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DOE OSTI2024

Interpreting and Accelerating Transformers for Jet Tagging

Attention-based transformers are ubiquitous in machine learning applications from natural language processing to computer vision. In high energy physics, one central application is to classify collimated particle showers in colliders based on the particle of origin, known as jet tagging. In this work, we study the interpretatbility and prospects for acceleration of Particle Transformer (ParT), a state-of-the-art model, leverages particle-level attention to improve jet-tagging performance. We analyzing ParT's attention maps and particle-pair correlations in the eta-phi plane, revealing intriguing features, such as a binary attention pattern that identifies critical substructure in jets. These insights enhance our understanding of the model's internal workings and learning process and hint at ways to improve its efficiency. Along these lines, we also explore low-rank attention, attention alternatives, and dynamic quantization to accelerate transformers for jet tagging. With quantization, we achieve a 50% reduction in model size and a 10% increase in inference speed without compromising accuracy. These combined efforts enhance both the performance and the interpretability of transformers in high-energy physics, opening avenues for more efficient and physics-driven model designs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Understanding protein-complex assembly through grand canonical maximum entropy modeling

Inside a cell, heterotypic proteins assemble in inhomogeneous, crowded systems where the abundance of these proteins vary with cell types. While some protein complexes form putative structures that can be visualized with imaging, there are far more protein complexes that are yet to be solved because of their dynamic associations with one another. Nevertheless, it is possible to infer these protein complexes through a physical model. However, it is often not clear to physicists what kind of data from biology is necessary for such a modeling endeavor. Here, we aim to model these clusters of coarse-grained protein assemblies from multiple subunits through the constraints of interactions among the subunits and the chemical potential of each subunit. We obtained the constraints on the interactions among subunits from the known protein structures. We inferred the chemical potential that dictates the particle number distribution of each protein subunit from the knowledge of protein abundance from experimental data. Guided by the maximum entropy principle, we formulated an inverse statistical mechanical method to infer the distribution of particle numbers from the data of protein abundance as chemical potentials for a grand canonical multicomponent mixture. Using grand canonical Monte Carlo simulations, we captured a distribution of high-order clusters in a protein complex of succinate dehydrogenase with four known subunits. The complexity of hierarchical clusters varies with the relative protein abundance of each subunit in distinctive cell types such as lung, heart, and brain. When the crowding content increases, we observed that crowding stabilizes emergent clusters that do not exist in dilute conditions. We, therefore, proposed a testable hypothesis that the hierarchical complexity of protein clusters on a molecular scale is a plausible biomarker of predicting the phenotypes of a cell.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

GCoD: Graph Convolutional Network Acceleration via Dedicated Algorithm and Accelerator Co-Design

Graph Convolutional Networks (GCNs) have emerged as the state-of-the-art graph learning model. However, it remains notoriously challenging to inference GCNs over large graph datasets, limiting their application to large real-world graphs and hindering the exploration of deeper and more sophisticated GCN graphs. This is because real-world graphs can be extremely large and sparse. Furthermore, the node degree of GCNs tends to follow the power-law distribution and therefore have highly irregular adjacency matrices, resulting in prohibitive inefficiencies in both data processing and movement and thus substantially limiting the achievable GCN acceleration efficiency. To this end, this paper proposes the first GCN algorithm and accelerator Co-Design framework dubbed GCoD which can largely alleviate the aforementioned GCN irregularity and boost GCNs' inference efficiency. Specifically, on the algorithm level, GCoD integrates a divide and conquer GCN training strategy that polarizes the graphs to be either denser or sparser in local neighborhoods without compromising the model accuracy, resulting in graph adjacency matrices that (mostly) have merely two levels of workload and enjoys largely enhanced regularity and thus ease of acceleration. On the hardware level, we further develop a dedicated two-pronged accelerator with a separated engine to process each of the aforementioned workloads, further boosting the overall utilization and acceleration efficiency. Extensive experiments and ablation studies validate that our GCoD consistently outperforms state-of-the-art designs in terms of accelerator efficiency while maintaining or even improving the task accuracy. Additionally, we visualize GCoD trained graph adjacency matrices to better understand its advantages. All codes and pre-trained models will be released upon acceptance.

