Cosmology from HSC Y1 weak lensing data with combined higher-order statistics and simulation-based inference
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Novaes, Camila P. (ORCID:0000000258453649)↗
SEARCH · Engineering Papers
Results for “probability and statistical methods”
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Machine learning assisted bayesian inference of mix and hot-spot conditions in NIF implosions
Experiments on the National Ignition Facility (NIF) have provided clear evidence of ablator material mixing into the Hot-Spot, leading to degraded performance. However, inferring the amount of mix and Hot-Spot conditions from typical experimental observations (e.g. x-ray spectra and images) is highly challenging. Here, we have developed an analysis method that utilizes machine learning assisted Bayesian inference to find the probability distributions of the Hot-Spot and mix conditions. This approach uses a neural network, trained on an idealized 2-dimensional representation of the Hot-Spot and mix distribution, and Bayesian inference to find the statistical distributions of Hot-Spot conditions that provide a match with observations. We have tested this method with synthetic data from simulations.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Numerical Analysis of High-Order Modes in SRF Resonators for Particle Accelerators
Over the past decades, superconducting technology has rapidly evolved towards high accelerating gradients and low surface resistance, making it possible to operate particle accelerators with high average beam currents and large duty factors. However, RF losses due to coherent excitation of the HOM become the limiting factor for these regimes. Unlike the cavity operating mode, which is tuned separately, the HOM parameters can significantly vary from one cavity to another due to finite mechanical tolerances during the manufacturing process. Thus, it is of utmost importance to know the HOM parameter spread in advance in order to predict unexpected cryogenic losses, overheating of beam line components and maintain stable beam dynamics. In this paper, we present a method for generating cavity geometry with an arbitrary spread of mechanical imperfections and numerically evaluating HOM statistics. Knowing the spread of HOM parameters, we calculated the probability of resonant HOM losses in SRF accelerating cavities used in CW beam current machines such as the PIP-II and LCLS-II linacs, as well as for the SRF crab-cavity for the ILC project. Finally, we present experimental results of HOM spectra measurements in hundreds of 1.3 GHz cavities installed in LCLS-II cryomodules. Studying the effects of HOM excitation results in specifications of the SRF cavity and cryomodule and can significantly impact the efficiency and reliability of the machine operation.
Lunin, Andrei [Fermilab] (ORCID:0000000290096792)↗
Statistical analysis for the neutrinoless double-β-decay matrix element of 48 Ca
Neutrinoless double-β-decay (0vββ) nuclear matrix elements (NME) are the object of many theoretical calculation methods, and are very important for analysis and guidance of a large number of experimental efforts. However, there are large discrepancies between the NME values provided by different methods. Here, in this paper, we propose a statistical analysis of the 48 Ca 0vββ NME using the interacting shell model, emphasizing the range of the NME probable values and their correlations with observables that can be obtained from the existing nuclear data. Based on this statistical analysis with three independent effective Hamiltonians, we propose a common probability distribution function for the 0vββ NME, which has a range of (0.45–0.95) at 90% confidence level, and a mean value of 0.68.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
How to Obtain the Redshift Distribution from Probabilistic Redshift Estimates
Abstract A reliable estimate of the redshift distribution n ( z ) is crucial for using weak gravitational lensing and large-scale structures of galaxy catalogs to study cosmology. Spectroscopic redshifts for the dim and numerous galaxies of next-generation weak-lensing surveys are expected to be unavailable, making photometric redshift (photo- z ) probability density functions (PDFs) the next best alternative for comprehensively encapsulating the nontrivial systematics affecting photo- z point estimation. The established stacked estimator of n ( z ) avoids reducing photo- z PDFs to point estimates but yields a systematically biased estimate of n ( z ) that worsens with a decreasing signal-to-noise ratio, the very regime where photo- z PDFs are most necessary. We introduce Cosmological Hierarchical Inference with Probabilistic Photometric Redshifts ( CHIPPR ), a statistically rigorous probabilistic graphical model of redshift-dependent photometry that correctly propagates the redshift uncertainty information beyond the best-fit estimator of n ( z ) produced by traditional procedures and is provably the only self-consistent way to recover n ( z ) from photo- z PDFs. We present the chippr prototype code, noting that the mathematically justifiable approach incurs computational cost. The CHIPPR approach is applicable to any one-point statistic of any random variable, provided the prior probability density used to produce the posteriors is explicitly known; if the prior is implicit, as may be the case for popular photo- z techniques, then the resulting posterior PDFs cannot be used for scientific inference. We therefore recommend that the photo- z community focus on developing methodologies that enable the recovery of photo- z likelihoods with support over all redshifts, either directly or via a known prior probability density.
