Direct Simulation Monte Carlo Studies of the Gas Sampling for the VATMOS-SR Mission Concept
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direct simulation Monte Carlo↗
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A Linear Analysis for the Flight Path Control of the Cassini Grand Finale Orbits
Cassini’s Grand Finale Mission begins after the last targeted Titan flyby on April 22, 2017 and ends with a series of 22 ballistic orbits each passing within a few thousand kilometers of the cloud tops of Saturn, ultimately impacting the planet on September 15, 2017. Despite the ballistic nature of the trajectory, the absence of targeted maneuvers throughout the final orbits causes position uncertainties to grow exponentially with time, posing a significant difficulty for the science sequence planning team. Thus, a strategy that incorporates trajectory correction maneuvers was developed to significantly reduce dispersions from the reference path and maintain dispersions below 250 km (1- ). In this paper, the linear method used to determine the optimal number and location of the maneuvers to control the trajectory, along with the corresponding targets, is detailed. A nonlinear Monte Carlo trajectory dispersion tool served as a testbed to validate the linear analysis results. Based on orbit determination covariance sampling with Monte Carlo simulations, the linear approach allowed the Cassini maneuver analysts to run thousands of maneuver combinations in little time, eventually finding an optimal strategy with three statistical maneuvers ( V99 < 1.5 m/s) to adequately control most of the trajectory.
Vaquero, Mar↗
Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach
This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.
Warner, James E.↗
Improving Computational Efficiency of Prognostics Algorithms in Resource-Constrained Settings
In engineering and aerospace applications, it is vital to operational success to have insight into the expected performance and health of physical systems. The field of prognostics and health management provides quantitative methods for monitoring, predicting, and managing system health. Prognostics algorithms can be employed to assess the current state of a system, propagate the system throughout time, and predict potential anomalies or failures that may occur. While they can provide accurate prediction results, effective prognostics algorithms can be challenging to use in resource-constrained settings due to computational limitations and high computational latency, leading to obsolete predictions. Thus, computationally efficient and accurate algorithms are necessary for future remaining useful life predictions. In this work, we implement new algorithmic approaches for prediction, quantitatively compare them via a battery degradation use-case, and provide recommendations of potential improvements to a prognostics framework. One approach to prediction is through sampling, whereby the current state of a physical system is sampled many times and each sample is propagated forward until failure is reached, resulting in a distribution of failure values. To improve the efficiency of this process, we implemented five new algorithmic approaches to prediction, including three distinct sampling methods (standard Monte Carlo, Quasi-Monte Carlo, and Latin Hypercube Sampling), a variable time step algorithm, and a variable sample size algorithm. To compare the algorithms, we employ a variety of metrics designed specifically to analyze both computational efficiency and model accuracy. Our metrics include accuracy to compare the average predicted value to ground truth, mean absolute deviation to illustrate dispersion, specific percentile error to describe accuracy within a user-defined risk tolerance, and code run-time. To quantitatively analyze our results, we employ a use-case of degradation of a Lithium-ion battery. We use an electrochemistry-based model to describe the current health state of the battery, and implement our prediction algorithms to propagate forward in time until end-of-discharge (EOD) is reached. Notably, through this work it was found that none of our sampling approaches had a significant impact on computational efficiency or model accuracy in predicting EOD of the battery. We find that while the sampling methods are unique, the distributions they generate are similar, ultimately producing final predictions that are nearly identical. In exploring the effect of the time step within the prediction algorithm, we found that prediction accuracy was highly dependent on the time step used, and that implementing a variable time step within a particular prediction may provide an increase in computational efficiency while also maintaining prediction accuracy. Finally, implementing a variable sample size also affected prediction, and our results show that tuning both the magnitude and timing of the sample size adjustment can result in improved computation speed and maintained prediction accuracy. Taken together, our findings highlight the challenge of performing prognostics in resource-constrained settings, and illustrate the potential of developing new prediction algorithms to improve computational efficiency.
