We perform a model-independent reconstruction of the cosmic distances using the Multi-Task Gaussian Process (MTGP) framework as well as knot-based spline techniques with DESI-DR2 BAO and DES-SN5YR datasets. We calibrate the comoving sound horizon at the baryon drag epoch $r_d$ to the Planck value, ensuring consistency with early-universe physics. With the reconstructed cosmic distances and their derivatives, we obtain seven characteristic redshifts in the range $0.3 \leq z \leq 1.7$. We derive the normalized expansion rate of the Universe $E(z)$ at these redshifts. Our findings reveal significant deviations of approximately $4$ to $5σ$ from the Planck 2018 $Λ$CDM predictions, particularly pronounced in the redshift range $z \sim 0.35-0.55$. These anomalies are consistently observed across both reconstruction methods and combined datasets, indicating robust late-time tensions in the expansion rate of the Universe and which are distinct from the existing "Hubble Tension". This could signal new physics beyond the standard cosmological framework at this redshift range. Our findings underscore the role of characteristic redshifts as sensitive indicators of expansion rate anomalies and motivate further scrutiny with forthcoming datasets from DESI-5YR BAO, Euclid, and LSST. These future surveys will tighten constraints and will confirm whether these late-time anomalies arise from new fundamental physics or unresolved systematics in the data.

We construct a neural network to perform regression on the local dark-matter density field given line-of-sight peculiar velocities of dark-matter halos, biased tracers of the dark matter field. Our architecture combines a convolutional U-Net with a point-cloud DeepSets. This combination enables efficient use of small-scale information and improves reconstruction quality relative to a U-Net-only approach. Specifically, our hybrid network recovers both clustering amplitudes and phases better than the U-Net on small scales.

We study the performance of the Topological Uncertainty (TU) constructed with a trained feedforward neural network (FNN) for Anomaly Detection. Generally, meaningful information can be stored in the hidden layers of the trained FNN, and the TU implementation is one tractable recipe to extract buried information by means of the Topological Data Analysis. We explicate the concept of the TU and the numerical procedures. Then, for a concrete demonstration of the performance test, we employ the Neutron Star data used for inference of the equation of state (EoS). For the training dataset consisting of the input (Neutron Star data) and the output (EoS parameters), we can compare the inferred EoSs and the exact answers to classify the data with the label $k$. The subdataset with $k=0$ leads to the normal inference for which the inferred EoS approximates the answer well, while the subdataset with $k=1$ ends up with the unsuccessful inference. Once the TU is prepared based on the $k$-labled subdatasets, we introduce the cross-TU to quantify the uncertainty of characterizing the $k$-labeled data with the label $j$. The anomaly or unsuccessful inference is correctly detected if the cross-TU for $j=k=1$ is smaller than that for $j=0$ and $k=1$. In our numerical experiment, for various input data, we calculate the cross-TU and estimate the performance of Anomaly Detection. We find that performance depends on FNN hyperparameters, and the success rate of Anomaly Detection exceeds $90\%$ in the best case. We finally discuss further potential of the TU application to retrieve the information hidden in the trained FNN.

We present a set-based machine learning framework that infers posterior distributions of galaxy cluster masses from projected galaxy dynamics. Our model combines Deep Sets and conditional normalizing flows to incorporate both positional and velocity information of member galaxies to predict residual corrections to the $M$-$σ$ relation for improved interpretability. Trained on the Uchuu-UniverseMachine simulation, our approach significantly reduces scatter and provides well-calibrated uncertainties across the full mass range compared to traditional dynamical estimates.

How many simulations do we need to train machine learning methods to extract information available from summary statistics of the cosmological density field? Neural methods have shown the potential to extract non-linear information available from cosmological data. Success depends critically on having sufficient simulations for training the networks and appropriate network architectures. In the first detailed convergence study of neural network training for cosmological inference, we show that currently available simulation suites, such as the Quijote Latin Hypercube(LH) with 2000 simulations, do not provide sufficient training data for a generic neural network to reach the optimal regime, even for the dark matter power spectrum, and in an idealized case. We discover an empirical neural scaling law that predicts how much information a neural network can extract from a highly informative summary statistic, the dark matter power spectrum, as a function of the number of simulations used to train the network, for a wide range of architectures and hyperparameters. We combine this result with the Cramer-Rao information bound to forecast the number of training simulations needed for near-optimal information extraction. To verify our method we created the largest publicly released simulation data set in cosmology, the Big Sobol Sequence(BSQ), consisting of 32,768 $\Lambda$CDM n-body simulations uniformly covering the $\Lambda$CDM parameter space. Our method enables efficient planning of simulation campaigns for machine learning applications in cosmology, while the BSQ dataset provides an unprecedented resource for studying the convergence behavior of neural networks in cosmological parameter inference. Our results suggest that new large simulation suites or new training approaches will be necessary to achieve information-optimal parameter inference from non-linear simulations.

