Local Bayesian Dirichlet mixing of imperfect models

Kejzlar, Vojtech; Neufcourt, Léo; Nazarewicz, Witold

doi:10.1038/s41598-023-46568-0

Local Bayesian Dirichlet mixing of imperfect models

Journal Article · Fri Nov 10 00:00:00 EST 2023 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-023-46568-0· OSTI ID:2205360

; ;

Abstract

To improve the predictability of complex computational models in the experimentally-unknown domains, we propose a Bayesian statistical machine learning framework utilizing the Dirichlet distribution that combines results of several imperfect models. This framework can be viewed as an extension of Bayesian stacking. To illustrate the method, we study the ability of Bayesian model averaging and mixing techniques to mine nuclear masses. We show that the global and local mixtures of models reach excellent performance on both prediction accuracy and uncertainty quantification and are preferable to classical Bayesian model averaging. Additionally, our statistical analysis indicates that improving model predictions through mixing rather than mixing of corrected models leads to more robust extrapolations.

View Journal Article

Research Organization:: Michigan State Univ., East Lansing, MI (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0013365; SC0023688

OSTI ID:: 2205360

Alternate ID(s):: OSTI ID: 2217277

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 13; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (47)

Bayesian Model Selection and Model Averaging Wasserman, Larry Journal of Mathematical Psychology, Vol. 44, Issue 1 https://doi.org/10.1006/jmps.1999.1278	journal	March 2000
Machine learning the nuclear mass Gao, Ze-Peng; Wang, Yong-Jia; Lü, Hong-Liang Nuclear Science and Techniques, Vol. 32, Issue 10 https://doi.org/10.1007/s41365-021-00956-1	journal	October 2021
Combining forecasts: A review and annotated bibliography Clemen, Robert T. International Journal of Forecasting, Vol. 5, Issue 4 https://doi.org/10.1016/0169-2070(89)90012-5	journal	January 1989
Towards a better parametrisation of Skyrme-like effective forces: A critical study of the SkM force Bartel, J.; Quentin, P.; Brack, M. Nuclear Physics A, Vol. 386, Issue 1 https://doi.org/10.1016/0375-9474(82)90403-1	journal	September 1982
Hartree-Fock-Bogolyubov description of nuclei near the neutron-drip line Dobaczewski, J.; Flocard, H.; Treiner, J. Nuclear Physics A, Vol. 422, Issue 1 https://doi.org/10.1016/0375-9474(84)90433-0	journal	June 1984
Nuclear ground-state masses and deformations: FRDM(2012) Möller, P.; Sierk, A. J.; Ichikawa, T. Atomic Data and Nuclear Data Tables, Vol. 109-110 https://doi.org/10.1016/j.adt.2015.10.002	journal	May 2016
The Ame2003 atomic mass evaluation Audi, G.; Wapstra, A. H.; Thibault, C. Nuclear Physics A, Vol. 729, Issue 1 https://doi.org/10.1016/j.nuclphysa.2003.11.003	journal	December 2003
Controlling extrapolations of nuclear properties with feature selection Navarro Pérez, Rodrigo; Schunck, Nicolas Physics Letters B, Vol. 833 https://doi.org/10.1016/j.physletb.2022.137336	journal	October 2022
Precision mass measurement of lightweight self-conjugate nucleus 80Zr Hamaker, A.; Leistenschneider, E.; Jain, R. Nature Physics, Vol. 17, Issue 12 https://doi.org/10.1038/s41567-021-01395-w	journal	November 2021
Model Mixing Using Bayesian Additive Regression Trees Yannotty, John C.; Santner, Thomas J.; Furnstahl, Richard J. Technometrics https://doi.org/10.1080/00401706.2023.2257765	journal	September 2023
