arXiv subjects

Aaron Smith

Publications and source records attributed to Aaron Smith.

At least 91 records · Page 5Linked to original sources

arXiv2024

No Free Lunch for Stochastic Gradient Langevin Dynamics

As sample sizes grow, scalability has become a central concern in the development of Markov chain Monte Carlo (MCMC) methods. One general approach to this problem, exemplified by the popular stochastic gradient Langevin dynamics (SGLD) algorithm, is to use a small random subsample of the data at every time step. This paper, building on recent work such as \cite{nagapetyan2017true,JohndrowJamesE2020NFLf}, shows that this approach often fails: while decreasing the sample size increases the speed of each MCMC step, for typical datasets this is balanced by a matching decrease in accuracy. This result complements recent work such as \cite{nagapetyan2017true} (which came to the same conclusion, but analyzed only specific upper bounds on errors rather than actual errors) and \cite{JohndrowJamesE2020NFLf} (which did not analyze nonreversible algorithms and allowed for logarithmic improvements).

stat.CO↗

arXiv2024

No Free Lunch for Approximate MCMC

It is widely known that the performance of Markov chain Monte Carlo (MCMC) can degrade quickly when targeting computationally expensive posterior distributions, such as when the sample size is large. This has motivated the search for MCMC variants that scale well to large datasets. One popular general approach has been to look at only a subsample of the data at every step. In this note, we point out that well-known MCMC convergence results often imply that these ``subsampling'' MCMC algorithms cannot greatly improve performance. We apply these abstract results to realistic statistical problems and proposed algorithms, and also discuss some design principles suggested by the results. Finally, we develop estimates for the singular values of random matrices bounds that may be of independent interest.

stat.CO↗

arXiv2024

The THESAN project: tracking the expansion and merger histories of ionized bubbles during the Epoch of Reionization

The growth of ionized hydrogen bubbles in the intergalactic medium around early luminous objects is a fundamental process during the Epoch of Reionization (EoR). In this study, we analyze bubble sizes and their evolution using the state-of-the-art THESAN radiation-hydrodynamics simulation suite, which self-consistently models radiation transport and realistic galaxy formation throughout a large (95.5 cMpc)^3 volume of the Universe. Analogous to the accretion and merger tree histories employed in galaxy formation simulations, we characterize the growth and merger rates of ionized bubbles by focusing on the spatially-resolved redshift of reionization. By tracing the chronological expansion of bubbles, we partition the simulation volume and construct a natural ionization history. We identify three distinct stages of ionized bubble growth: (1) initial slow expansion around the earliest ionizing sources seeding formation sites, (2) accelerated growth through percolation as bubbles begin to merge, and (3) rapid expansion dominated by the largest bubble. Notably, we find that the largest bubble emerges by z=9-10, well before the midpoint of reionization. This bubble becomes dominant during the second growth stage, and defines the third stage by rapidly expanding to eventually encompass the remainder of the simulation volume and becoming one of the few bubbles actively growing. Additionally, we observe a sharp decline in the number of bubbles with radii around ~10 cMpc compared to smaller sizes, indicating a characteristic scale in the final segmented bubble size distribution. Overall, these chronologically sequenced spatial reconstructions offer crucial insights into the physical mechanisms driving ionized bubble growth during the EoR and provide a framework for interpreting the structure and evolution of reionization itself.

astro-ph.GA↗

arXiv2024

TODDLERS: A New UV to Millimeter Emission Library for Star-Forming Regions. II. Star Formation Rate Indicators Using Auriga Zoom Simulations

