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In physics, density $\rho(\cdot)$ is a fundamentally important scalar function to model, since it describes a scalar field or a probability density function that governs a physical process. Modeling $\rho(\cdot)$ typically scales poorly with parameter space, however, and quickly becomes prohibitively difficult and computationally expensive. One promising avenue to bypass this is to leverage the capabilities of denoising diffusion models often used in high-fidelity image generation to parameterize $\rho(\cdot)$ from existing scientific data, from which new samples can be trivially sampled from. In this paper, we propose $\rho$-Diffusion, an implementation of denoising diffusion probabilistic models for multidimensional density estimation in physics, which is currently in active development and, from our results, performs well on physically motivated 2D and 3D density functions. Moreover, we propose a novel hashing technique that allows $\rho$-Diffusion to be conditioned by arbitrary amounts of physical parameters of interest., Comment: 6 pages, 2 figures, accepted for publication at the NeurIPS 2023 workshop "Machine Learning and the Physical Sciences"

Simulating the evolution of the gravitational N-body problem becomes extremely computationally expensive as N increases since the problem complexity scales quadratically with the number of bodies. We study the use of Artificial Neural Networks (ANNs) to replace expensive parts of the integration of planetary systems. Neural networks that include physical knowledge have grown in popularity in the last few years, although few attempts have been made to use them to speed up the simulation of the motion of celestial bodies. We study the advantages and limitations of using Hamiltonian Neural Networks to replace computationally expensive parts of the numerical simulation. We compare the results of the numerical integration of a planetary system with asteroids with those obtained by a Hamiltonian Neural Network and a conventional Deep Neural Network, with special attention to understanding the challenges of this problem. Due to the non-linear nature of the gravitational equations of motion, errors in the integration propagate. To increase the robustness of a method that uses neural networks, we propose a hybrid integrator that evaluates the prediction of the network and replaces it with the numerical solution if considered inaccurate. Hamiltonian Neural Networks can make predictions that resemble the behavior of symplectic integrators but are challenging to train and in our case fail when the inputs differ ~7 orders of magnitude. In contrast, Deep Neural Networks are easy to train but fail to conserve energy, leading to fast divergence from the reference solution. The hybrid integrator designed to include the neural networks increases the reliability of the method and prevents large energy errors without increasing the computing cost significantly. For this problem, the use of neural networks results in faster simulations when the number of asteroids is >70., Comment: Accepted for publication in the Journal of Computational Physics

Previous investigations have revealed that eccentric super-Earths represent a class of planets which are particularly effective at transporting minor bodies towards white dwarfs and subsequently polluting their atmospheres with observable chemical signatures. However, the lack of discoveries of these planets beyond a few astronomical units from their host stars prompts a better understanding of their orbital architectures from their nascent birth cluster. Here, we perform stellar cluster simulations of 3-planet and 7-planet systems containing super-Earths on initially circular, coplanar orbits. We adopt the typical stellar masses of main-sequence progenitors of white dwarfs ($1.5\,\mathrm{M}_{\odot}$-$2.5\,\mathrm{M}_{\odot}$) as host stars and include 8,000 main-sequence stars following a Kroupa initial mass function in our clusters. Our results reveal that about 30 per cent of the simulated planets generate eccentricities of at least 0.1 by the time of cluster dissolution, which would aid white dwarf pollution. We provide our output parameters to the community for potential use as initial conditions for subsequent evolution simulations., Comment: 16 pages, 18 figures, accepted for publication in MNRAS

The gravitational $N$-body problem, which is fundamentally important in astrophysics to predict the motion of $N$ celestial bodies under the mutual gravity of each other, is usually solved numerically because there is no known general analytical solution for $N>2$. Can an $N$-body problem be solved accurately by a neural network (NN)? Can a NN observe long-term conservation of energy and orbital angular momentum? Inspired by Wistom & Holman (1991)'s symplectic map, we present a neural $N$-body integrator for splitting the Hamiltonian into a two-body part, solvable analytically, and an interaction part that we approximate with a NN. Our neural symplectic $N$-body code integrates a general three-body system for $10^{5}$ steps without diverting from the ground truth dynamics obtained from a traditional $N$-body integrator. Moreover, it exhibits good inductive bias by successfully predicting the evolution of $N$-body systems that are no part of the training set., Comment: 7 pages, 2 figures, accepted for publication at the NeurIPS 2021 workshop "Machine Learning and the Physical Sciences"

