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At least 181 records · Page 10

Bayesian differential programming for robust systems identification under uncertainty

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling. This allows an efficient inference of the posterior distributions over plausible models with quantified uncertainty, while the use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed methods, including nonlinear oscillators, predator–prey systems and examples from systems biology. Taken together, our findings put forth a flexible and robust workflow for data-driven model discovery under uncertainty. All codes and data accompanying this article are available at https://bit.ly/34FOJMj .

Science & Technology - Other Topics↗

SU-F-J-102: Lower Esophagus Margin Implications Based On Rapid Computational Algorithm for SBRT

Purpose: To quantify inter-fraction esophagus-variation. Methods: Computed tomography and daily on-treatment 0.3-T MRI data sets for 7 patients were analyzed using a novel Matlab-based (Mathworks, Natick, MA) rapid computational method. Rigid registration was performed from the cricoid to the gastro-esophageal junction. CT and MR-based contours were compared at slice intervals of 3mm. Variation was quantified by “expansion,” defined as additional length in any radial direction from CT contour to MR contour. Expansion computations were performed with 360° of freedom in each axial slice. We partitioned expansions into left anterior, right anterior, right posterior, and left posterior quadrants (LA, RA, RP, and LP, respectively). Sample means were compared by analysis of variance (ANOVA) and Fisher’s Protected Least Significant Difference test. Results: Fifteen fractions and 1121 axial slices from 7 patients undergoing SBRT for primary lung cancer (3) and metastatic lung disease (4) were analyzed, generating 41,970 measurements. Mean LA, RA, RP, and LP expansions were 4.30±0.05 mm, 3.71±0.05mm, 3.17±0.07, and 3.98±0.06mm, respectively. 50.13% of all axial slices showed variation > 5 mm in one or more directions. Variation was greatest in lower esophagus with mean LA, RA, RP, and LP expansion (5.98±0.09 mm, 4.59±0.09 mm, 4.04±0.16 mm, and 5.41±0.16 mm, respectively). The difference was significant compared to mid and upper esophagus (p<.0001). The 95th percentiles of expansion for LA, RA, RP, LP were 13.36 mm, 9.97 mm, 11.29 mm, and 12.19 mm, respectively. Conclusion: Analysis of on-treatment MR imaging of the lower esophagus during thoracic SBRT suggests margin expansions of 13.36 mm LA, 9.97 mm RA, 11.29 mm RP, 12.19 mm LP would account for 95% of measurements. Our novel algorithm for rapid assessment of margin expansion for critical structures with 360° of freedom in each axial slice enables continuously adaptive patient-specific margins which may reduce overlap with high-dose regions.

60 APPLIED LIFE SCIENCES↗

A fast particle-based approach for calibrating a 3-D model of the Antarctic ice sheet

We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases. Here, we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high-performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea level projections when we account for a larger number of uncertain parameters. For example, based on the same ice sheet model and data set, the 99th percentile of the Antarctic ice sheet contribution to sea level rise in 2300 increases from 6.5 m to 13.1 m when we increase the number of calibrated parameters from three to 11. With previous calibration methods, it would be challenging to go beyond five parameters. Here, this work provides an important next step toward improving the uncertainty quantification of complex, computationally intensive and decision-relevant models.

54 ENVIRONMENTAL SCIENCES↗

PROVABGS: The Probabilistic Stellar Mass Function of the BGS One-percent Survey

We present the probabilistic stellar mass function (pSMF) of galaxies in the DESI Bright Galaxy Survey (BGS), observed during the One-percent Survey. The One-percent Survey was one of DESI's survey validation programs conducted from 2021 April to May, before the start of the main survey. It used the same target selection and similar observing strategy as the main survey and successfully observed the spectra and redshifts of 143,017 galaxies in the r < 19.5 magnitude-limited BGS Bright sample and 95,499 galaxies in the fainter surface-brightness- and color-selected BGS Faint sample over z < 0.6. We derive pSMFs from posteriors of stellar mass, M*, inferred from DESI photometry and spectroscopy using the Hahn et al. PRObabilistic Value-Added BGS (PROVABGS) Bayesian spectral energy distribution modeling framework. We use a hierarchical population inference framework that statistically and rigorously propagates the M* uncertainties. Furthermore, we include correction weights that account for the selection effects and incompleteness of the BGS observations. We present the redshift evolution of the pSMF in BGS, as well as the pSMFs of star-forming and quiescent galaxies classified using average specific star formation rates from PROVABGS. Overall, the pSMFs show good agreement with previous stellar mass function measurements in the literature. Our pSMFs showcase the potential and statistical power of BGS, which in its main survey will observe >100 × more galaxies. Moreover, we present the statistical framework for subsequent population statistics measurements using BGS, which will characterize the global galaxy population and scaling relations at low redshifts with unprecedented precision.