Current galaxy formation simulations often approximate star-formation, necessitating models of star-forming regions to produce observables. In the first paper of the series, we introduced TODDLERS, a time-resolved model of UV-mm emission from star-forming regions implemented in the radiative transfer code SKIRT. This work uses SKIRT-TODDLERS to produce synthetic observations, demonstrating its potential through observables related to star-formation and comparing results with existing models in SKIRT. We calculate broadband and line emission maps for 30 Milky Way-like galaxies from the Auriga simulation at z=0. Analyzing FUV and IR data, we calculate kpc-resolved IR correction factors (k_IR), quantifying the ratio of FUV luminosity absorbed by dust to reprocessed IR luminosity. We use IR maps to calculate kpc-scale MIR (8 micron / 24 micron) and FIR (70 micron / 500 micron) colors. H alpha and H beta line maps are used to study the Balmer decrement and dust correction. We also verify the fidelity of our model FIR fine structure lines as SFR indicators. We find that the Auriga integrated UV-mm SEDs show higher FUV/NUV attenuation and lower 24 micron emission when using TODDLERS instead of the existing models in SKIRT, alleviating tensions with observations. The light-weighted mean k_IR increases with aperture and inclination, while its correlation with kpc-resolved sSFR is weaker than literature values. Kpc-scale MIR-FIR colors agree excellently with local observations, with anti-correlation degree varying by galaxy morphology. The Balmer decrement effectively corrects for dust, with attenuation law varying with dust amount. H alpha emission attenuation levels are comparable to high-density regions in state-of-the-art simulations. FIR fine-structure line emission-based luminosity-SFR relations align with global observations, [CII] showing best agreement.

astro-ph.GA↗

arXiv2024

Counting simplicial pairs in hypergraphs

We present two ways to measure the simplicial nature of a hypergraph: the simplicial ratio and the simplicial matrix. We show that the simplicial ratio captures the frequency, as well as the rarity, of simplicial interactions in a hypergraph while the simplicial matrix provides more fine-grained details. We then compute the simplicial ratio, as well as the simplicial matrix, for 10 real-world hypergraphs and, from the data collected, hypothesize that simplicial interactions are more and more deliberate as edge size increases. We then present a new Chung-Lu model that includes a parameter controlling (in expectation) the frequency of simplicial interactions. We use this new model, as well as the real-world hypergraphs, to show that multiple stochastic processes exhibit different behaviour when performed on simplicial hypergraphs vs. non-simplicial hypergraphs.

cs.SI↗

arXiv2024

Analytical strong line diagnostics and their redshift evolution

The \textit{JWST} is allowing new measurements of gas-phase metallicities in galaxies between cosmic noon and cosmic dawn. The most robust approach uses luminosity ratios between the excited auroral transition, [\oiii] 4364\,Å, and the lower [\oiii] 5008\,Å/4960\,Å lines to determine the gas temperature. The ratio of the luminosities in the latter transitions to those in hydrogen Balmer series lines then yield relatively clean metallicity estimates. In the absence of detection of the [\oiii] auroral line, the ratios of various [\oiii], [\oii], [\nii], and Balmer lines are used to determine metallicities. Here we present a refined approach for extracting metallicities from these ``strong line diagnostics''. Our method exploits empirical correlations between the temperature of \oiii/\oii\ regions and gas-phase metallicity. We then show, from first principles, how to extract metallicities and break degeneracies in these estimates using traditional strong line diagnostics, R2, R3, R23, and O3O2, and N2O2. We show that these ratios depend also on volume correction factors, i.e. on accounting for the fraction of the volume of HII regions that are in \oiii\ and \oii, but that these can be determined self-consistently along with the metallicities. We quantify the success of our method using metallicities derived from galaxies with auroral line determinations and show that it generally works better than previous empirical approaches. The scatter in the observed line ratios and redshift evolution are largely explained by O3O2 variations. We provide publicly available routines for extracting metallicities from strong line diagnostics using our methodology.

astro-ph.GA↗

arXiv2024

Importance is Important: Generalized Markov Chain Importance Sampling Methods

We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient, and rejection-free Markov chain Monte Carlo (MCMC) sampling scheme. By further leveraging the importance sampling perspective on Metropolis--Hastings algorithms, we propose an alternative MCMC sampler on discrete spaces that is also outside the Metropolis--Hastings framework, along with a general theory on its complexity. Numerical examples suggest that the proposed algorithms are consistently more efficient than the original Metropolis--Hastings versions.

stat.CO↗

arXiv2024

On the Precision of the Spectral Profile Bound for the Mixing Time of Continuous State Markov Chains

We investigate the sharpness of the spectral profile bound presented by Goel et al. and Chen et al. on the $L^{2}$ mixing time of Markov chains on continuous state spaces. We show that the bound provided by Chen et al. is sharp up to a factor of $\log\log$ of the initial density. This result extends the findings of Kozma, which showed the analogous result for the original spectral profile bound of Goel et al. for Markov chains on finite state spaces. Kozma shows that the spectral profile bound is sharp up to a multiplicative factor of $\log(\log(π_{min}))$, where $π_{\min}$ is the smallest value of the probability mass function of the stationary distribution. We discuss the application of our primary finding to the comparison of Markov chains. Our main result can be used as a comparison bound, indicating that it is possible to compare chains even when only non-spectral bounds exist for a known chain.