prognostics↗
Accelerating multicanonical sampling with irreversibility
Flat-histogram Monte Carlo simulations are well-established, robust methods to perform random walks in a physical observable or parameter space, making them suitable for finding ground states or studying phase transitions in complex systems in statistical physics. However, their efficiency can be limited by the time to attain the desired flat distribution, which is generally unknown prior to the simulations. In particular, they might suffer from slowing down towards the end of a simulation due to the diffusive nature of random walks. In this work we apply irreversibility to the multicanonical Monte Carlo method via the lifting approach to alleviate this behavior. We achieve a 2–4 times speedup in ground-state search for a two-dimensional (2D) Ising model, and up to an order of magnitude of speedup for finding the ground-state energy in an Edwards–Anderson spin glass, compared to traditional multicanonical sampling. In conclusion, the round-trip times between ground states show a narrower distribution and are significantly shorter compared to the reversible counterpart, suggesting that a lower convergence time with a smaller time variance is feasible.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Monte Carlo Simulation of a Knudsen Effusion Mass Spectrometer Sampling System
Knudsen flow is easily simulated with a Monte Carlo method. In this study we develop a Visual Basic for Excel (VBA) code to simulate the molecular beam from a vaporizing solid. The system at NASA Glenn uses the restricted collimation method of Chatillon and colleagues, which consists of two apertures between the effusion cell and the ionizer. The diameter of the first aperture is smaller than the diameter of the effusion cell orifice, so the ionizer effectively only sees inside the effusion cell. The code is able to calculate the transmission coefficient through the cell orifice, through the cell orifice and the first aperture, and through the cell orifice and first and second aperatures. Calculated transmission coefficients through the cell orifice are compared to tabulated values to validate the code. Then transmission coefficients are calculated through the cell orifice and both apertures to the ionizer. This allows the geometry (aperture spacing and diameters) of the sampling system the sampling system to be optimized. Calculated transmission factors are also compared to literature values calculated via an analytic method.
Radke, Michael J.↗
𝑁-dimensional maximum-entropy tomography via particle sampling
We propose a modified maximum-entropy (MENT) algorithm for six-dimensional phase space tomography. The algorithm uses particle sampling and low-dimensional density estimation to approximate large sets of high-dimensional integrals in the original MENT formulation. We implement this approach using Markov Chain Monte Carlo (MCMC) sampling techniques and demonstrate convergence of six-dimensional MENT on both synthetic and measured data.
Hoover, Austin [Oak Ridge National Laboratory (ORN↗
Probabilistic Calibration of Expensive Models using Efficiently Trained Surrogates
Calibration of computational models in the presence of uncertainty is often cast as a Bayesian inference problem and solved via sampling methods, e.g., Markov chain Monte Carlo. When the computational model is expensive, this task becomes intractable due to the large number of samples required to accurately estimate the posterior distribution of the calibration parameters. A popular solution to this problem is to use machine learning to develop a faster-to-evaluate, lower-fidelity substitute for the original model to serve as a surrogate while solving the inference problem. Although considered an offline cost, generating training data to construct this surrogate model can still be an expensive task in practice. An active learning algorithm is presented that focuses training on improving surrogate accuracy specifically in and around the bulk of the posterior distribution, as this is where the model is exercised during calibration. Candidate samples are drawn from families of distributions related to an approximation of the posterior. The sample maximizing predictive variance is then selected for evaluation by the original computational model, yielding a label for the training point. Iterating this approach increases efficiency relative to space filling designs (e.g., Latin hypercube sampling) by avoiding low probability points. Practical considerations are discussed, including the benefits of using a sequential Monte Carlo sampling approach, convergence heuristics, and the importance of both exploration and exploitation given that the true posterior is unknown a priori.