79 ASTRONOMY AND ASTROPHYSICS↗

Invertible neural networks for E3SM land model calibration and simulation

We apply an invertible neural network (INN) for E3SM land model calibration and simulation with eight parameters at the Missouri Ozark AmeriFlux forest site. INN provides bijective (two-way) mappings between inputs and outputs, thus it can solve probabilistic inverse problems and forward approximations simultaneously. We demonstrate INN's inverse and forward capability in both synthetic and real-data applications. Results indicate that INN produces accurate parameter posterior distributions similar to Markov Chain Monte Carlo sampling and it generates model outputs close to the forward model simulations. Additionally, both the inverse and forward evaluations in INN are computationally efficient which allows for rapid integration of observations for parameter estimation and fast model predictions.

Lu, Dan↗

Deep Active Learning for Solvability Prediction in Power Systems

Traditional methods for solvability region analysis can only have inner approximations with inconclusive conservatism and handle limited types of power flow models. In this letter, we propose a deep active learning framework for solvability prediction in power systems. Compared with passive learning where the training is performed after all instances are labeled, active learning selects most informative instances to be labeled and therefore significantly reduces the size of the labeled dataset for training. In the active learning framework, the acquisition functions, which correspond to different sampling strategies, are defined in terms of the on-the-fly posterior probability from the classifier. First, the IEEE 39-bus system is employed to validate the proposed framework, where a two-dimensional case is illustrated to visualize the effectiveness of the sampling method followed by the high-dimensional numerical experiments. Then, the Northeast Power Coordinating Council (NPCC) 140-bus system is used to validate the performance on large-scale power systems.

42 ENGINEERING↗

A technique for extracting blood samples from mice in fire toxicity tests

The extraction of adequate blood samples from moribund and dead mice has been a problem because of the small quantity of blood in each animal and the short time available between the animals' death and coagulation of the blood. These difficulties are particularly critical in fire toxicity tests because removal of the test animals while observing proper safety precautions for personnel is time-consuming. Techniques for extracting blood samples from mice were evaluated, and a technique was developed to obtain up to 0.8 ml of blood from a single mouse after death. The technique involves rapid exposure and cutting of the posterior vena cava and accumulation of blood in the peritoneal space. Blood samples of 0.5 ml or more from individual mice have been consistently obtained as much as 16 minutes after apparent death. Results of carboxyhemoglobin analyses of blood appeared reproducible and consistent with carbon monoxide concentrations in the exposure chamber.

Bucci, T. J.↗

The redshift distribution of cosmological samples: a forward modeling approach

Determining the redshift distribution n ( z ) of galaxy samples is essential for several cosmological probes including weak lensing. For imaging surveys, this is usually done using photometric redshifts estimated on an object-by-object basis. We present a new approach for directly measuring the global n ( z ) of cosmological galaxy samples, including uncertainties, using forward modeling. Our method relies on image simulations produced using \textsc(UFig) (Ultra Fast Image Generator) and on ABC (Approximate Bayesian Computation) within the MCCL (Monte-Carlo Control Loops) framework. The galaxy population is modeled using parametric forms for the luminosity functions, spectral energy distributions, sizes and radial profiles of both blue and red galaxies. We apply exactly the same analysis to the real data and to the simulated images, which also include instrumental and observational effects. By adjusting the parameters of the simulations, we derive a set of acceptable models that are statistically consistent with the data. We then apply the same cuts to the simulations that were used to construct the target galaxy sample in the real data. The redshifts of the galaxies in the resulting simulated samples yield a set of n ( z ) distributions for the acceptable models. We demonstrate the method by determining n ( z ) for a cosmic shear like galaxy sample from the 4-band Subaru Suprime-Cam data in the COSMOS field. We also complement this imaging data with a spectroscopic calibration sample from the VVDS survey. We compare our resulting posterior n ( z ) distributions to the one derived from photometric redshifts estimated using 36 photometric bands in COSMOS and find good agreement. This offers good prospects for applying our approach to current and future large imaging surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