You, Haoran↗

DOE OSTI2018

Impact of three-dimensional hot-spot flow asymmetry on ion-temperature measurements in inertial confinement fusion experiments

Three-dimensional (3-D) implosion asymmetries lead to signficant variations in ion-temperature measurements in inertial confinement fusion experiments. We present an analytical method to generalize the physical properties of velocity variance in the Brysk ion-temperature model. This analysis provides a consistent explanation for the 3-D effects of inferred ion-temperature variations for various single modes and multimodes modeled by the deceleration-phase hydrocode DEC3D and the neutron transport code IRIS3D . The effect of the hot-spot ow asymmetry on variations in ion-temperature measurement is shown uniquely determined by a complete set of six hot-spot flow parameters. An approximated solution to the minimum inferred ion temperature is derived and shown to be close to the thermal ion temperature for low mode l = 1, which exhibits the largest anisotropic velocity variance in the single-mode spectrum. In conclusion, the isotropic velocity variance for low mode l = 2 is shown to result in the minimum inferred ion temperatures being well above the thermal ion temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Are Terrestrial Biosphere Models Fit for Simulating the Global Land Carbon Sink?

The Global Carbon Project estimates that the terrestrial biosphere has absorbed about one-third of anthropogenic CO 2 emissions during the 1959–2019 period. This sink-estimate is produced by an ensemble of terrestrial biosphere models and is consistent with the land uptake inferred from the residual of emissions and ocean uptake. The purpose of our study is to understand how well terrestrial biosphere models reproduce the processes that drive the terrestrial carbon sink. One challenge is to decide what level of agreement between model output and observation-based reference data is adequate considering that reference data are prone to uncertainties. To define such a level of agreement, we compute benchmark scores that quantify the similarity between independently derived reference data sets using multiple statistical metrics. Models are considered to perform well if their model scores reach benchmark scores. Our results show that reference data can differ considerably, causing benchmark scores to be low. Model scores are often of similar magnitude as benchmark scores, implying that model performance is reasonable given how different reference data are. While model performance is encouraging, ample potential for improvements remains, including a reduction in a positive leaf area index bias, improved representations of processes that govern soil organic carbon in high latitudes, and an assessment of causes that drive the inter-model spread of gross primary productivity in boreal regions and humid tropics. The success of future model development will increasingly depend on our capacity to reduce and account for observational uncertainties.

58 GEOSCIENCES↗

DOE OSTI2021

System risk quantification and decision making support using functional modeling and dynamic Bayesian network

Risk-informed decision-making requires a probabilistic assessment of the likelihood of success of control action, given the system status. This paper presents a systematic state transition modeling approach integrating dynamic probabilistic risk assessment with a decision-making process using a dynamic Bayesian network (DBN) coupled with functional modeling. A functional model designed with multilevel flow modeling (MFM) technique was used to build a system state structure inferred by energy, mass, and information flow so that one can verify the developed model with respect to system functionality. The MFM model represents the causal relationship among the nodes, which captures the structure of process parameters and control units. Each node may have multiple possible states, and the DBN structured by the MFM model represents the time-domain transitions among the defined states. Furthermore, the MFM-DBN integrated state transition modeling is a white-box approach that allows one to draw the system's risk profile by updating the system states and supports the decisions probabilistically with physical inference. An example of a simple heating system has been used to illustrate this process, including decision-making support based on quantitative risk profile. For demonstrating its applicability to a complex system operational decision making, a case study of station blackout accident scenario leading to the seal loss of coolant accident in a nuclear power plant is presented. The proposed approach effectively provided the risk profile along time for each option so that the operators can make the best decision, which minimizes the plant risk.