math.PR↗

arXiv2024

The THESAN project: galaxy sizes during the epoch of reionization

We investigate galaxy sizes at redshift $z\gtrsim 6$ with the cosmological radiation-magneto-hydrodynamic simulation suite THESAN(-HR). These simulations simultaneously capture the reionization of the large-scale intergalactic medium and resolved galaxy properties. The intrinsic size ($r^{\ast}_{1/2}$) of simulated galaxies increases moderately with stellar mass at $M_{\ast} \lesssim 10^{8}\,{\rm M}_{\odot}$ and decreases fast at larger masses, resulting in a hump feature at $M_{\ast}\sim 10^{8}\,{\rm M}_{\odot}$ that is insensitive to redshift. Low-mass galaxies are in the initial phase of size growth and are better described by a spherical shell model with feedback-driven gas outflows competing with the cold inflows. In contrast, massive galaxies fit better with the disk formation model. They generally experience a phase of rapid compaction and gas depletion, likely driven by internal disk instability rather than external processes. We identify four compact quenched galaxies in the $(95.5\,{\rm cMpc})^{3}$ volume of THESAN-1 at $z\simeq 6$, and their quenching follows reaching a characteristic stellar surface density akin to the massive compact galaxies at cosmic noon. Compared to observations, we find that the median UV effective radius ($R^{\rm UV}_{\rm eff}$) of simulated galaxies is at least three times larger than the observed ones at $M_{\ast}\lesssim 10^{9}\,{\rm M}_{\odot}$ or $M_{\rm UV}\gtrsim -20$ at $6 \lesssim z \lesssim 10$. This inconsistency, related to the hump feature of the intrinsic size--mass relation, persists across many other cosmological simulations with different galaxy formation models and demonstrates the potential of using galaxy morphology to constrain the physics of galaxy formation at high redshifts.

astro-ph.GA↗

arXiv2024

RIGEL: Simulating dwarf galaxies at solar mass resolution with radiative transfer and feedback from individual massive stars

We introduce the RIGEL model, a novel framework to self-consistently model the effects of stellar feedback in the multiphase ISM of dwarf galaxies with radiative transfer (RT) on a star-by-star basis. The RIGEL model integrates detailed implementations of feedback from individual massive stars into the RHD code, AREPO-RT. It forms individual massive stars from the resolved multiphase ISM by sampling the IMF and tracks their evolution individually. The lifetimes, photon production rates, mass-loss rates, and wind velocities of these stars are determined by their initial masses and metallicities based on a library that incorporates a variety of stellar models. The RT equations are solved in seven spectral bins accounting for the IR to HeII ionizing bands, using an M1 RT scheme. The thermochemistry model tracks the non-equilibrium H, He chemistry and the equilibrium abundance of CI, CII, OI, OII, and CO to capture the thermodynamics of all ISM phases. We evaluated the performance of the RIGEL model using $1\,{\rm M}_\odot$ resolution simulations of isolated dwarf galaxies. We found that the SFR and ISRF show strong positive correlations to the metallicity of the galaxy. Photoionization and photoheating can reduce the SFR by an order of magnitude by removing the available cold-dense gas fuel for star formation. The ISRF also changes the thermal structure of the ISM. Radiative feedback occurs immediately after the birth of massive stars and rapidly disperses the molecular clouds within 1 Myr. As a consequence, radiative feedback reduces the age spread of star clusters to less than 2 Myr, prohibits the formation of massive star clusters, and shapes the cluster initial mass function to a steep power-law form with a slope of $\sim-2$. The mass-loading factor of the fiducial galaxy has a median of $\sim50$, while turning off radiative feedback reduces this factor by an order of magnitude.

astro-ph.GA↗

arXiv2024

The THESAN project: connecting ionized bubble sizes to their local environments during the Epoch of Reionization