Stan : A Probabilistic Programming Language

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the No-U-Turn sampler, an adaptive form of Hamiltonian Monte Carlo sampling. Penalized maximum likelihood estimates are calculated using optimization methods such as the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Stan is also a platform for computing log densities and their gradients and Hessians, which can be used in alternative algorithms such as variational Bayes, expectation propagation, and marginal inference using approximate integration. To this end, Stan is set up so that the densities, gradients, and Hessians, along with intermediate quantities of the algorithm such as acceptance probabilities, are easily accessible. Stan can also be called from the command line using the cmdstan package, through R using the rstan package, and through Python using the pystan package. All three interfaces support sampling and optimization-based inference with diagnostics and posterior analysis. rstan and pystan also provide access to log probabilities, gradients, Hessians, parameter transforms, and specialized plotting.

97 MATHEMATICS AND COMPUTING↗

A Scalable Gradient Free Method for Bayesian Experimental Design with Implicit Models

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.

Zhang, Jiaxin↗

Scalable Algorithms for Inverse Problems With High-Dimensional Parameter Spaces

Inverse problems, which involve inferring unknown parameters from observed data, present significant computational challenges, especially in large-scale settings with high-dimensional unknown parameters and nonlinear relationships between the unknowns and observations. Bayesian inference provides an approach for addressing these problems, often relying on sequential sampling methods like Markov chain Monte Carlo (MCMC) to approximate the posterior distribution of the parameters. However, MCMC methods become computationally demanding as the dimensionality of the problem increases, particularly in large-scale systems where likelihood evaluations rely on solving partial differential equations (PDEs) on large spatial domains with finely resolved meshes. To overcome these limitations, recent advancements have focused on designing scalable computa tional techniques – for both PDE simulations and sampling strategies – to make Bayesian methods feasible for high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗

Deterministic and Monte Carlo Nuclear Data Adjustment Methods [Slides]

For the Bayesian Monte Carlo methodology, a need to understand convergence of the posterior moments as a function of the number of parameter realizations is required. In high-dimensional systems, it can be very costly to sample entire parameter space and perform functional evaluation for every realization. Bayesian Monte Carlo allows one to relax the GLLS approximations of model linearity and prior/posterior PDF shape. The Bayesian Stochastic Collocation Method is a deterministic approach to “sample” the parameter space. It allows one to relax the GLLS approximations of model linearity and posterior PDF shape. Higher-order posterior moments (i.e., skewness, kurtosis, etc.) can be studied through polynomial expansion. Tensor product quadrature scales poorly and can use sparse grid quadrature methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

BEYONDPLANCK XIII. Intensity foreground sampling, degeneracies, and priors

We present the intensity foreground algorithms and model employed within the BEYONDPLANCK analysis framework. The BEYONDPLANCK analysis is aimed at integrating component separation and instrumental parameter sampling within a global framework, leading to complete end-to-end error propagation in the Planck Low Frequency Instrument (LFI) data analysis. Given the scope of the BEYONDPLANCK analysis, a limited set of data is included in the component separation process, leading to foreground parameter degeneracies. In order to properly constrain the Galactic foreground parameters, we improve upon the previous Commander component separation implementation by adding a suite of algorithmic techniques. These algorithms are designed to improve the stability and computational efficiency for weakly constrained posterior distributions. These are: (1) joint foreground spectral parameter and amplitude sampling, building on ideas from MIRAMARE; (2) component-based monopole determination; (3) joint spectral parameter and monopole sampling; and (4) application of informative spatial priors for component amplitude maps. We find that the only spectral parameter with a significant signal-to-noise ratio using the current BEYONDPLANCK data set is the peak frequency of the anomalous microwave emission component, for which we find $ν$ p = 25.3 ± 0.5 GHz; all others must be constrained through external priors. Future works will be aimed at integrating many more data sets into this analysis, both map and time-ordered based, thereby gradually eliminating the currently observed degeneracies in a controlled manner with respect to both instrumental systematic effects and astrophysical degeneracies. When this happens, the simple LFI-oriented data model employed in the current work will need to be generalized to account for both a richer astrophysical model and additional instrumental effects. This work will be organized within the Open Science-based COSMOGLOBE community effort.