79 ASTRONOMY AND ASTROPHYSICS↗
A data science approach for analysis and reconstruction of spinodal-like composition fields in irradiated FeCrAl alloys
A statistical method for the analysis of continuously distributed data representative of composition fluctuations in irradiated FeCrAl alloys acquired using Energy Dispersive X-ray Spectroscopy (EDS) method is presented. Using probability distribution functions, direct and cross-covariances between the elemental compositions, the effects of alloy composition and irradiation dose were investigated on the spatial distribution and length scale of composition fluctuations at the nanoscale. We have observed that, for neutron-irradiated FeCrAl alloys, the distribution of Fe and Cr followed a left-skewed and right-skewed distribution, respectively for all (average) alloy compositions and irradiation doses. The analysis also revealed enhanced spatial gradients in the elemental compositions at higher irradiation dose. Direct and cross-covariance estimates of the experimental data were also utilized for reconstruction of composition data through fitting it to a parametric form of the covariance functions. Linear Model of Coregionalization was used to determine the parameters of the covariance functions. Subsequently, a spectral method was utilized for simulating a realization of the alloy compositions. Close correspondence was observed between the experimental and the reconstructed data which was analyzed using probability distribution functions and covariance functions. Composition space of the experimental and reconstructed data and dislocation velocities as a function of applied stress and line directions over the entire composition maps were also examined.
36 MATERIALS SCIENCE↗
Asymptotic inconsistency of the cumulative algorithm for laser-induced damage probability analysis
The “cumulative algorithm” is a data analysis method that has been proposed to provide an objective, nonparametric determination of laser-induced damage probability as a function of fluence from experimental data that contain both damaged sites and undamaged sites (i.e., 1-on-1 or S-on-1 testing protocols). In this work, the limitations of this approach are explored by considering the asymptotic limit of a large number of test sites. It is shown that the cumulative algorithm does not converge to the true probability distribution and significantly underestimates the damage probability near the damage onset. Here, based on the results of this work, the cumulative algorithm is not recommended for accurate estimation of damage probability.
Computational methods↗
Risk-Adaptive Experimental Design for High-Consequence Systems: LDRD Final Report
Constructing accurate statistical models of critical system responses typically requires an enormous amount of data from physical experiments or numerical simulations. Unfortunately, data generation is often expensive and time consuming. To streamline the data generation process, optimal experimental design determines the 'best' allocation of experiments with respect to a criterion that measures the ability to estimate some important aspect of an assumed statistical model. While optimal design has a vast literature, few researchers have developed design paradigms targeting tail statistics, such as quantiles. In this project, we tailored and extended traditional design paradigms to target distribution tails. Our approach included (i) the development of new optimality criteria to shape the distribution of prediction variances, (ii) the development of novel risk-adapted surrogate models that provably overestimate certain statistics including the probability of exceeding a threshold, and (iii) the asymptotic analysis of regression approaches that target tail statistics such as superquantile regression. To accompany our theoretical contributions, we released implementations of our methods for surrogate modeling and design of experiments in two complementary open source software packages, the ROL/OED Toolkit and PyApprox.
97 MATHEMATICS AND COMPUTING↗
Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders
Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.