An important characteristic of cosmic hydrogen reionization is the growth of ionized gas bubbles surrounding early luminous objects. Ionized bubble sizes are beginning to be probed using Lyman-$α$ emission from high-redshift galaxies, and will also be probed by upcoming 21-cm maps. We present results from a study of bubble sizes using the state-of-the-art THESAN radiation-hydrodynamics simulation suite, which self-consistently models radiation transport and realistic galaxy formation. We employ the mean-free path method, and track the evolution of the effective ionized bubble size at each point ($R_{\rm eff}$) throughout the Epoch of Reionization. We show there is a slow growth period for regions ionized early, but a rapid "flash ionization" process for regions ionized later as they immediately enter a large, pre-existing bubble. We also find that bright sources are preferentially in larger bubbles, and find consistency with recent observational constraints at $z \gtrsim 9$, but tension with idealized Lyman-$α$ damping-wing models at $z \approx 7$. We find that high overdensity regions have larger characteristic bubble sizes, but the correlation decreases as reionization progresses, likely due to runaway formation of large percolated bubbles. Finally, we compare the redshift at which a region transitions from neutral to ionized ($z_{\rm reion}$) with the time it takes to reach a given bubble size and conclude that $z_{\rm reion}$ is a reasonable local probe of small-scale bubble size statistics ($R_\text{eff} \lesssim 1\,\rm{cMpc}$). However, for larger bubbles, the correspondence between $z_{\rm reion}$ and size statistics weakens due to the time delay between the onset of reionization and the expansion of large bubbles, particularly at high redshifts.

astro-ph.GA↗

arXiv2024

Digital Twin Generators for Disease Modeling

A patient's digital twin is a computational model that describes the evolution of their health over time. Digital twins have the potential to revolutionize medicine by enabling individual-level computer simulations of human health, which can be used to conduct more efficient clinical trials or to recommend personalized treatment options. Due to the overwhelming complexity of human biology, machine learning approaches that leverage large datasets of historical patients' longitudinal health records to generate patients' digital twins are more tractable than potential mechanistic models. In this manuscript, we describe a neural network architecture that can learn conditional generative models of clinical trajectories, which we call Digital Twin Generators (DTGs), that can create digital twins of individual patients. We show that the same neural network architecture can be trained to generate accurate digital twins for patients across 13 different indications simply by changing the training set and tuning hyperparameters. By introducing a general purpose architecture, we aim to unlock the ability to scale machine learning approaches to larger datasets and across more indications so that a digital twin could be created for any patient in the world.

cs.LG↗

arXiv2024

Adapting AREPO-RT for Exascale Computing: GPU Acceleration and Efficient Communication

Radiative transfer (RT) is a crucial ingredient for self-consistent modelling of numerous astrophysical phenomena across cosmic history. However, on-the-fly integration into radiation-hydrodynamics (RHD) simulations is computationally demanding, particularly due to the stringent time-stepping conditions and increased dimensionality inherent in multi-frequency collisionless Boltzmann physics. The emergence of exascale supercomputers, equipped with extensive CPU cores and GPU accelerators, offers new opportunities for enhancing RHD simulations. We present a novel optimization of AREPO-RT explicitly tailored for such high-performance computing environments. We implement a novel node-to-node communication strategy that utilizes shared memory to substitute intra-node communication with direct memory access. Furthermore, combining multiple inter-node messages into a single message substantially enhances network bandwidth utilization and performance for large-scale simulations on modern supercomputers. The single-message node-to-node approach also improves performance on smaller-scale machines with less optimized networks. Furthermore, by transitioning all RT-related calculations to GPUs, we achieve a significant computational speedup of around 15 for standard benchmarks compared to the original CPU implementation. As a case study, we perform cosmological RHD simulations of the Epoch of Reionization, employing a similar setup as the THESAN project. In this context, RT becomes sub-dominant such that even without modifying the core AREPO codebase, there is an overall threefold improvement in efficiency. The advancements presented here have broad implications, potentially transforming the complexity and scalability of future simulations for a wide variety of astrophysical studies.

astro-ph.IM↗

arXiv2024

Perturbations of Markov Chains

This chapter surveys progress on three related topics in perturbations of Markov chains: the motivating question of when and how "perturbed" MCMC chains are developed, the theoretical problem of how perturbation theory can be used to analyze such chains, and finally the question of how the theoretical analyses can lead to practical advice.

stat.ME↗

arXiv2024

The thesan project: public data release of radiation-hydrodynamic simulations matching reionization-era JWST observations