Sampling-based inference techniques are central to modern cosmological data analysis; these methods, however, scale poorly with dimensionality and typically require approximate or intractable likelihoods. In this paper we describe how Truncated Marginal Neural Ratio Estimation (TMNRE) (a new approach in so-called simulation-based inference) naturally evades these issues, improving the $(i)$ efficiency, $(ii)$ scalability, and $(iii)$ trustworthiness of the inferred posteriors. Using measurements of the Cosmic Microwave Background (CMB), we show that TMNRE can achieve converged posteriors using orders of magnitude fewer simulator calls than conventional Markov Chain Monte Carlo (MCMC) methods. Remarkably, the required number of samples is effectively independent of the number of nuisance parameters. In addition, a property called \emph{local amortization} allows the performance of rigorous statistical consistency checks that are not accessible to sampling-based methods. TMNRE promises to become a powerful tool for cosmological data analysis, particularly in the context of extended cosmologies, where the timescale required for conventional sampling-based inference methods to converge can greatly exceed that of simple cosmological models such as $\Lambda$CDM. To perform these computations, we use an implementation of TMNRE via the open-source code \texttt{swyft}., Comment: v2: accepted journal version. v1: 37 pages, 13 figures. \texttt{swyft} is available at https://github.com/undark-lab/swyft, and demonstration code for cosmological examples is available at https://github.com/acole1221/swyft-CMB

We present a chronology of the formation and early evolution of the Oort cloud by simulations. These simulations start with the Solar System being born with planets and asteroids in a stellar cluster orbiting the Galactic center. Upon ejection from its birth environment, we continue to follow the evolution of the Solar System while it navigates the Galaxy as an isolated planetary system. We conclude that the range in semi-major axis between 100au and several 10$^3$\,au still bears the signatures of the Sun being born in a 1000MSun/pc$^3$ star cluster, and that most of the outer Oort cloud formed after the Solar System was ejected. The ejection of the Solar System, we argue, happened between 20Myr and 50Myr after its birth. Trailing and leading trails of asteroids and comets along the Sun's orbit in the Galactic potential are the by-product of the formation of the Oort cloud. These arms are composed of material that became unbound from the Solar System when the Oort cloud formed. Today, the bulk of the material in the Oort cloud ($\sim 70$\%) originates from the region in the circumstellar disk that was located between $\sim 15$\,au and $\sim 35$\,au, near the current location of the ice giants and the Centaur family of asteroids. According to our simulations, this population is eradicated if the ice-giant planets are born in orbital resonance. Planet migration or chaotic orbital reorganization occurring while the Solar System is still a cluster member is, according to our model, inconsistent with the presence of the Oort cloud. About half the inner Oort cloud, between 100 and $10^4$\,au, and a quarter of the material in the outer Oort cloud, $\apgt 10^4$\,au, could be non-native to the Solar System but was captured from free-floating debris in the cluster or from the circumstellar disk of other stars in the birth cluster., Comment: Corrected proofs for publication in A&A

Inside-Out Planet Formation (IOPF) is a theory addressing the origin of Systems of Tightly-Packed Inner Planets (STIPs) via {\it in situ} formation and growth of the planets. It predicts that a pebble ring is established at the pressure maximum associated with the dead zone inner boundary (DZIB) with an inner disk magnetorotational instability (MRI)-active region. Using direct $N$-body simulations, we study the collisional evolution of planetesimals formed from such a pebble ring, in particular examining whether a single dominant planet emerges. We consider a variety of models, including some in which the planetesimals are continuing to grow via pebble accretion. We find that the planetesimal ring undergoes oligarchic evolution, and typically turns into 2 or 3 surviving oligarchs on nearly coplanar and circular orbits, independent of the explored initial conditions or form of pebble accretion. The most massive oligarchs typically consist of about $70\%$ of the total mass, with the building-up process typically finishing within $\sim 10^5$ years. However, a relatively massive secondary planet always remains with $\sim30-65\%$ of the mass of the primary. Such secondary planets have properties that are inconsistent with the observed properties of the innermost pairs of planets in STIPs. Thus, for IOPF to be a viable theory for STIP formation, it needs to be shown how oligarchic growth of a relatively massive secondary from the initial pebble ring can be avoided. We discuss some potential additional physical processes that should be included in the modeling and explored as next steps., Comment: 15 pages, 10 figures, accepted for publication in MNRAS

