Cosmological simulations play an important role in the interpretation of astronomical data, in particular in comparing observed data to our theoretical expectations. However, to compare data with these simulations, the simulations in principle need to include gravity, magneto-hydrodyanmics, radiative transfer, etc. These ideal large-volume simulations (gravo-magneto-hydrodynamical) are incredibly computationally expensive which can cost tens of millions of CPU hours to run. In this paper, we propose a deep learning approach to map from the dark-matter-only simulation (computationally cheaper) to the galaxy distribution (from the much costlier cosmological simulation). The main challenge of this task is the high sparsity in the target galaxy distribution: space is mainly empty. We propose a cascade architecture composed of a classification filter followed by a regression procedure. We show that our result outperforms a state-of-the-art model used in the astronomical community, and provides a good trade-off between computational cost and prediction accuracy.

Constraining planet formation models based on the observed exoplanet population requires generating large samples of synthetic planetary systems, which can be computationally prohibitive. A significant bottleneck is simulating the giant impact phase, during which planetary embryos evolve gravitationally and combine to form planets, which may themselves experience later collisions. To accelerate giant impact simulations, we present a machine learning (ML) approach to predicting collisional outcomes in multiplanet systems. Trained on more than 500,000 $N$-body simulations of three-planet systems, we develop an ML model that can accurately predict which two planets will experience a collision, along with the state of the post-collision planets, from a short integration of the system's initial conditions. Our model greatly improves on non-ML baselines that rely on metrics from dynamics theory, which struggle to accurately predict which pair of planets will experience a collision. By combining with a model for predicting long-term stability, we create an efficient ML-based giant impact emulator, which can predict the outcomes of giant impact simulations with a speedup of up to four orders of magnitude. We expect our model to enable analyses that would not otherwise be computationally feasible. As such, we release our full training code, along with an easy-to-use API for our collision outcome model and giant impact emulator.

Modeling the complex three-dimensional (3D) dynamics of relational systems is an important problem in the natural sciences, with applications ranging from molecular simulations to particle mechanics. Machine learning methods have achieved good success by learning graph neural networks to model spatial interactions. However, these approaches do not faithfully capture temporal correlations since they only model next-step predictions. In this work, we propose Equivariant Graph Neural Operator (EGNO), a novel and principled method that directly models dynamics as trajectories instead of just next-step prediction. Different from existing methods, EGNO explicitly learns the temporal evolution of 3D dynamics where we formulate the dynamics as a function over time and learn neural operators to approximate it. To capture the temporal correlations while keeping the intrinsic SE(3)-equivariance, we develop equivariant temporal convolutions parameterized in the Fourier space and build EGNO by stacking the Fourier layers over equivariant networks. EGNO is the first operator learning framework that is capable of modeling solution dynamics functions over time while retaining 3D equivariance. Comprehensive experiments in multiple domains, including particle simulations, human motion capture, and molecular dynamics, demonstrate the significantly superior performance of EGNO against existing methods, thanks to the equivariant temporal modeling.

Finding the initial conditions that led to the current state of the universe is challenging because it involves searching over an intractable input space of initial conditions, along with modeling their evolution via tools such as N-body simulations which are computationally expensive. Recently, deep learning has emerged as a surrogate for N-body simulations by directly learning the mapping between the linear input of an N-body simulation and the final nonlinear output from the simulation, significantly accelerating the forward modeling. However, this still does not reduce the search space for initial conditions. In this work, we pioneer the use of a deterministic convolutional neural network for learning the reverse mapping and show that it accurately recovers the initial linear displacement field over a wide range of scales ($<1$-$2\%$ error up to nearly $k\simeq0.8$-$0.9 \text{ Mpc}^{-1}h$), despite the one-to-many mapping of the inverse problem (due to the divergent backward trajectories at smaller scales). Specifically, we train a V-Net architecture, which outputs the linear displacement of an N-body simulation, given the nonlinear displacement at redshift $z=0$ and the cosmological parameters. The results of our method suggest that a simple deterministic neural network is sufficient for accurately approximating the initial linear states, potentially obviating the need for the more complex and computationally demanding backward modeling methods that were recently proposed.

We introduce a diffusion-based generative model to describe the distribution of galaxies in our Universe directly as a collection of points in 3-D space (coordinates) optionally with associated attributes (e.g., velocities and masses), without resorting to binning or voxelization. The custom diffusion model can be used both for emulation, reproducing essential summary statistics of the galaxy distribution, as well as inference, by computing the conditional likelihood of a galaxy field. We demonstrate a first application to massive dark matter haloes in the Quijote simulation suite. This approach can be extended to enable a comprehensive analysis of cosmological data, circumventing limitations inherent to summary statistic -- as well as neural simulation-based inference methods.