42 ENGINEERING↗

DOE OSTI2024

Topological Interpretability for Deep Learning

With the growing adoption of AI-based systems across everyday life, the need to understand their decision-making mechanisms is correspondingly increasing. The level at which we can trust the statistical inferences made from AI-based decision systems is an increasing concern, especially in high-risk systems such as criminal justice or medical diagnosis, where incorrect inferences may have tragic consequences. Despite their successes in providing solutions to problems involving real-world data, deep learning (DL) models cannot quantify the certainty of their predictions. These models are frequently quite confident, even when their solutions are incorrect. This work presents a method to infer prominent features in two DL classification models trained on clinical and non-clinical text by employing techniques from topological and geometric data analysis. We create a graph of a model's feature space and cluster the inputs into the graph's vertices by the similarity of features and prediction statistics. We then extract subgraphs demonstrating high-predictive accuracy for a given label. These subgraphs contain a wealth of information about features that the DL model has recognized as relevant to its decisions. We infer these features for a given label using a distance metric between probability measures, and demonstrate the stability of our method compared to the LIME and SHAP interpretability methods. This work establishes that we may gain insights into the decision mechanism of a DL model. This method allows us to ascertain if the model is making its decisions based on information germane to the problem or identifies extraneous patterns within the data.

Spannaus, Adam↗

DOE OSTI2024

Distributed-Memory Sparse Deep Neural Network Inference Using Global Arrays

Partitioned Global Address Space (PGAS) models exhibit tremendous promise in developing efficient and productive distributed-memory parallel applications. They have been used extensively in scientific computations due to conveniently offering a ``shared-memory''-like model and convenient interfaces that separate communication with synchronization. Traditionally, PGAS communication models have been applied to dense/contiguously distributed data, but most modern applications depict varied levels of sparsity. Existing PGAS models require certain adaptations to support distributed sparse computations, since associated computations often require matrix arithmetic, in addition to data movement. The Global Arrays toolkit from Pacific Northwest National Laboratory (PNNL) is one of the earliest PGAS models to combine one-sided data communication and distributed matrix operations and is still used in the popular NWChem quantum chemistry suite. Recently, we have expanded the Global Arrays toolkit to support common sparse operations, like sparse matrix-dense matrix multiplies (SpMM), sparse matrix-sparse matrix multiplication (SpGEMM) and Sampled Dense-Dense Matrix Multiplication (SDDMM). As it turns out, these operations are the bedrock of sparse Deep Learning (DL); sparse deep neural networks and Graph Neural Networks (GNNs) have gained increasing attention recently in achieving speedups on training and inference with reduced memory footprints. Unlike scientific applications in High Performance Computing (HPC), modern (distributed-memory capable) DL toolkits often rely on non-standardized and closed-source vendor software optimizations, creating challenges in software-hardware co-design at scale. Our goal is to support a variety of distributed-memory sparse matrix operations and helper functions in the newly created Sparse Global Arrays (SGA), such that it is possible to build portable and productive Machine Learning scenarios for algorithm/software and hardware codesign purposes. Contemporary data-parallel schemes for training/inference are undergoing a major overhaul since model replication limits scalability and causes resource inefficiencies. As such, we have adopted tensor parallelism in decomposing the model and inputs, to mitigate memory issues. Current implementation is built on top of MPI and uses CPUs to maximize the portability across the platforms.

Distributed computing, machine learning↗

DOE OSTI2024

Differentiable stochastic halo occupation distribution

ABSTRACT In this work, we demonstrate how differentiable stochastic sampling techniques developed in the context of deep reinforcement learning can be used to perform efficient parameter inference over stochastic, simulation-based, forward models. As a particular example, we focus on the problem of estimating parameters of halo occupation distribution (HOD) models that are used to connect galaxies with their dark matter haloes. Using a combination of continuous relaxation and gradient re-parametrization techniques, we can obtain well-defined gradients with respect to HOD parameters through discrete galaxy catalogue realizations. Having access to these gradients allows us to leverage efficient sampling schemes, such as Hamiltonian Monte Carlo, and greatly speed up parameter inference. We demonstrate our technique on a mock galaxy catalogue generated from the Bolshoi simulation using a standard HOD model and find near-identical posteriors as standard Markov chain Monte Carlo techniques with an increase of ∼8× in convergence efficiency. Our differentiable HOD model also has broad applications in full forward model approaches to cosmic structure and cosmological analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Active learning for SNAP interatomic potentials via Bayesian predictive uncertainty