uncertainty quantification↗
Data-Efficient Strategies for Probabilistic Voltage Envelopes under Network Contingencies
This work presents an efficient data-driven method to construct probabilistic voltage envelopes (PVE) using power flow learning in grids with network contingencies. First, a network-aware Gaussian process (GP) termed Vertex-Degree Kernel (VDK-GP), developed in prior work, is used to estimate voltage–power functions for a few network configurations. The paper introduces a novel multi-task vertex degree kernel (MT-VDK) that amalgamates the learned VDK-GPs to determine power flows for unseen networks, with a significant reduction in the computational complexity and hyperparameter requirements compared to alternate approaches. Simulations on the IEEE 30-Bus network demonstrate the retention and transfer of power flow knowledge in both N-1 and N-2 contingency scenarios. The MT-VDK-GP approach achieves over 50 % reduction in mean prediction error for novel N-1 contingency network configurations in low training data regimes (50–250 samples) over VDK-GP. Additionally, MT-VDK-GP outperforms a hyper-parameter based transfer learning approach in over 75 % of N-2 contingency network structures, even without historical N-2 outage data. Furthermore, the proposed method demonstrates the ability to achieve PVEs using sixteen times fewer power flow solutions compared to Monte-Carlo sampling-based methods.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Accelerating multilevel Markov Chain Monte Carlo using machine learning models
Here, this work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to accelerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive the expression for cost reduction due to machine learning model to facilitate cost analysis of the hierarchical sampling algorithm. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.
97 MATHEMATICS AND COMPUTING↗
Probing Physics beyond the Standard Model through Combined Analyses of Next-generation Type Ia Supernova, Cosmic Microwave Background, and Baryon Acoustic Oscillation Surveys
Observations of Type Ia supernovae (SNe Ia), which probe the late Universe, together with baryon acoustic oscillations (BAO) and the cosmic microwave background (CMB), which probe the intermediate and early epochs, provide complementary constraints on the expansion history of the Universe. In this work, we forecast constraints on dark energy and other extensions to the standard cosmological model by combining the SN Ia sample expected from the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), data from current and forthcoming CMB surveys, and BAO measurements from the Dark Energy Spectroscopic Instrument (DESI). For the CMB, we use temperature, polarization, and lensing power spectra (TT/EE/TE/ϕϕ) from the South Pole Telescope, the planned Advanced Simons Observatory, and a CMB-S4–like experiment. We derive constraints on ΛCDM and its extensions involving the dark energy equation-of-state parameters (w 0 , w a ) and the sum of neutrino masses ∑m ν using a Markov Chain Monte Carlo (MCMC) sampling framework. We find that the LSST Year 3 SN Ia sample can improve upon the DES Year 5 dark energy constraints by a factor of 2−2.5×, with the gains driven primarily by the significantly higher SN Ia density in the LSST sample. Similarly, DESI-DR3 shows up to a 1.8× improvement on dark energy parameters over DR2, driven largely by the substantial increase in the low-redshift sample. Combining CMB with LSST-Y3-SN Ia and DESI-DR3-BAO yields σ(w 0 ) = 0.028 and σ(w a ) = 0.11 for w 0 w a CDM cosmology with the results being largely independent of the CMB dataset. The constraints weaken by 10%–30% when freeing ∑m ν and spatial curvature. Moreover, the joint analysis of the three datasets can enable a 2σ–3σ detection of ∑m ν .