97 MATHEMATICS AND COMPUTING↗
Risk Ratio and Risk Difference Estimation in Case-cohort Studies
Background: In case-cohort studies with binary outcomes, ordinary logistic regression analyses have been widely used because of their computational simplicity. However, the resultant odds ratio estimates cannot be interpreted as relative risk measures unless the event rate is low. The risk ratio and risk difference are more favorable outcome measures that are directly interpreted as effect measures without the rare disease assumption. Methods: We provide pseudo-Poisson and pseudo-normal linear regression methods for estimating risk ratios and risk differences in analyses of case-cohort studies. These multivariate regression models are fitted by weighting the inverses of sampling probabilities. Also, the precisions of the risk ratio and risk difference estimators can be improved using auxiliary variable information, specifically by adapting the calibrated or estimated weights, which are readily measured on all samples from the whole cohort. Finally, we provide computational code in R (R Foundation for Statistical Computing, Vienna, Austria) that can easily perform these methods. Results: Through numerical analyses of artificially simulated data and the National Wilms Tumor Study data, accurate risk ratio and risk difference estimates were obtained using the pseudo-Poisson and pseudo-normal linear regression methods. Also, using the auxiliary variable information from the whole cohort, precisions of these estimators were markedly improved. Conclusion: The ordinary logistic regression analyses may provide uninterpretable effect measure estimates, and the risk ratio and risk difference estimation methods are effective alternative approaches for case-cohort studies. These methods are especially recommended under situations in which the event rate is not low.
60 APPLIED LIFE SCIENCES↗
Rapid attribution analysis of the extraordinary heat wave on the Pacific coast of the US and Canada in June 2021
Towards the end of June 2021, temperature records were broken by several degrees Celsius in several cities in the Pacific Northwest areas of the US and Canada, leading to spikes in sudden deaths and sharp increases in emergency calls and hospital visits for heat-related illnesses. Here we present a multi-model, multi-method attribution analysis to investigate the extent to which human-induced climate change has influenced the probability and intensity of extreme heat waves in this region. Based on observations, modelling and a classical statistical approach, the occurrence of a heat wave defined as the maximum daily temperature (TXx) observed in the area 45–52 °N, 119–123 °W, was found to be virtually impossible without human-caused climate change. The observed temperatures were so extreme that they lay far outside the range of historical temperature observations. This makes it hard to state with confidence how rare the event was. Using a statistical analysis that assumes that the heat wave is part of the same distribution as previous heat waves in this region led to a first-order estimation of the event frequency of the order of once in 1000 years under current climate conditions. Using this assumption and combining the results from the analysis of climate models and weather observations, we found that such a heat wave event would be at least 150 times less common without human-induced climate change. Also, this heat wave was about 2 °C hotter than a 1-in-1000-year heat wave would have been in 1850–1900, when global mean temperatures were 1.2 °C cooler than today. Looking into the future, in a world with 2 °C of global warming (0.8 °C warmer than today), a 1000-year event would be another degree hotter. Our results provide a strong warning: our rapidly warming climate is bringing us into uncharted territory with significant consequences for health, well-being and livelihoods. Adaptation and mitigation are urgently needed to prepare societies for a very different future.
