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.
In this work, we present Solar Feature Tracking: granules (SoFTg), a new hybrid algorithm within the SoFT library designed for the segmentation and tracking of solar granulation. By combining a heuristic approach based on a custom adaptive-thresholding technique with the speed and robustness of deep-learning methods, SoFTg provides a fast, reliable and user-friendly solution for granule segmentation, followed by the standard SoFT approach for tracking. We present a comprehensive evaluation of the algorithm's performance using multiple metrics and analyse the different stages of the processing pipeline. The method is tested on three datasets acquired with the Visible Broadband Imager operating in the red continuum at the Daniel K. Inouye Solar Telescope in Maui, Hawaii. We present distributions of both the lifetime and equivalent diameter of the thousands of granules tracked, providing, for the first time, statistically robust evidence of turbulent convection at the spatial scales now accessible through the high-resolution imaging capabilities of DKIST.
The solar interior and atmosphere constitute a strongly coupled, multiscale dynamical system defined by continuous temporal evolution. Predicting the state of this system requires modeling physical interactions that span disparate spatial and temporal scales, constrained by heterogeneous and sparse data. This chapter formalizes the Sun within the mathematical framework of dynamical systems theory, defining a global state vector ($\vec{S}$) governed by thermodynamical, kinetic, and magnetic properties. Because solar observations represent projected, multi-modal, and partially observable measurements ($\vec{O}[\vec{S}]$) of this hidden state, pure physics-based deduction is fundamentally constrained. We present a unifying thesis: the primary role of machine learning in heliophysics is to act as a structured family of mathematical operators---specifically Inference ($\mathcal{I}$), Emulation ($\mathcal{E}$), Propagation ($\mathcal{P}$), and Control ($\mathcal{C}$)---that reconstruct, simulate, and couple this global state vector across disparate physical layers. By framing the vast, multi-disciplinary literature within this unified state-space taxonomy, we demonstrate how data-driven techniques bridge observational gaps to resolve hidden multiscale couplings and dramatically accelerate the simulation of non-linear processes, establishing a rigorous pathway to predict the global evolution of the Sun.
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.
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 problem of predicting when a multi-planet system will become dynamically unstable has defied analytical progress over the past three hundred years. Recent machine learning advances achieve high predictive performance of instability dynamics, but as black-box systems cannot be interpreted to connect to existing scientific understanding. Here we show analytic equations that predict when a multi-planet system will undergo instability. We discover these equations by first training a neural network on a dataset of N-body simulations, and then distilling its latent knowledge into closed-form algebraic expressions. Our two-stage pipeline first learns an interpretable variable basis, then searches for equations using symbolic regression. The resulting equations outperform existing analytic estimates of instability and apply across wide ranges of mass ratios, spacing, and orbital eccentricities. They capture structure in the prediction landscape with a small number of variables amenable to dynamical interpretation. These results demonstrate how symbolic learning can be combined with neural networks to extract scientific insight from complex dynamical systems.
The data acquisition of axion haloscopes commonly implements sequential adaptive frequency scans. We present a method to calculate likelihood-based upper confidence limits on axion-photon coupling under this circumstance. We compare the likelihood-based method conceptually and quantitatively with tailor-made methods, i.e. the one proposed by Brubaker et al. (Geometric) and its upgrade the Bayesian Power-Measured (BPM) framework proposed by Palken et al. We find that the likelihood method yields average upper limits that are significantly more constraining than those obtained from these methods. For example, expected constraints improve by a factor of 1.4 as compared with the current state of the art when applied to projections for the ALPHA Plasma-haloscope. We further clarify the statistical basis for the Geometric and BPM methods. In particular, we point out the correspondence of BPM to e-values, proposed as an alternative to conventional p-values in statistics.
High-speed solar wind streams (HSSs) originating from coronal holes (CHs) are an important driver of recurrent geomagnetic activity. Since HSSs are associated to coronal structures visible in extreme-ultraviolet observations, this provides a natural basis for forecasting several days in advance. In this work, we investigate whether the topology of coronal structures observed in extreme ultraviolet (EUV) images contains predictive information on the subsequent occurrence of CH-driven HSSs at Earth. To this end, we consider Topological Data Analysis (TDA), and in particular persistent homology, to classify EUV solar images according to the occurrence of HSSs at Earth four days later. The target is a binary classification of HSS occurrence at a four-day lead time, defined using an HSS interval catalog and solar wind speed thresholds. Several combinations of topological representations and classifiers are evaluated under a common cross-validation framework. The results indicate that the topology of EUV coronal structures alone contains predictive information on subsequent CH-driven HSS occurrence, despite the absence of explicit CH geometric descriptors in the model input. To investigate the origin of this predictive information, we develop a model-level explainability framework based on cross-validation-aggregated feature weights and spatial evidence maps. A fully traced example connects persistence diagrams and persistence-image features to the classifier output and to their spatial localization in the original EUV observation. The proposed framework provides a transparent and computationally lightweight approach for investigating the relationship between coronal topology and subsequent high-speed solar wind streams.
Space weather is the study of the near-Earth impact of the processes on the Sun. In a this era of technology, space weather emerges as a crucial area of study wherein the state of the near-Earth conditions need to be modeled and forecasted. Crucially, the advent of machine learning provides us with opportunities to study this subject in a rather comprehensive manner. In this chapter, we treat the the processes arising from Sun to the impact on the ground as a set of coupled systems, which can be studied in isolation or in a coupled manner. We define these individual systems in terms of their state vector $\vec{S}$, which provides us with an opportunity to define the physical variables determining the system. This also allows us to consider the systems in terms of their observables, obtained through the action of operators as $\vec{O}[\vec{S}]$. In such a formalism, the machine learning algorithms serve as {\it learned operators}, defined generally as inference ($\mathcal{I}$), propagation ($\mathcal{P}$), and emulation ($\mathcal{E}$). Through such a formalism, we present how machine learning helps advance our understanding of the physical systems under study, while also accelerating the development of operational models for space weather forecasting.
The Babylonian Astronomical Diaries record the sky over nearly six centuries. Many tablets are broken and have lost their date formula. Experts dated many of them one tablet at a time in the standard edition, Astronomical Diaries and Related Texts from Babylonia (ADART). They used the recorded sky and other evidence, such as year formulas and royal names. Our system automates the astronomical part for all tablets with the same rules. A rule-based parser turns the recorded observations into clauses, short statements with fixed fields. A language model checks them against the text and adds observations that the parser missed. Astronomical tools test the clauses in all 701 years from 626 BCE to AD 75. The system ranks the years by how well they agree with the clauses. The system withholds published dates until its results are final, and the output lists the passages and computed positions behind each candidate year. On 120 dated tablets, the years tied at the top of the ranking include the published year in 96% of cases. For 86 of them, this top group is a single year, the published year in 84. In 119 of the 120, the reported candidate set contains it. For 56 undated entries of ADART IV, the system gives ranked candidate years. For each tablet, the results show how far astronomy alone narrows the year. An interactive page at https://tingyuansen.github.io/Babylonian_Dating/ follows each tablet and links the code, protocol and results.