Cosmological simulations serve as invaluable tools for understanding the Universe. However, the technical complexity and substantial computational resources required to generate such simulations often limit their accessibility within the broader research community. Notable exceptions exist, but most are not suited for simultaneously studying the physics of galaxy formation and cosmic reionization during the first billion years of cosmic history. This is especially relevant now that a fleet of advanced observatories (e.g. James Webb Space Telescope, Nancy Grace Roman Space Telescope, SPHEREx, ELT, SKA) will soon provide an holistic picture of this defining epoch. To bridge this gap, we publicly release all simulation outputs and post-processing products generated within the THESAN simulation project at https://thesan-project.com. This project focuses on the $z \geq 5.5$ Universe, combining a radiation-hydrodynamics solver (AREPO-RT), a well-tested galaxy formation model (IllustrisTNG) and cosmic dust physics to provide a comprehensive view of the Epoch of Reionization. The THESAN suite includes 16 distinct simulations, each varying in volume, resolution, and underlying physical models. This paper outlines the unique features of these new simulations, the production and detailed format of the wide range of derived data products, and the process for data retrieval. Finally, as a case study, we compare our simulation data with a number of recent observations from the James Webb Space Telescope, affirming the accuracy and applicability of THESAN. The examples also serve as prototypes for how to utilise the released dataset to perform comparisons between predictions and observations.

astro-ph.CO↗

arXiv2024

The nature of diffuse ionised gas in star-forming galaxies

We present an analysis of the diffuse ionised gas (DIG) in a high-resolution simulation of an isolated Milky Way-like galaxy, incorporating on-the-fly radiative transfer and non-equilibrium thermochemistry. We utilise the Monte-Carlo radiative transfer code COLT to self-consistently obtain ionisation states and line emission in post-processing. We find a clear bimodal distribution in the electron densities of ionised gas ($n_{\rm e}$), allowing us to define a threshold of $n_{\rm e}=10\,\mathrm{cm}^{-3}$ to differentiate DIG from HII regions. The DIG is primarily ionised by stars aged 5-25 Myr, which become exposed directly to low-density gas after HII regions have been cleared. Leakage from recently formed stars ($<5$ Myr) is only moderately important for DIG ionisation. We forward model local observations and validate our simulated DIG against observed line ratios in [SII]/H$α$, [NII]/H$α$, [OI]/H$α$, and [OIII]/H$β$ against $Σ_{\rm Hα}$. The mock observations not only reproduce observed correlations, but also demonstrate that such trends are related to an increasing temperature and hardening ionising radiation field with decreasing $n_{\rm e}$. The hardening of radiation within the DIG is caused by the gradual transition of the dominant ionising source with decreasing $n_{\rm e}$ from 0 Myr to 25 Myr stars, which have progressively harder intrinsic ionising spectra primarily due to the extended Wolf-Rayet phase caused by binary interactions. Consequently, the DIG line ratio trends can be attributed to ongoing star formation, rather than secondary ionisation sources, and therefore present a potent test for stellar feedback and stellar population models.

astro-ph.GA↗

arXiv2024

On Cyclical MCMC Sampling

Cyclical MCMC is a novel MCMC framework recently proposed by Zhang et al. (2019) to address the challenge posed by high-dimensional multimodal posterior distributions like those arising in deep learning. The algorithm works by generating a nonhomogeneous Markov chain that tracks -- cyclically in time -- tempered versions of the target distribution. We show in this work that cyclical MCMC converges to the desired probability distribution in settings where the Markov kernels used are fast mixing, and sufficiently long cycles are employed. However in the far more common settings of slow mixing kernels, the algorithm may fail to produce samples from the desired distribution. In particular, in a simple mixture example with unequal variance, we show by simulation that cyclical MCMC fails to converge to the desired limit. Finally, we show that cyclical MCMC typically estimates well the local shape of the target distribution around each mode, even when we do not have convergence to the target.

stat.CO↗

arXiv2023

Perturbation Analysis of Markov Chain Monte Carlo for Graphical Models

The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the change in stationary distribution is small as long as the change in the kernel is much less than some measure of the convergence rate. This result is essentially sharp for generic Markov chains. In this paper we show that much larger errors, up to size roughly the square root of the convergence rate, are permissible for many target distributions associated with graphical models. The main motivation for this work comes from computational statistics, where there is often a tradeoff between the per-step error and per-step cost of approximate MCMC algorithms. Our results show that larger perturbations (and thus less-expensive chains) still give results with small error.

math.PR↗