Raghunathan, Srinivasan [University of California;↗
From optimal observables to machine learning: an effective-field-theory analysis of e + e − → W + W − at future lepton colliders
We apply machine-learning techniques to the effective-field-theory analysis of the e + e − → W + W − processes at future lepton colliders, and demonstrate their advantages in comparison with conventional methods, such as optimal observables. In particular, we show that machine-learning methods are more robust to detector effects and backgrounds, and could in principle produce unbiased results with sufficient Monte Carlo simulation samples that accurately describe experiments. This is crucial for the analyses at future lepton colliders given the outstanding precision of the e + e − → W + W − measurement (~ 10−4 in terms of anomalous triple gauge couplings or even better) that can be reached. Our framework can be generalized to other effective-field-theory analyses, such as the one of e + e − → t t ¯ or similar processes at muon colliders.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Why the electron chooses one of two symmetry-related paths in the type II bacterial photosynthetic reaction centers
A series of electron and proton transfer reactions are carried out in photosynthetic reaction centers that convert the energy of light into high energy reduced products and add to the proton gradient. All photosynthetic reaction centers (photosystems I, II, and different bacterial reaction centers (bRCs)) have their charge separating cofactors arranged with two, c 2 -symmetric paths from a primary donor to a terminal acceptor. In Type II reaction centers (PSII and bRCs), electrons utilize only one active branch. In bRCs the electron transfer occurs in the A branch from the excited state of the bacteriochlorophyll (BChl) dimer P 860 through BChl A , bacteriopheophytin A (BPh A ), to ubiquinone Q A , and then to the B-branch Q B . B-branch BChl B and BPh B do not participate. A similar path is found in PSII. These proteins challenge our understanding of how proteins can turn on or turn off the activity of bound ligands. The shift of the electrochemical midpoint potential (E m ) of each cofactor by the protein environment is calculated using continuum electrostatics within the Multi-Conformation Continuum Electrostatic (MCCE) program. In bRCs from Rhodobacter sphaeroides, the electrostatic potentials favor reduction of the active branch cofactors. The residues that contribute to a more positive potential on the A branch are identified. These are often distant from the cofactors. The large difference of the potential at the competing BChls may direct the electron transfer to the A branch. Residues TyrM210 and PheL181 are at symmetrical positions on the A and B branches, near P 860 , between BChl A and BChl B . Mutated bRCs, that swap the Tyr and Phe (YF mutant), have been shown to support some electron transfer to the B-branch cofactors. Here, the calculated E m s with the YF swap show more positive B-branch potentials, which help explain why there is now electron transfer along the B branch.
Bacterial Reaction Center↗
Role of the likelihood for elastic scattering uncertainty quantification
In the last decade, uncertainty quantification (UQ) for optical model potentials (OMPs) has become a focal point for nuclear reaction theory, and several competing approaches for OMP UQ have recently been developed. Here, we clarify recent efforts to compare frequentist and Bayesian approaches in the context of OMP UQ [G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019)]. We replicate a portion of that OMP UQ study but use independent statistical tools. Specifically, we compare two methods for OMP parameter inference from elastic scattering data: the Levenberg-Marquardt algorithm for χ 2 minimization on one hand and Markov chain Monte Carlo (MCMC) sampling on the other. Separately, we assess the common practice of using a renormalized likelihood (χ 2 /N), N being the number of data points, instead of the canonical weighted-least-squares likelihood (χ 2 ), as a way of accounting for unknown data correlations. Here, we show that for a generic linear model and for a five-parameter OMP analysis, frequentist and uniform-prior Bayesian approaches recover the same optimum and uncertainty estimates—not systematically larger uncertainties for the Bayesian approach, as was concluded in G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019). Further, we show that if an additional, near-degenerate parameter is introduced into the same OMP analysis such that the parameter posterior becomes non-Gaussian, then covariance-based estimates of uncertainty become unreliable. Finally, we show that regardless of optimization approach, if χ 2 /N is used for the likelihood, the resulting parametric uncertainties increase by $\sqrt{N}$, and that this is responsible for the conclusions drawn in the revisited study. Based on our replication results, we find that a fortuitous cancellation of unreported errors and the renormalization factor can lead to improvement in empirical coverages, as was the case in the original comparative study. We emphasize that developing and applying a realistic likelihood function is an essential task in a UQ analysis, and that several recent UQ studies that employed a renormalized likelihood (i.e., including a 1/N factor) may have yielded unrealistically large uncertainties for elastic-scattering observables. If the parameter posterior deviates from multivariate-normal, a sampling-based approach like MCMC has a clear advantage over methods that assume the Laplace approximation holds. We note that empirical coverage can serve as an important internal check for the analyst whose model or data may have additional, unaccounted-for uncertainties.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Improving neutrino energy estimation of charged-current interaction events with recurrent neural networks in MicroBooNE
