Publications

List of Publications

Neural Symplectic Integrator with Hamiltonian Inductive Bias for the Gravitational N-body Problem

Cai, Maxwell X. ; Portegies Zwart, Simon ; Podareanu, Damian

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.

Fast and Credible Likelihood-Free Cosmology with Truncated Marginal Neural Ratio Estimation

Cole, Alex ; Miller, Benjamin Kurt ; Witte, Samuel J. ; Cai, Maxwell X. ; Grootes, Meiert W. ; Nattino, Francesco ; Weniger, Christoph

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 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 Λ CDM. To perform these computations, we use an implementation of TMNRE via the open-source code swyft.

Oort cloud Ecology II: The chronology of the formation of the Oort cloud

Portegies Zwart, Simon ; Torres, Santiago ; Cai, Maxwell X. ; Brown, Anthony

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 103\,au still bears the signatures of the Sun being born in a 1000MSun/pc3 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 (∼70\%) originates from the region in the circumstellar disk that was located between ∼15\,au and ∼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 104\,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.

Inside-Out Planet Formation: VI. Oligarchic Coagulation of Planetesimals from a Pebble Ring?

Cai, Maxwell X. ; Tan, Jonathan C. ; Portegies Zwart, Simon

Inside-Out Planet Formation (IOPF) is a theory addressing the origin of Systems of Tightly-Packed Inner Planets (STIPs) via 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 ∼105 years. However, a relatively massive secondary planet always remains with ∼30−65% 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.

Deep-learning enhancement of large scale numerical simulations

van Leeuwen, Caspar; Podareanu, Damian; Codreanu, Valeriu; Cai, Maxwell X.; Berg, Axel; Portegies Zwart, Simon; Stoffer, Robin; Veerman, Menno; van Heerwaarden, Chiel; Otten, Sydney; Caron, Sascha; Geng, Cunliang; Ambrosetti, Francesco; Bonvin, Alexandre M. J. J.

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

DeepGalaxy: Deducing the Properties of Galaxy Mergers from Images Using Deep Neural Networks

Cai, Maxwell X.; Bédorf, Jeroen; Saletore, Vikram A.; Codreanu, Valeriu; Podareanu, Damian; Chaibi, Adel; Qian, Penny X.

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 ∼105.

On the survival of resonant and non-resonant planetary systems in star clusters

Stock, Katja; Cai, Maxwell X.; Spurzem, Rainer; Kouwenhoven, M. B. N.; Portegies Zwart, Simon

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 105 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 MJup 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.

Linking the formation and fate of exo-Kuiper belts within Solar system analogues

Veras, Dimitri; Reichert, Katja; Flammini Dotti, Francesco; Cai, Maxwell X.; Mustill, Alexander J.; Shannon, Andrew; McDonald, Catriona H.; Portegies Zwart, Simon; Kouwenhoven, M. B. N.; Spurzem, Rainer

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 ≳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 (≪103 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.

On the survivability of planets in young massive clusters and its implication of planet orbital architectures in globular clusters

Cai, Maxwell X.; Portegies Zwart, S.; Kouwenhoven, M. B. N.; Spurzem, Rainer

As of 2019 August, among the more than 4000 confirmed exoplanets, only one has been detected in a globular cluster (GC) M4. The scarce of exoplanet detections motivates us to employ direct N-body simulations to investigate the dynamical stability of planets in young massive clusters (YMC), which are potentially the progenitors of GCs. In an N = 128 k cluster of virial radius 1.7 pc (comparable to Westerlund-1), our simulations show that most wide-orbit planets (a ≥ 20 au) will be ejected within a time-scale of 10 Myr. Interestingly, more than 70 per cent of planets with a < 5 au survive in the 100 Myr simulations. Ignoring planet-planet scattering and tidal damping, the survivability at t Myr as a function of initial semimajor axis a0 in au in such a YMC can be described as fsurv(a0, t) = -0.33log10(a0)(1 - e-0.0482t) + 1. Upon ejection, about 28.8 per cent of free-floating planets (FFPs) have sufficient speeds to escape from the host cluster at a crossing time-scale. The other FFPs will remain bound to the cluster potential, but the subsequent dynamical evolution of the stellar system can result in the delayed ejection of FFPs from the host cluster. Although a full investigation of planet population in GCs requires extending the simulations to multiGyr, our results suggest that wide-orbit planets and free-floating planets are unlikely to be found in GCs.

Planetary systems in a star cluster I: the Solar system scenario

lammini Dotti, Francesco; Kouwenhoven, M. B. N.; Cai, Maxwell Xu; Spurzem, Rainer

Young stars are mostly found in dense stellar environments, and even our own Solar system may have formed in a star cluster. Here, we numerically explore the evolution of planetary systems similar to our own Solar system in star clusters. We investigate the evolution of planetary systems in star clusters. Most stellar encounters are tidal, hyperbolic, and adiabatic. A small fraction of the planetary systems escape from the star cluster within 50 Myr; those with low escape speeds often remain intact during and after the escape process. While most planetary systems inside the star cluster remain intact, a subset is strongly perturbed during the first 50 Myr. Over the course of time, 0.3% - 5.3% of the planets escape, sometimes up to tens of millions of years after a stellar encounter occurred. Survival rates are highest for Jupiter, while Uranus and Neptune have the highest escape rates. Unless directly affected by a stellar encounter itself, Jupiter frequently serves as a barrier that protects the terrestrial planets from perturbations in the outer planetary system. In low-density environments, Jupiter provides protection from perturbations in the outer planetary system, while in high-density environments, direct perturbations of Jupiter by neighbouring stars is disruptive to habitable-zone planets. The diversity amongst planetary systems that is present in the star clusters at 50 Myr, and amongst the escaping planetary systems, is high, which contributes to explaining the high diversity of observed exoplanet systems in star clusters and in the Galactic field.