Galaxy mergers, the dynamical process during which two galaxies collide, are among the most spectacular phenomena in the Universe. During this process, the two colliding galaxies are tidally disrupted, producing significant visual features that evolve as a function of time. These visual features contain valuable clues for deducing the physical properties of the galaxy mergers. In this work, we propose DeepGalaxy, a visual analysis framework trained to predict the physical properties of galaxy mergers based on their morphology. Based on an encoder-decoder architecture, DeepGalaxy encodes the input images to a compressed latent space $z$, and determines the similarity of images according to the latent-space distance. DeepGalaxy consists of a fully convolutional autoencoder (FCAE) which generates activation maps at its 3D latent-space, and a variational autoencoder (VAE) which compresses the activation maps into a 1D vector, and a classifier that generates labels from the activation maps. The backbone of the FCAE can be fully customized according to the complexity of the images. DeepGalaxy demonstrates excellent scaling performance on parallel machines. On the Endeavour supercomputer, the scaling efficiency exceeds 0.93 when trained on 128 workers, and it maintains above 0.73 when trained with 512 workers. Without having to carry out expensive numerical simulations, DeepGalaxy makes inferences of the physical properties of galaxy mergers directly from images, and thereby achieves a speedup factor of $\sim 10^5$., Comment: 7 pages, 7 figures. Accepted for publication at the 2020 IEEE/ACM Fifth Workshop on Deep Learning on Supercomputers (DLS)

Despite the discovery of thousands of exoplanets in recent years, the number of known exoplanets in star clusters remains tiny. This may be a consequence of close stellar encounters perturbing the dynamical evolution of planetary systems in these clusters. Here, we present the results from direct $N$-body simulations of multiplanetary systems embedded in star clusters containing $N = 8k, 16k, 32k$, and $64k$ stars. The planetary systems, which consist of the four Solar system giant planets Jupiter, Saturn, Uranus, and Neptune, are initialized in different orbital configurations, to study the effect of the system architecture on the dynamical evolution of the entire planetary system, and on the escape rate of the individual planets. We find that the current orbital parameters of the Solar system giants (with initially circular orbits, as well as with present-day eccentricities) and a slightly more compact configuration, have a high resilience against stellar perturbations. A configuration with initial mean-motion resonances of 3:2, 3:2, and 5:4 between the planets, which is inspired by the Nice model, and for which the two outermost planets are usually ejected within the first $10^5$ yr, is in many cases stabilized due to the removal of the resonances by external stellar perturbation and by the rapid ejection of at least one planet. Assigning all planets the same mass of 1 Jovian mass almost equalizes the survival fractions. Our simulations reproduce the broad diversity amongst observed exoplanet systems. We find not only many very wide and/or eccentric orbits, but also a significant number of (stable) retrograde orbits., Comment: 21 pages, 21 figures, accepted by MNRAS

Traditional simulations on High-Performance Computing (HPC) systems typically involve modeling very large domains and/or very complex equations. HPC systems allow running large models, but limits in performance increase that have become more prominent in the last 5-10 years will likely be experienced. Therefore new approaches are needed to increase application performance. Deep learning appears to be a promising way to achieve this. Recently deep learning has been employed to enhance solving problems that traditionally are solved with large-scale numerical simulations using HPC. This type of application, deep learning for high-performance computing, is the theme of this whitepaper. Our goal is to provide concrete guidelines to scientists and others that would like to explore opportunities for applying deep learning approaches in their own large-scale numerical simulations. These guidelines have been extracted from a number of experiments that have been undertaken in various scientific domains over the last two years, and which are described in more detail in the Appendix. Additionally, we share the most important lessons that we have learned., Comment: White paper consists of 36 pages and 15 figures

Escalating observations of exo-minor planets and their destroyed remnants both passing through the solar system and within white dwarf planetary systems motivate an understanding of the orbital history and fate of exo-Kuiper belts and planetesimal discs. Here we explore how the structure of a 40-1000 au annulus of planetesimals orbiting inside of a solar system analogue that is itself initially embedded within a stellar cluster environment varies as the star evolves through all of its stellar phases. We attempt this computationally challenging link in four parts: (1) by performing stellar cluster simulations lasting 100 Myr, (2) by making assumptions about the subsequent quiescent 11 Gyr main-sequence evolution, (3) by performing simulations throughout the giant branch phases of evolution, and (4) by making assumptions about the belt's evolution during the white dwarf phase. Throughout these stages, we estimate the planetesimals' gravitational responses to analogues of the four solar system giant planets, as well as to collisional grinding, Galactic tides, stellar flybys, and stellar radiation. We find that the imprint of stellar cluster dynamics on the architecture of $\gtrsim 100$ km-sized exo-Kuiper belt planetesimals is retained throughout all phases of stellar evolution unless violent gravitational instabilities are triggered either (1) amongst the giant planets, or (2) due to a close ($\ll 10^3$ au) stellar flyby. In the absence of these instabilities, these minor planets simply double their semimajor axis while retaining their primordial post-cluster eccentricity and inclination distributions, with implications for the free-floating planetesimal population and metal-polluted white dwarfs., Comment: Accepted for publication in MNRAS