79 ASTRONOMY AND ASTROPHYSICS↗

Bayesian Uncertainty Quantification in Predictions of Flows in Highly Heterogeneous Media and Its Applications to the CO 2 Sequestration

In this proposal, we have worked on Bayesian uncertainty quantification for predictions of fows in highly heterogeneous media. The research in this proposal is broad and includes: prior modeling for heterogeneous permeability fields; effective parametrization of heterogeneous spatial priors; efficient ensemble- level solution techniques; efficient multiscale approximation techniques; study of the regularity of complex posterior distribution and the error estimates due to parameter reduction; efficient sampling techniques; applications to multi-phase ow and transport. We list our publications below and describe some of our main research activities. Our multi-disciplinary team includes experts from the areas of multiscale modeling, multilevel solvers, Bayesian statistics, spatial permeability modeling, and the application domain.

97 MATHEMATICS AND COMPUTING↗

Constraining physical models at gigabar pressures

High-energy-density (HED) experiments in convergent geometry are able to test physical models at pressures beyond hundreds of millions of atmospheres. The measurements from these experiments are generally highly integrated and require unique analysis techniques to procure quantitative infor mation. This work describes a methodology to constrain the physics in convergent HED experiments by adapting the methods common to many other fields of physics. As an example, a mechanical model of an imploding shell is constrained by data from a thin-shelled direct-drive exploding-pusher experiment on the OMEGA Laser System using Bayesian inference, resulting in the reconstruction of the shell dynamics and energy transfer during the implosion. The model is tested by analyzing synthetic data from a 1-D hydrodynamics code and is sampled using a Markov chain Monte Carlo to generate the posterior distributions of the model parameters. As a result, the goal of this work is to demonstrate a general methodology that can be used to draw conclusions from a wide variety of HED experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Constraining Physical Models at Gigabar Pressures

High-energy-density (HED) experiments in convergent geometry are able to test physical models at pressures beyond hundreds of millions of atmospheres. The measurements from these experiments are generally highly integrated and require unique analysis techniques to procure quantitative information. This work describes a methodology to constrain the physics in convergent HED experiments by adapting the methods common to many other fields of physics. As an example, a mechanical model of an imploding shell is constrained by data from a thin-shelled direct-drive exploding-pusher experiment on the OMEGA Laser System using Bayesian inference, resulting in the reconstruction of the shell dynamics and energy transfer during the implosion. The model is tested by analyzing synthetic data from a 1-D hydrodynamics code and is sampled using a Markov chain Monte Carlo to generate the posterior distributions of the model parameters. The goal of this work is to demonstrate a general methodology that can be used to draw conclusions from a wide variety of HED experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Estimating Cosmological Constraints from Galaxy Cluster Abundance using Simulation-Based Inference

Inferring the values and uncertainties of cosmological parameters in a cosmology model is of paramount importance for modern cosmic observations. In this paper, we use the simulation-based inference (SBI) approach to estimate cosmological constraints from a simplified galaxy cluster observation analysis. Using data generated from the Quijote simulation suite and analytical models, we train a machine learning algorithm to learn the probability function between cosmological parameters and the possible galaxy cluster observables. The posterior distribution of the cosmological parameters at a given observation is then obtained by sampling the predictions from the trained algorithm. Our results show that the SBI method can successfully recover the truth values of the cosmological parameters within the 2σ limit for this simplified galaxy cluster analysis, and acquires similar posterior constraints obtained with a likelihood-based Markov Chain Monte Carlo method, the current state-of the-art method used in similar cosmological studies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