We perform a model-independent reconstruction of the angular diameter distance ($D_{A}$) using the Multi-Task Gaussian Process (MTGP) framework with DESI-DR1 BAO and DES-SN5YR datasets. We calibrate the comoving sound horizon at the baryon drag epoch $r_d$ to the Planck best-fit value, ensuring consistency with early-universe physics. With the reconstructed $D_A$ at two key redshifts, $z\sim 1.63$ (where $D_{A}^{\prime} =0$) and at $z\sim 0.512$ (where $D_{A}^{\prime} = D_{A}$), we derive the expansion rate of the Universe $H(z)$ at these redshifts. Our findings reveal that at $z\sim 1.63$, the $H(z)$ is fully consistent with the Planck-2018 $\Lambda$CDM prediction, confirming no new physics at that redshift. However, at $z \sim 0.512$, the derived $H(z)$ shows a more than $5\sigma$ discrepancy with the Planck-2018 $\Lambda$CDM prediction, suggesting a possible breakdown of the $\Lambda$CDM model as constrained by Planck-2018 at this lower redshift. This emerging $\sim 5\sigma$ tension at $z\sim 0.512$, distinct from the existing ``Hubble Tension'', may signal the first strong evidence for new physics at low redshifts.

Metrics for rigorously defining a distance between two events have been used to study the properties of the dataspace manifold of particle collider physics. The probability distribution of pairwise distances on this dataspace is unique with probability 1, and so this suggests a method to search for and identify new physics by the deviation of measurement from a null hypothesis prediction. To quantify the deviation statistically, we directly calculate the probability distribution of the number of event pairs that land in the bin a fixed distance apart. This distribution is not generically Gaussian and the ratio of the standard deviation to the mean entries in a bin scales inversely with the square-root of the number of events in the data ensemble. If the dataspace manifold exhibits some enhanced symmetry, the number of entries is Gaussian, and further fluctuations about the mean scale away like the inverse of the number of events. We define a robust measure of the non-Gaussianity of the bin-by-bin statistics of the distance distribution, and demonstrate in simulated data of jets from quantum chromodynamics sensitivity to the parton-to-hadron transition and that the manifold of events enjoys enhanced symmetries as their energy increases.

Here we explore certain subtle features imprinted in data from the completed Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) as a combined probe for the background and perturbed Universe. We reconstruct the baryon Acoustic Oscillation (BAO) and Redshift Space Distortion (RSD) observables as functions of redshift, using measurements from SDSS alone. We apply the Multi-Task Gaussian Process (MTGP) framework to model the interdependencies of cosmological observables $D_M(z)/r_d$, $D_H(z)/r_d$, and $f\sigma_8(z)$, and track their evolution across different redshifts. Subsequently, we obtain constrained three-dimensional phase space containing $D_M(z)/r_d$, $D_H(z)/r_d$, and $f\sigma_8(z)$ at different redshifts probed by the SDSS-IV eBOSS survey. Furthermore, assuming the $\Lambda$CDM model, we obtain constraints on model parameters $\Omega_{m}$, $H_{0}r_{d}$, $\sigma_{8}$ and $S_{8}$ at each redshift probed by SDSS-IV eBOSS. This indicates redshift-dependent trends in $H_0$, $\Omega_m$, $\sigma_8$ and $S_8$ in the $\Lambda$CDM model, suggesting a possible inconsistency in the $\Lambda$CDM model. Ours is a template for model-independent extraction of information for both background and perturbed Universe using a single galaxy survey taking into account all the existing correlations between background and perturbed observables and this can be easily extended to future DESI-3YR as well as Euclid results.

The application of machine learning to the study of coronal mass ejections (CMEs) and their impacts on Earth has seen significant growth recently. Understanding and forecasting CME geoeffectiveness is crucial for protecting infrastructure in space and ensuring the resilience of technological systems on Earth. Here we present GeoCME, a deep-learning framework designed to predict, deterministically or probabilistically, whether a CME event that arrives at Earth will cause a geomagnetic storm. A geomagnetic storm is defined as a disturbance of the Earth's magnetosphere during which the minimum Dst index value is less than -50 nT. GeoCME is trained on observations from the instruments including LASCO C2, EIT and MDI on board the Solar and Heliospheric Observatory (SOHO), focusing on a dataset that includes 136 halo/partial halo CMEs in Solar Cycle 23. Using ensemble and transfer learning techniques, GeoCME is capable of extracting features hidden in the SOHO observations and making predictions based on the learned features. Our experimental results demonstrate the good performance of GeoCME, achieving a Matthew's correlation coefficient of 0.807 and a true skill statistics score of 0.714 when the tool is used as a deterministic prediction model. When the tool is used as a probabilistic forecasting model, it achieves a Brier score of 0.094 and a Brier skill score of 0.493. These results are promising, showing that the proposed GeoCME can help enhance our understanding of CME-triggered solar-terrestrial interactions.

Conventional calibration of Baryon Acoustic Oscillations (BAO) data relies on estimation of the sound horizon at drag epoch $r_d$ from early universe observations by assuming a cosmological model. We present a recalibration of two independent BAO datasets, SDSS and DESI, by employing deep learning techniques for model-independent estimation of $r_d$, and explore the impacts on $\Lambda$CDM cosmological parameters. Significant reductions in both Hubble ($H_0$) and clustering ($S_8$) tensions are observed for both the recalibrated datasets. Moderate shifts in some other parameters hint towards further exploration of such data-driven approaches.