Comets in the Oort cloud evolve under the influence of internal and external perturbations, such as giant planets, stellar passages, and the galactic tidal field. We aim to study the dynamical evolution of the comets in the Oort cloud, accounting for external perturbations (passing stars and the galactic tide). We first construct an analytical model of stellar encounters. We find that individual perturbations do not modify the dynamics of the comets in the cloud unless very close (< 0.5pc) encounters occur. Using proper motions, parallaxes, and radial velocities from Gaia DR2, we construct an astrometric catalogue of 14,659 stars that are within 50pc from the Sun. For all these stars we calculate the time and the closest distance to the Sun. We find that the cumulative effect of relatively distant ($\leq1$ pc) passing stars can perturb the comets in the Oort cloud. Finally, we study the dynamical evolution of the comets in the Oort cloud under the influence of multiple stellar encounters within 2.5pc from the Sun and the galactic tidal field over $\pm10$Myr. We considered two models for the Oort cloud, compact (a $\leq$0.25 pc) and extended (a$ \leq0.5$ pc). We find that the cumulative effect of stellar encounters is the major perturber of the Oort cloud for a compact configuration while for the extended, the galactic tide is the major perturber. In both cases, the effect of passing stars and the galactic tide raises the semi-major axis of $\sim1.1$\% of the comets at the edge of the cloud up to interstellar regions ($a >0.5$pc). This leads to the creation of transitional interstellar comets, which might become interstellar objects due to external perturbations. This raises the question about the existence of a cloud of objects in the interstellar space which might overlap with our Oort cloud if we consider that other planetary systems face similar processes for the ejection of comets., Comment: 13 pages, 13 figures, accepted for publication in Astronomy & Astrophysics

We determine the orbital eccentricities of individual small Kepler planets, through a combination of asteroseismology and transit light-curve analysis. We are able to constrain the eccentricities of 51 systems with a single transiting planet, which supplement our previous measurements of 66 planets in multi-planet systems. Through a Bayesian hierarchical analysis, we find evidence that systems with only one detected transiting planet have a different eccentricity distribution than systems with multiple detected transiting planets. The eccentricity distribution of the single-transiting systems is well described by the positive half of a zero-mean Gaussian distribution with a dispersion $\sigma_e = 0.32 \pm 0.06$, while the multiple-transit systems are consistent with $\sigma_e = 0.083^{+0.015}_{-0.020}$. A mixture model suggests a fraction of $0.76^{+0.21}_{-0.12}$ of single-transiting systems have a moderate eccentricity, represented by a Rayleigh distribution that peaks at $0.26^{+0.04}_{-0.06}$. This finding may reflect differences in the formation pathways of systems with different numbers of transiting planets. We investigate the possibility that eccentricities are "self-excited" in closely packed planetary systems, as well as the influence of long-period giant companion planets. We find that both mechanisms can qualitatively explain the observations. We do not find any evidence for a correlation between eccentricity and stellar metallicity, as has been seen for giant planets. Neither do we find any evidence that orbital eccentricity is linked to the detection of a companion star. Along with this paper we make available all of the parameters and uncertainties in the eccentricity distributions, as well as the properties of individual systems, for use in future studies., Comment: Accepted for publication in The Astronomical Journal

The Kepler mission has detected a number of transiting circumbinary planets (CBPs). Although currently not detected, exomoons could be orbiting some of these CBPs, and they might be suitable for harboring life. A necessary condition for the existence of such exomoons is their long-term dynamical stability. Here, we investigate the stability of exomoons around the Kepler CBPs using numerical $N$-body integrations. We determine regions of stability and obtain stability maps in the (a_m,i_pm) plane, where a_m is the initial exolunar semimajor axis with respect to the CBP, and i_pm is the initial inclination of the orbit of the exomoon around the planet with respect to the orbit of the planet around the stellar binary. Ignoring any dependence on i_pm, for most Kepler CBPs the stability regions are well described by the location of the 1:1 mean motion commensurability of the binary orbit with the orbit of the moon around the CBP. This is related to a destabilizing effect of the binary compared to the case if the binary were replaced by a single body, and which is borne out by corresponding 3-body integrations. For high inclinations, the evolution is dominated by Lidov-Kozai oscillations, which can bring moons in dynamically stable orbits to close proximity within the CBP, triggering strong interactions such as tidal evolution, tidal disruption, or direct collisions. This suggests that there is a dearth of highly-inclined exomoons around the Kepler CBPs, whereas coplanar exomoons are dynamically allowed., Comment: Accepted for publication by MNRAS. 12 pages, 7 figures