Bayesian inference with a simple Gaussian error model is used to efficiently compute prediction variances for energies, forces, and stresses in the linear SNAP interatomic potential. Here, the prediction variance is shown to have a strong correlation with the absolute error over approximately 24 orders of magnitude. Using this prediction variance, an active learning algorithm is constructed to iteratively train a potential by selecting the structures with the most uncertain properties from a pool of candidate structures. The relative importance of the energy, force, and stress errors in the objective function is shown to have a strong impact upon the trajectory of their respective net error metrics when running the active learning algorithm. Batched training of different batch sizes is also tested against singular structure updates, and it is found that batches can be used to significantly reduce the number of retraining steps required with only minor impact on the active learning trajectory.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Progress in Constraining Nuclear Symmetry Energy Using Neutron Star Observables Since GW170817

The density dependence of nuclear symmetry energy is among the most uncertain parts of the Equation of State (EOS) of dense neutron-rich nuclear matter. It is currently poorly known especially at suprasaturation densities partially because of our poor knowledge about isovector nuclear interactions at short distances. Because of its broad impacts on many interesting issues, pinning down the density dependence of nuclear symmetry energy has been a longstanding and shared goal of both astrophysics and nuclear physics. New observational data of neutron stars including their masses, radii, and tidal deformations since GW170817 have helped improve our knowledge about nuclear symmetry energy, especially at high densities. Based on various model analyses of these new data by many people in the nuclear astrophysics community, while our brief review might be incomplete and biased unintentionally, we learned in particular the following: (1) The slope parameter L of nuclear symmetry energy at saturation density ρ0 of nuclear matter from 24 new analyses of neutron star observables was about L≈57.7±19 MeV at a 68% confidence level, consistent with its fiducial value from surveys of over 50 earlier analyses of both terrestrial and astrophysical data within error bars. (2) The curvature Ksym of nuclear symmetry energy at ρ0 from 16 new analyses of neutron star observables was about Ksym≈−107±88 MeV at a 68% confidence level, in very good agreement with the systematics of earlier analyses. (3) The magnitude of nuclear symmetry energy at 2ρ0, i.e., Esym(2ρ0)≈51±13 MeV at a 68% confidence level, was extracted from nine new analyses of neutron star observables, consistent with the results from earlier analyses of heavy-ion reactions and the latest predictions of the state-of-the-art nuclear many-body theories. (4) While the available data from canonical neutron stars did not provide tight constraints on nuclear symmetry energy at densities above about 2ρ0, the lower radius boundary R2.01=12.2 km from NICER’s very recent observation of PSR J0740+6620 of mass 2.08±0.07M⊙ and radius R=12.2–16.3 km at a 68% confidence level set a tight lower limit for nuclear symmetry energy at densities above 2ρ0. (5) Bayesian inferences of nuclear symmetry energy using models encapsulating a first-order hadron–quark phase transition from observables of canonical neutron stars indicated that the phase transition shifted appreciably both L and Ksym to higher values, but with larger uncertainties compared to analyses assuming no such phase transition. (6) The high-density behavior of nuclear symmetry energy significantly affected the minimum frequency necessary to rotationally support GW190814’s secondary component of mass (2.50–2.67) M⊙ as the fastest and most massive pulsar discovered so far. Overall, thanks to the hard work of many people in the astrophysics and nuclear physics community, new data of neutron star observations since the discovery of GW170817 have significantly enriched our knowledge about the symmetry energy of dense neutron-rich nuclear matter.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Machine learning for analysis of atomic spectral data

