How Bayesian methods can improve $R$-matrix analyses of data: the example of the $dt$ Reaction

Odell, Daniel; Brune, Carl; Phillips, Daniel

doi:10.48550/arxiv.2105.06541

Cited by 2 publications

(3 citation statements)

References 22 publications

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“…VI. There are also numerous studies using BO for UQ on reaction model parameters; some recent examples include R-matrix analyses of cross sections (Odell, Brune, and Phillips, 2021), optical model parameters (Lovell and Nunes, 2018;King et al, 2019;Yang et al, 2020;Lovell et al, 2021), and sensitivity analyses (Catacora-Rios et al, 2019. In the future, it is anticipated that ML will help identify those measurements that most effectively constrain theoretical models, optimize model parameters simultaneously across multiple reaction channels for many isotopes, and provide guidance to theory through global systematic studies that can be efficiently executed with surrogate models.…”

Section: Nuclear Reactionsmentioning

confidence: 99%

Colloquium: Machine learning in nuclear physics

et al. 2022

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TABLE I. Table of ML methods discussed in this Colloquium with an indication of the main type of learning (S, supervised; U, unsupervised; semi-S, semisupervised). Acronym Method Description Learning type AE, VAE Autoencoders, Variational autoencoders ANN capable of learning efficient representations of the input data without any supervision U ANN Artificial neural network Models for learning defined by connected units (or nodes) and hidden layers with well-defined inputs and outputs S BED Bayesian experimental design Bayesian inference for experimental design S BM Boltzmann machine Generative ANN that can learn a probability distribution from sets of changing inputs U BMA, BMM Bayesian model averaging, Bayesian model mixing Bayesian inference applied to model selection or the combined estimation, or performed over a mixture model S BNN Bayesian neural network ANN where the parameters of the network are represented by probabilities learned by Bayesian inference S BO Bayesian optimization Optimization of functions without an a priori knowledge of functional forms. S and semi-S CNN Convolutional neural network ANN where convolution is used to reduce dimensionalities S EMB Ensemble methods and boosting Methods based on collections of decision trees as simple learners S GAN Generative adversarial network System of two ANNs where a generative network generates outputs while a discriminative network evaluates them U GP Gaussian process Collection of random variables that have a joint Gaussian distribution used in Bayesian inference Semi-S KNN k-nearest neighbors Nonparametric method where inputs consist of the k closest training examples in a dataset S KR Kernel regression Extension of linear regression methods to include nonlinear function kernels S LR Logistic regression Convex optimization method based on maximum likelihood estimate for classification problems S LSTM Long short-term memory RNN capable of learning long-term dependencies S PCA Principal component analysis Dimensionality reduction technique based on retaining the largest eigenvalues of the covariance matrix U REG Linear regression Linear algebra methods used for modeling continuous functions in terms of their explanatory variables S RL Reinforcement learning Learning achieved by trial and error of desired and undesired events Neither S nor U RNN Recurrent neural network ANN where connections between nodes allow for temporal dynamic behavior S SVM Support vector machine Convex optimization techniques with efficient ways to distinguish features in datasets S

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Section: Nuclear Reactionsmentioning

confidence: 99%

Colloquium: Machine learning in nuclear physics

et al. 2022

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“…where H ≡ X † HX is the Hamiltonian projected into the subspace spanned by X, and N ≡ X † X is the norm matrix. The meaning of E can be understood by substituting these relationships back into the variational form (7):…”

Section: A Derivationmentioning

confidence: 99%

“…Nuclear physics calculations often need to be repeated many times for different values of some model parameters, for example when sampling the model space for Bayesian uncertainty quantification [1][2][3][4][5][6][7][8][9] and experimental design [10][11][12]. The computational burden can be alleviated by using emulators, or surrogate models, which accurately approximate the response of the original (i.e., high-fidelity) model but are much cheaper to evaluate.…”

Section: Introductionmentioning

confidence: 99%

Model reduction methods for nuclear emulators

Melendez,

Drischler,

Furnstahl

et al. 2022

Preprint

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The field of model order reduction (MOR) is growing in importance due to its ability to extract the key insights from complex simulations while discarding computationally burdensome and superfluous information. We provide an overview of MOR methods for the creation of fast & accurate emulators of memory-and compute-intensive nuclear systems. As an example, we describe how "eigenvector continuation" is a special case of a much more general and well-studied MOR formalism for parameterized systems. We continue with an introduction to the Ritz and Galerkin projection methods that underpin many such emulators, while pointing to the relevant MOR theory and its successful applications along the way. We believe that this will open the door to broader applications in nuclear physics and facilitate communication with practitioners in other fields.

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How Bayesian methods can improve $R$-matrix analyses of data: the example of the $dt$ Reaction

Cited by 2 publications

References 22 publications

Colloquium: Machine learning in nuclear physics

Colloquium: Machine learning in nuclear physics

Model reduction methods for nuclear emulators

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