We present a deep learning-based method for estimating the neutrino energy of charged-current neutrino-argon interactions. We employ a recurrent neural network (RNN) architecture for neutrino energy estimation in the MicroBooNE experiment, utilizing liquid argon time projection chamber (LArTPC) detector technology. Traditional energy estimation approaches in LArTPCs, which largely rely on reconstructing and summing visible energies, often experience sizable biases and resolution smearing because of the complex nature of neutrino interactions and the detector response. The estimation of neutrino energy can be improved after considering the kinematics information of reconstructed final-state particles. Utilizing kinematic information of reconstructed particles, the deep learning-based approach shows improved resolution and reduced bias for the muon neutrino Monte Carlo simulation sample compared to the traditional approach. In order to address the common concern about the effectiveness of this method on experimental data, the RNN-based energy estimator is further examined and validated with dedicated data-simulation consistency tests using MicroBooNE data. We also assess its potential impact on a neutrino oscillation study after accounting for all statistical and systematic uncertainties and show that it enhances physics sensitivity. This method has good potential to improve the performance of other physics analyses. Published by the American Physical Society 2024
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Uncertainty Visualization of Critical Points of 2D Scalar Fields for Parametric and Nonparametric Probabilistic Models
This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. Here, in this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets.
97 MATHEMATICS AND COMPUTING↗
Efficient Probabilistic Visualization of Local Divergence of 2D Vector Fields with Independent Gaussian Uncertainty
This work focuses on visualizing uncertainty of local divergence of two-dimensional vector fields. Divergence is one of the fundamental attributes of fluid flows, as it can help domain scientists analyze potential positions of sources (positive divergence) and sinks (negative divergence) in the flow. However, uncertainty inherent in vector field data can lead to erroneous divergence computations, adversely impacting downstream analysis. While Monte Carlo (MC) sampling is a classical approach for estimating divergence uncertainty, it suffers from slow convergence and poor scalability with increasing data size and sample counts. Thus, we present a two-fold contribution that tackles the challenges of slow convergence and limited scalability of the MC approach. (1) We derive a closed-form approach for highly efficient and accurate uncertainty visualization of local divergence, assuming independently Gaussian-distributed vector uncertainties. (2) We further integrate our approach into Viskores, a platform-portable parallel library, to accelerate uncertainty visualization. In our results, we demonstrate significantly enhanced efficiency and accuracy of our serial analytical (speed-up up to 1946×) and parallel Viskores (speed-up up to 19698×) algorithms over the classical serial MC approach. We also demonstrate qualitative improvements of our probabilistic divergence visualizations over traditional mean-field visualization, which disregards uncertainty. We validate the accuracy and efficiency of our methods on wind forecast and ocean simulation datasets.
Ouermi, Timbwaoga [University of Utah]↗
Uncertainty propagation and sensitivity analysis for constrained optimization of nuclear waste vitrification
Abstract The vitrification of high‐level waste (HLW) by heating a mixture of glass‐forming chemicals (GFCs) with the waste can be improved using a constrained optimization problem. This study explores how different uncertainty propagation (UP) methods implemented with the optimization process can affect the glass formulation of nuclear waste glasses. UP is the effort of propagating uncertain inputs through a system to understand and quantify output distributions. Uncertainty intervals are crafted from output distributions to inform the optimization algorithm. UP is often implemented with Monte Carlo (MC) sampling for large nonlinear systems, which can be difficult to implement within a constrained optimization algorithm that requires derivative information. Other UP methods often used for optimization under uncertainty (OUU) can be designed to work within an established constrained optimization framework. Methods of UP are evaluated in this study including iterative sampling approaches, first‐order approximations, and surrogate modeling with machine learning (ML). A method of dimensional reduction based on global sensitivity analysis is introduced to support the UP methods for the large dimensionality of the problem. Analytical UP methods able to achieve similar optimums 10 times faster than the baseline MC approach, and produce 93.9% similar output distributions are reported.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