Physics based forward models are the basis on which many experimental diagnostics are interpreted. For some diagnostics, models can be computationally expensive which precludes their use in real time analysis. Reduced models have the potential to capture sufficient physics thereby enabling the desired real time analysis. Using statistical inference and machine learning techniques the application of reduced models for inversion of atomic spectral data used to diagnose magnetic fields in a plasma will be examined. Two approaches are considered, (a) a reduction of the forward model where traditional inversion can be performed on the proxy model, and (b) a reduction of the direct inverse where parameters are a function of measured signal. The resulting inversion is sufficiently fast to be utilized in an online context for digital twinning, and ultimately real-time prediction, design, and control of plasma systems, such as tokamaks. Furthermore, these methods will be demonstrated on both simulated and experimentally measured data.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2017

Accurate Holdup Calculations with Predictive Modeling & Data Integration

In facilities that process special nuclear material (SNM) it is important to account accurately for the fissile material that enters and leaves the plant. Although there are many stages and processes through which materials must be traced and measured, the focus of this project is material that is “held-up” in equipment, pipes, and ducts during normal operation and that can accumulate over time into significant quantities. Accurately estimating the holdup is essential for proper SNM accounting (vis-à-vis nuclear non-proliferation), criticality and radiation safety, waste management, and efficient plant operation. Usually it is not possible to directly measure the holdup quantity and location, so these must be inferred from measured radiation fields, primarily gamma and less frequently neutrons. Current methods to quantify holdup, i.e. Generalized Geometry Holdup (GGH), primarily rely on simple source configurations and crude radiation transport models aided by ad hoc correction factors. This project seeks an alternate method of performing measurement-based holdup calculations using a predictive model that employs state-of-the-art radiation transport codes capable of accurately simulating such situations. Inverse and data assimilation methods use the forward transport model to search for a source configuration that best matches the measured data and simultaneously provide an estimate of the level of confidence in the correctness of such configuration. In this work the holdup problem is re-interpreted as an inverse problem that is under-determined, hence may permit multiple solutions. A probabilistic approach is applied to solving the resulting inverse problem. This approach rates possible solutions according to their plausibility given the measurements and initial information. This is accomplished through the use of Bayes’ Theorem that resolves the issue of multiple solutions by giving an estimate of the probability of observing each possible solution. To use Bayes’ Theorem, one must have a model y(x) that maps the state variables x (the solution in this case) to the measurements y. In this case, the unknown state variables are the configuration and composition of the heldup SNM. The measurements are the detector readings. Thus, the natural model is neutral-particle radiation transport where a wealth of computational tools exists for performing these simulations accurately and efficiently. The combination of predictive model and Bayesian inference forms the Data Integration with Modeled Predictions (DIMP) method that serves as foundation for this project. The cost functional describing the model-to-data misfit is computed via a norm created by the inverse of the covariance matrix of the model parameters and responses. Since the model y(x) for the holdup problem is nonlinear, a nonlinear optimization on Q is conducted via Newton-type iterative methods to find the optimal values of the model parameters x. This project comprised a collaboration between NC State University (NCSU), the University of South Carolina (USC), and Oak Ridge National Laboratory (ORNL). The project was originally proposed in seven main tasks with an eighth contingency task to be performed if time and funding permitted; in fact time did not permit commencement of the contingency task and it was not performed. The remaining tasks involved holdup analysis with gamma detection strategies and separately with neutrons based on coincidence counting. Early in the project, and upon consultation with experts in coincidence counting it became evident that this approach is not viable for holdup applications and this task was replaced with an alternative, but valuable investigation that was carried out by the USC partner. Nevertheless, the experimental 4 measurements at ORNL of both gamma and neutron sources for the purpose of constructing Detector Response Functions (DRFs) with the associated uncertainties were indeed completed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2016