Measuring the sum of the three active neutrino masses, $M_\nu$, is one of the most important challenges in modern cosmology. Massive neutrinos imprint characteristic signatures on several cosmological observables in particular on the large-scale structure of the Universe. In order to maximize the information that can be retrieved from galaxy surveys, accurate theoretical predictions in the non-linear regime are needed. Currently, one way to achieve those predictions is by running cosmological numerical simulations. Unfortunately, producing those simulations requires high computational resources -- several hundred to thousand core-hours for each neutrino mass case. In this work, we propose a new method, based on a deep learning network, to quickly generate simulations with massive neutrinos from standard $\Lambda$CDM simulations without neutrinos. We computed multiple relevant statistical measures of deep-learning generated simulations, and conclude that our approach is an accurate alternative to the traditional N-body techniques. In particular the power spectrum is within $\simeq 6\%$ down to non-linear scales $k=0.7$~\rm h/Mpc. Finally, our method allows us to generate massive neutrino simulations 10,000 times faster than the traditional methods.

N-body simulations are the most powerful method to study the non-linear evolution of large-scale structure. However, they require large amounts of computational resources, making unfeasible their direct adoption in scenarios that require broad explorations of parameter spaces. In this work, we show that it is possible to perform fast dark matter density field emulations with competitive accuracy using simple machine-learning approaches. We build an emulator based on dimensionality reduction and machine learning regression combining simple Principal Component Analysis and supervised learning methods. For the estimations with a single free parameter, we train on the dark matter density parameter, $\Omega_m$, while for emulations with two free parameters, we train on a range of $\Omega_m$ and redshift. The method first adopts a projection of a grid of simulations on a given basis; then, a machine learning regression is trained on this projected grid. Finally, new density cubes for different cosmological parameters can be estimated without relying directly on new N-body simulations by predicting and de-projecting the basis coefficients. We show that the proposed emulator can generate density cubes at non-linear cosmological scales with density distributions within a few percent compared to the corresponding N-body simulations. The method enables gains of three orders of magnitude in CPU run times compared to performing a full N-body simulation while reproducing the power spectrum and bispectrum within $\sim 1\%$ and $\sim 3\%$, respectively, for the single free parameter emulation and $\sim 5\%$ and $\sim 15\%$ for two free parameters. This can significantly accelerate the generation of density cubes for a wide variety of cosmological models, opening the doors to previously unfeasible applications, such as parameter and model inferences at full survey scales as the ESA/NASA Euclid mission.

Methods based on Deep Learning have recently been applied on astrophysical parameter recovery thanks to their ability to capture information from complex data. One of these methods is the approximate Bayesian Neural Networks (BNNs) which have demonstrated to yield consistent posterior distribution into the parameter space, helpful for uncertainty quantification. However, as any modern neural networks, they tend to produce overly confident uncertainty estimates and can introduce bias when BNNs are applied to data. In this work, we implement multiplicative normalizing flows (MNFs), a family of approximate posteriors for the parameters of BNNs with the purpose of enhancing the flexibility of the variational posterior distribution, to extract $\Omega_m$, $h$, and $\sigma_8$ from the QUIJOTE simulations. We have compared this method with respect to the standard BNNs, and the flipout estimator. We found that MNFs combined with BNNs outperform the other models obtaining predictive performance with almost one order of magnitude larger that standard BNNs, $\sigma_8$ extracted with high accuracy ($r^2=0.99$), and precise uncertainty estimates. The latter implies that MNFs provide more realistic predictive distribution closer to the true posterior mitigating the bias introduced by the variational approximation and allowing to work with well-calibrated networks.

The use of accelerators is increasing every year, with software developers taking advantage of GPUs in particular to run a variety of HPC and AI algorithms on highly parallel systems. The data center accelerator market is projected to grow from $13.7 billion in 2021 to $65.3 billion by 2026 according to research from MarketsandMarkets1. During the past decade or so software developers have largely been bound to CUDA* to write highly parallel software that can make use of GPUs that, whilst originally designed for graphics processing, are now being used in a wide range of disciplines that include AI and machine learning. The challenge with this approach for software developers is that CUDA is a proprietary programming interface and can only be used to run on processors from NVIDIA. This ties organizations into a single vendor and limits the ability to innovate with the latest processor architectures.

By applying a machine-learning technique, a neural network method, to gigantic amounts of simulation data about the formation of cosmic structures in the universe, a team of researchers has developed a very fast and highly efficient software program that can make theoretical predictions about structure formation. By comparing model predictions to actual observational datasets, the team succeeded in accurately measuring cosmological parameters, reports a study in Physical Review D. When the biggest galaxy survey to date in the world, the Sloan Digital Sky Survey (SDSS), created a three-dimensional map of the universe via the observed distribution of galaxies, it became clear that galaxies had certain characteristics. Some would clump together, or spread out in filaments, and in some places there were voids where no galaxies existed at all. All these show galaxies did not evolve in a uniform way, they formed as a result of their local environment. In general, researchers agree this non-uniform distribution of galaxies is because of the effects of gravity caused by the distribution of "invisible" dark matter, the mysterious matter that no one has yet directly observed. By studying the data in the three-dimensional map of galaxies in detail, researchers could uncover the fundamental quantities such as the amount of dark matter in the universe.