54 ENVIRONMENTAL SCIENCES↗
High bias machine learning for antineutrino-based safeguards for small reactors
The statistical methods used for antineutrino detection will need to be improved to effectively monitor the inventory of next-generation nuclear reactors. In this sensitivity study, we evaluate machine learning models compared to previously used statistical approaches to identify diversion scenarios in a simulated Advanced Fast Reactor (AFR)-100. A chi-square goodness-of-fit technique, which individually compares the simulated antineutrino yields to the expected antineutrino yield, resulted in precise but low diversion detection probability. Various support vector machine (SVM) models were applied with diverse training datasets to evaluate the robustness of the method towards unexpected or “unseen” diversion scenarios. Furthermore, our results indicate that while the SVM models significantly improved the detection probability of near-field antineutrino-based safeguards, up to a probability of ~0.04, for the simulated small reactor, the detection system still needs improvements to reach the 0.2 detection limit established by the International Atomic Energy Agency.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
Unsupervised anomaly detection in MeV ultrafast electron diffraction
MeV ultrafast electron diffraction (MUED) is a pump-probe technique used to study the dynamic structural evolution of materials. An ultrashort laser pulse triggers structural changes, which are then probed by an ultrashort relativistic electron beam. To overcome low signal-to-noise ratios, diffraction patterns are averaged over thousands of shots. However, shot-to-shot instabilities in the electron beam can distort individual patterns, introducing uncertainty. Improving MUED accuracy requires detecting and removing these anomalous patterns from large datasets. In this work, we developed a fully unsupervised methodology for the detection of anomalous diffraction patterns. Using a convolutional autoencoder, we calculate the reconstruction mean squared error of the diffraction patterns. Based on the statistical analysis of this error, we provide the user an estimation of the probability that the pattern is normal, which also allows a posterior visual inspection of the images that are difficult to classify. This method has been trained with only 100 diffraction patterns and tested on 1521 patterns, resulting in a false positive rate between 0.2% and 0.4%, with a training time of 10 s per image and a test time of about 1 s per image. Here, the proposed methodology can also be applied to other diffraction techniques in which large datasets are collected that include faulty images due to instrumental instabilities.
43 PARTICLE ACCELERATORS↗
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↗
Optimal Zeno Dragging for Quantum Control: A Shortcut to Zeno with Action-Based Scheduling Optimization
The quantum Zeno effect asserts that quantum measurements inhibit simultaneous unitary dynamics when the “collapse” events are sufficiently strong and frequent. This applies in the limit of strong continuous measurement or dissipation. It is possible to implement a dissipative control that is known as “Zeno dragging” by dynamically varying the monitored observable, and hence also the eigenstates, which are attractors under Zeno dynamics. This is similar to adiabatic processes, in that the Zeno-dragging fidelity is highest when the rate of eigenstate change is slow compared to the measurement rate. We demonstrate here two theoretical methods for using such dynamics to achieve control of quantum systems. The first, which we shall refer to as “shortcut to Zeno,” is analogous to the shortcuts to adiabaticity (counterdiabatic driving) that are frequently used to accelerate unitary adiabatic evolution. In the second approach, we apply the Chantasri-Dressel-Jordan stochastic action [PRA 88, 042110 (2013)], and demonstrate that the extremal-probability readout paths derived from this are well suited to setting up a Pontryagin-style optimization of the Zeno-dragging schedule. A fundamental contribution of the latter approach is to show that an action suitable for measurement-driven control optimization can be derived quite generally from statistical arguments. Implementing these methods on the Zeno dragging of a qubit, we find that both approaches yield the same solution, namely, that the optimal control is a unitary that matches the motion of the Zeno-monitored eigenstate. We then show that such a solution can be more robust than a unitary-only operation and we comment on solvable generalizations of our qubit example embedded in larger systems. These methods open up new pathways toward systematically developing dynamic control of Zeno subspaces to realize dissipatively stabilized quantum operations. Published by the American Physical Society 2024
Physics↗
A probabilistic-phase field model for the fracture of brittle materials
Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abeet al2003J. Am. Ceram. Soc.861019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.
Materials Science↗
Uncertainty propagation in feed-forward neural network models
We develop new uncertainty propagation methods for feed-forward neural network architectures with leaky ReLU activation functions subject to random perturbations in the input vectors. In particular, we derive analytical expressions for the probability density function (PDF) of the neural network output and its statistical moments as a function of the input uncertainty and the parameters of the network, i.e., weights and biases. A key finding is that an appropriate linearization of the leaky ReLU activation function yields accurate statistical results even for large perturbations in the input vectors. This can be attributed to the way information propagates through the network. We also propose new analytically tractable Gaussian copula surrogate models to approximate the full joint PDF of the neural network output. To validate our theoretical results, we conduct Monte Carlo simulations and a thorough error analysis on a multi-layer neural network representing a nonlinear integro-differential operator between two polynomial function spaces. Our findings demonstrate excellent agreement between the theoretical predictions and Monte Carlo simulations.
MLP networks↗