THE KEY ROLE OF SOLAR DYNAMICS IN THE CHROMOSPHERIC HANLE POLARIZATION

The quantum theory of polarized light allows one to model scattering in the solar atmosphere for inferring its properties. This powerful approach has revealed two key long-standing problems in solar physics: the puzzling dilemmas between theory and observations in several anomalously polarized spectral lines and the need for inferring the ubiquitous weak chromospheric magnetic fields, which requires discriminating the Hanle effect in dynamic optically thick plasmas. However, the ever-present dynamics, i.e., the temporal evolution of heatings and macroscopic motions, has been widely disregarded when modeling and interpreting the scattering polarization. This has hindered a consistent theoretical solution to the puzzle while falsifying the Hanle diagnosis. Here, we show that the dynamical evolution is a keystone for solving both problems because its systematic impact allows an explanation of the observations from “anomalous” instantaneous polarization signals. Evolution accounted for, we reproduce amplitudes and (spectral and spatial) shapes of the Ca i 4227 Å polarization at solar disk center, identifying a restrictive arrangement of magnetic fields, kinematics, heatings, and spatio-temporal resolution. We find that the joint action of dynamics, Hanle effect, and low temporal resolutions mimics Zeeman linear polarization profiles, the true weak-field Zeeman signals being negligible. Our results allow reinterpretation of many polarization signals of the solar spectra and support time-dependent scattering polarization as a powerful tool for deciphering the spatio-temporal distribution of chromospheric heatings and fields. This approach may be a key aid in developing the Hanle diagnosis for the solar atmosphere.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Detection of the significant impact of source clustering on higher order statistics with DES Year 3 weak gravitational lensing data

We measure the impact of source galaxy clustering on higher order summary statistics of weak gravitational lensing data. By comparing simulated data with galaxies that either trace or do not trace the underlying density field, we show that this effect can exceed measurement uncertainties for common higher order statistics for certain analysis choices. We evaluate the impact on different weak lensing observables, finding that third moments and wavelet phase harmonics are more affected than peak count statistics. Using Dark Energy Survey (DES) Year 3 (Y3) data, we construct null tests for the source-clustering-free case, finding a p-value of p = 4 × 10 −3 (2.6σ) using third-order map moments and p = 3 × 10 −11 (6.5σ) using wavelet phase harmonics. The impact of source clustering on cosmological inference can be either included in the model or minimized through ad hoc procedures (e.g. scale cuts). We verify that the procedures adopted in existing DES Y3 cosmological analyses were sufficient to render this effect negligible. Failing to account for source clustering can significantly impact cosmological inference from higher order gravitational lensing statistics, e.g. higher order N-point functions, wavelet-moment observables, and deep learning or field-level summary statistics of weak lensing maps.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Combining Computational Modeling with Reaction Kinetics Experiments for Elucidating the In Situ Nature of the Active Site in Catalysis

Microkinetic modeling based on density functional theory (DFT) derived energetics is important for addressing fundamental questions in catalysis. The quantitative fidelity of microkinetic models (MKMs), however, is often insufficient to conclusively infer the mechanistic details of a specific catalytic system. Here, this can be attributed to a number of factors such as an incorrect model of the active site for which DFT calculations are performed, deficiencies in the hypothesized reaction mechanism, inadequate consideration of the surface environment under reaction conditions, and intrinsic errors in the DFT exchange-correlation functional. Despite these limitations, we aim at developing a rigorous understanding of the reaction mechanism and of the nature of the active site for heterogeneous catalytic chemistries under reaction conditions. By achieving parity between experimental and modeling outcomes through robust parameter estimation and by ensuring coverage-consistency between DFT calculations and MKM predictions, it is possible to systematically refine the mechanistic model and, thereby, our understanding of the catalytic active site in situ.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Bayesian inference of Stochastic reaction networks using Multifidelity Sequential Tempered Markov Chain Monte Carlo

