random members. Handing subsequent selection to the promoted classifier recovers part of this loss in two systems. A paired intervention further shows that replacing nearby known classes with distant ones sharply reduces the confirmations needed for recognition. These results distinguish finding a new class from selecting examples that teach its extent: within the tested classes, concentrating confirmations at the top of the anomaly ranking makes learning less efficient.
Three-dimensional magnetohydrodynamic (MHD) turbulence, the flow of astrophysical and fusion plasmas, is costly to simulate. We present, to our knowledge, the first learned surrogates of three-dimensional resistive MHD turbulence, and compare three standard backbones in that role: a convolutional UNet, a shifted-window transformer and a Fourier neural operator. They are trained as autoregressive emulators of decaying MHD turbulence at a resolution of $128^3$ and Reynolds numbers of 1000, 3000 and 6000, on 500 simulations per Reynolds number, each with one two-stage procedure, single steps and then short rollouts, and stopped by one rule. Over a window of about one large-eddy turnover time, the UNet and the transformer reach relative velocity errors of 0.018 to 0.053 and keep the current sheets, the enstrophy, the current density and the energy spectra of the simulation; which of the two is the more accurate depends on the Reynolds number, the UNet leading at 3000 and 6000 and the transformer at 1000. Applied with the same backbones and training procedure to two public benchmarks, the models reach the lowest error reported to date on the isotropic turbulence set of FactFormer, 39% below the best published model. On the compressible MHD set of The Well, their rollout errors are a third to a half below those of the best of The Well's baselines. They also match a 1.3 B-parameter pretrained foundation model in its rollout windows, with 20-62 times fewer parameters. The code, the configuration of every model, the evaluation scripts and the data generator with the seed of every simulation will be released upon publication.
Simulation-trained generative models are emerging as a powerful framework for field-level inference in cosmology, particularly in strongly nonlinear regimes where analytical approaches become intractable. However, the finite size of training datasets often leads to variance shrinkage, indicating that part of the realization-level variability of the underlying physical process is not captured by the learned generative dynamics. In this Letter, we interpret variance shrinkage as a diagnostic of missing effective degrees of freedom and introduce physics-informed latent modifications to the generative dynamics of a continuous normalizing flow. We show that these latent corrections recover a substantial fraction of the missing variability without requiring additional training simulations. Using weak-lensing field-level inference as a representative cosmological application, we further demonstrate through posterior analysis that the learned latent directions are actively exploited during inference and behave as effective nuisance parameters that absorb part of the mismatch between the training and target distributions. As a result, the model exhibits improved robustness to out-of-distribution shifts in field-level inference. Our work establishes variance shrinkage as a practical diagnostic for identifying missing degrees of freedom in simulation-trained generative models and provides a framework for recovering them through physics-informed modifications of generative dynamics.
Unrecognized systematic errors can survive standard checks and undermine scientific discoveries. Null tests and experimental controls can expose these failures, but averaging measurements or reducing them to scalar statistics can hide important structure. We propose ensemble null tests that compare multivariate distributions with references from observations or simulations. We demonstrate their benefits across science. In cosmic microwave background simulations, they detect systematic effects missed by conventional $χ^2$ tests. In Gaia data, they detect velocity asymmetry as sensitively as an informed search. In a CRISPR screen, they expose a control mismatch in DNA damage and reveal which cellular profiles drive it. As scientific datasets grow, ensemble testing turns repeated measurements into a broader search for unknown unknowns, strengthening the empirical foundation for scientific discovery.
The Lane-Emden Equation is a class of nonlinear differential equations commonly used to model phenomena in astrophysics and mathematical physics, such as stellar structure and thermal behavior in polytropic gas spheres. This study presents a novel hybrid framework that integrates Physics-Informed Neural Networks (PINNs) with boosting methods to enhance the accuracy and robustness of solutions for Lane-Emden type differential equations. Standard PINNs leverage physical laws encoded within the loss function, but their predictive performance can be constrained by optimization challenges and approximation errors. To address this, we introduce a post-processing boosting stage where the residual errors from the PINN prediction are modeled using some regression algorithms - including LightGBM, Random Forest, XGBoost, and Support Vector Regression (SVR). The outputs from these boosted models are aggregated to generate a corrected, high-fidelity prediction. The proposed methodology is systematically validated through quantitative metrics and comparative analysis against the standard PINN baseline. The results demonstrate that the boosted PINN framework significantly reduces prediction error, and improves generalization, offering a powerful and flexible approach for solving scientific and engineering problems governed by differential equations.
Mock data challenges need long stretches of colored Gaussian noise with a prescribed spectrum. The candidates are the crossfade of independently drawn windows that the standard gravitational-wave libraries implement, overlap-save finite-impulse-response filtering, autoregressive and autoregressive moving-average (ARMA) models, and the reproducible filter of PyCBC. One measure ranks them all: the covariance error against the target over the analysis band, evaluated from each generator's algebra; generated noise only checks the implementations. We also measure throughput, retained state and the cost of bit-exact regeneration. With the target continued smoothly below the band, the crossfade with windows of 256 s or more reaches an error below $10^{-3}$ on all eleven detector curves as tabulated, at about 4.7 million samples per second from a state of a few hundred bytes. An overlap-save filter is faster but needs tens of thousands of taps for an error of a few percent, and no tested autoregressive or ARMA configuration lies on the accuracy--throughput fronts. An error of $10^{-3}$ needs a window of 8 to 235 s, longest on the design curves with narrow lines, where it also depends on the tabulation. With the target cut at the band edge, as current generators do by default, every method has an error above one half on the projected Advanced LIGO (aLIGO) O4 curve, and the crossfade on five other curves. The crossfade is cyclostationary. With the continued target, its cyclic part is the larger part of the error only at 8 s, on the aLIGO O4 and the Virgo and KAGRA design curves, and stays within a factor of two of the stationary part on the aLIGO O3 and the Virgo and KAGRA design curves. We recommend the crossfade with a window from the table of detector curves, and a smooth continuation of the target below the band.