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells.These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not directly measurable and must be inferred from experimental data. Bayesian inference provides a rigorous probabilistic frame-work for identifying these parameters by finding a posterior parameter distribution that captures their uncertainty.Traditional computational methods for solving inference problems such as Markov Chain Monte Carlo methods based on classical Metropolis-Hastings algorithm involve numerous serial evaluations of the likelihood function, which in turn requires expensive forward solutions of the chemical master equation (CME). We propose an alternate approach based on a multifidelity extension of the Sequential Tempered Markov Chain Monte Carlo (ST-MCMC) sampler. This algorithm is built upon Sequential Monte Carlo and solves the Bayesian inference problem by decomposing it into a sequence of efficiently solved subproblems that gradually increase both model fidelity and the influence of the observed data. We reformulate the finite state projection (FSP) algorithm, a well-known method for solving the CME, to produce a hierarchy of surrogate master equations to be used in this multifidelity scheme. To determine the appropriate fidelity, we introduce a novel information-theoretic criteria that seeks to extract the most information about the ultimate Bayesian posterior from each model in the hierarchy without inducing significant bias. This novel sampling scheme is tested with high performance computing resources using biologically relevant problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A ``Tail" of Two Cities: Fatality-based Modeling of COVID-19 Evolution in New York City and Cook County, IL

I describe $SIR$ modeling of the COVID-19 pandemic in two U.S. urban environments, New York City (NYC) and Cook County, IL, from onset through the month of June, 2020. Since testing was not widespread early in the pandemic in the U.S., I do not use data on confirmed cases and rely solely on public fatality data to estimate model parameters. Fits to the first 20 days of data determine a degenerate combination of the basic reproduction number, $R_0$, and the mean time to removal from the infectious population, $\gamma^{-1}$, with $\gamma (R_0-1) = 0.25 (0.21)$ inverse days for NYC (Cook County). Equivalently, the initial doubling time was $t_d = 2.8 (3.4)$ days for NYC (Cook). The early fatality data suggest that both locations had infections in early February. I model the mitigation measures implemented in mid-March in both locations (distancing, quarantine, isolation, etc) via a time-dependent reproduction number $R_t$ that declines monotonically from $R_0$ to a sma ller asymptotic value, with a parameterized functional form. The timing (mid-March) and duration (several days) of the transitions in $R_t$ appear well determined by the data. However, the fatality data determine only a degenerate combination of the parameters $R_0$, the percentage reduction in social contact due to mitigation measures, $X$, and the infection fatality rate (IFR), $f$. With flat priors, based on simulations the NYC model parameters have 95.45\% credible intervals of $R_0 = 3.0-5.4$, $X= 80-99.9\%$ and $f=2-6\%$, with $5-13\%$ of the population asymptotically infected. A strong external prior indicating a lower value of $f$ or of $\gamma^{-1}$ would imply lower values of $R_0$ and $X$ and higher percentage infection of the population. For Cook County, the evolution was qualitatively different: after mitigation measures were implemented, the daily fatality counts reached a plateau for about a month before tailing off. This is consistent with an $SIR$ model that exhibits ``critical slowing-down", in which $R_t$ plateaus ! at a value just above unity. For Cook County, the 95.45\% credible intervals for the model parameters are much broader and shifted downward, $R_0=1.4-4.7$, $X=26-54\%$, and $f=0.1-0.6\%$ with $15-88\%$ of the population asymptotically infected. Despite the apparently lower efficacy of its social contact reduction measures, Cook County has had significantly fewer fatalities per population than NYC, $D_\infty/N=100$ vs. 270 per 100,000. In the model, this is attributed to the lower inferred IFR for Cook; an external prior pointing to similar values of the IFR for the two locations would instead chalk up the difference in $D/N$ to differences in the relative growth rate of the disease. I derive a model-dependent threshold, $X^{crit}_e$, for `safe' re-opening, that is, for easing of contact reduction that would not trigger a second wave; for NYC, the models predict that increasing social contact by more than 20\% from post-mitigation levels will lead to renewed spread, while for Cook County the threshold value is very uncertain, given the parameter degeneracies. The timing of 2nd-wave growth will depend on the amplitude of contact increase relative to $X^{crit}_e$ and on the asymptotic growth rate, and the impact in terms of fatalities will depend on the parameter $f$.

Frieman, Joshua↗