Prediction via Orthogonalized Model Mixing Clyde, Merlise; Desimone, Heather; Parmigiani, Giovanni Journal of the American Statistical Association, Vol. 91, Issue 435 https://doi.org/10.1080/01621459.1996.10476989	journal	September 1996
New Skyrme effective forces for supernovae and neutron rich nuclei Chabanat, E.; Bonche, P.; Haensel, P. Physica Scripta, Vol. T56 https://doi.org/10.1088/0031-8949/1995/T56/034	journal	January 1995
Statistical aspects of nuclear mass models Kejzlar, V.; Neufcourt, L.; Nazarewicz, W. Journal of Physics G: Nuclear and Particle Physics, Vol. 47, Issue 9 https://doi.org/10.1088/1361-6471/ab907c	journal	July 2020
Get on the BAND Wagon: a Bayesian framework for quantifying model uncertainties in nuclear dynamics Phillips, D. R.; Furnstahl, R. J.; Heinz, U. Journal of Physics G: Nuclear and Particle Physics, Vol. 48, Issue 7 https://doi.org/10.1088/1361-6471/abf1df	journal	May 2021
The AME 2020 atomic mass evaluation (II). Tables, graphs and references* Wang, Meng; Huang, W. J.; Kondev, F. G. Chinese Physics C, Vol. 45, Issue 3 https://doi.org/10.1088/1674-1137/abddaf	journal	March 2021
Bayesian Model Averaging: Theoretical Developments and Practical Applications Montgomery, Jacob M.; Nyhan, Brendan Political Analysis, Vol. 18, Issue 2 https://doi.org/10.1093/pan/mpq001	journal	January 2010
Comparative study of radial basis function and Bayesian neural network approaches in nuclear mass predictions Niu, Z. M.; Fang, J. Y.; Niu, Y. F. Physical Review C, Vol. 100, Issue 5 https://doi.org/10.1103/PhysRevC.100.054311	journal	November 2019
Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei Neufcourt, Léo; Cao, Yuchen; Giuliani, Samuel Physical Review C, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevC.101.014319	journal	January 2020
Quantified limits of the nuclear landscape Neufcourt, Léo; Cao, Yuchen; Giuliani, Samuel A. Physical Review C, Vol. 101, Issue 4 https://doi.org/10.1103/PhysRevC.101.044307	journal	April 2020
Predicting nuclear masses with the kernel ridge regression Wu, X. H.; Zhao, P. W. Physical Review C, Vol. 101, Issue 5 https://doi.org/10.1103/PhysRevC.101.051301	journal	May 2020
Learning correlations in nuclear masses using neural networks Sharma, Aman; Gandhi, A.; Kumar, Ajay Physical Review C, Vol. 105, Issue 3 https://doi.org/10.1103/PhysRevC.105.L031306	journal	March 2022
Nuclear masses learned from a probabilistic neural network Lovell, A. E.; Mohan, A. T.; Sprouse, T. M. Physical Review C, Vol. 106, Issue 1 https://doi.org/10.1103/PhysRevC.106.014305	journal	July 2022
Interpolating between small- and large- g expansions using Bayesian model mixing Semposki, A. C.; Furnstahl, R. J.; Phillips, D. R. Physical Review C, Vol. 106, Issue 4 https://doi.org/10.1103/PhysRevC.106.044002	journal	October 2022
Variations on a theme by Skyrme: A systematic study of adjustments of model parameters Klüpfel, P.; Reinhard, P. -G.; Bürvenich, T. J. Physical Review C, Vol. 79, Issue 3 https://doi.org/10.1103/PhysRevC.79.034310	journal	March 2009
Nuclear energy density optimization Kortelainen, M.; Lesinski, T.; Moré, J. Physical Review C, Vol. 82, Issue 2 https://doi.org/10.1103/PhysRevC.82.024313	journal	August 2010
Nuclear energy density optimization: Large deformations Kortelainen, M.; McDonnell, J.; Nazarewicz, W. Physical Review C, Vol. 85, Issue 2 https://doi.org/10.1103/PhysRevC.85.024304	journal	February 2012
Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XIII. The 2012 atomic mass evaluation and the symmetry coefficient Goriely, S.; Chamel, N.; Pearson, J. M. Physical Review C, Vol. 88, Issue 2 https://doi.org/10.1103/PhysRevC.88.024308	journal	August 2013
Nuclear energy density optimization: Shell structure Kortelainen, M.; McDonnell, J.; Nazarewicz, W. Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.054314	journal	May 2014
Validating neural-network refinements of nuclear mass models Utama, R.; Piekarewicz, J. Physical Review C, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevC.97.014306	journal	January 2018
Bayesian approach to model-based extrapolation of nuclear observables Neufcourt, Léo; Cao, Yuchen; Nazarewicz, Witold Physical Review C, Vol. 98, Issue 3 https://doi.org/10.1103/PhysRevC.98.034318	journal	September 2018
Neutron Drip Line in the Ca Region from Bayesian Model Averaging Neufcourt, Léo; Cao, Yuchen; Nazarewicz, Witold Physical Review Letters, Vol. 122, Issue 6 https://doi.org/10.1103/PhysRevLett.122.062502	journal	February 2019
Phenomenological Constraints on the Transport Properties of QCD Matter with Data-Driven Model Averaging Everett, D.; Ke, W.; Paquet, J. -F. Physical Review Letters, Vol. 126, Issue 24 https://doi.org/10.1103/PhysRevLett.126.242301	journal	June 2021
Colloquium : Machine learning in nuclear physics Boehnlein, Amber; Diefenthaler, Markus; Sato, Nobuo Reviews of Modern Physics, Vol. 94, Issue 3 https://doi.org/10.1103/RevModPhys.94.031003	journal	September 2022
Bayesian Model Averaging: A Systematic Review and Conceptual Classification: BMA: A Systematic Review Fragoso, Tiago M.; Bertoli, Wesley; Louzada, Francisco International Statistical Review, Vol. 86, Issue 1 https://doi.org/10.1111/insr.12243	journal	December 2017
Probabilistic forecasts, calibration and sharpness Gneiting, Tilmann; Balabdaoui, Fadoua; Raftery, Adrian E. Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 69, Issue 2 https://doi.org/10.1111/j.1467-9868.2007.00587.x	journal	April 2007
Nuclear binding energy predictions using neural networks: Application of the multilayer perceptron Yüksel, Esra; Soydaner, Derya; Bahtiyar, Hüseyin International Journal of Modern Physics E, Vol. 30, Issue 03 https://doi.org/10.1142/S0218301321500178	journal	March 2021
Probabilistic Visibility Forecasting Using Bayesian Model Averaging Chmielecki, Richard M.; Raftery, Adrian E. Monthly Weather Review, Vol. 139, Issue 5 https://doi.org/10.1175/2010MWR3516.1	journal	May 2011
Strictly Proper Scoring Rules, Prediction, and Estimation Gneiting, Tilmann; Raftery, Adrian E. Journal of the American Statistical Association, Vol. 102, Issue 477 https://doi.org/10.1198/016214506000001437	journal	March 2007
Bayesian Data Analysis Gelman, Andrew; Carlin, John B.; Stern, Hal S. https://doi.org/10.1201/b16018	book	November 2013
A Bayes Interpretation of Stacking for M-Complete and M-Open Settings Le, Tri; Clarke, Bertrand Bayesian Analysis, Vol. 12, Issue 3 https://doi.org/10.1214/16-BA1023	journal	September 2017
Using Stacking to Average Bayesian Predictive Distributions (with Discussion) Yao, Yuling; Vehtari, Aki; Simpson, Daniel Bayesian Analysis, Vol. 13, Issue 3 https://doi.org/10.1214/17-BA1091	journal	September 2018
Bayesian Hierarchical Stacking: Some Models Are (Somewhere) Useful Yao, Yuling; Pirš, Gregor; Vehtari, Aki Bayesian Analysis, Vol. 17, Issue 4 https://doi.org/10.1214/21-BA1287	journal	December 2022
David Draper and E. I. George, and a rejoinder by the authors Volinsky, Chris T.; Raftery, Adrian E.; Madigan, David Statistical Science, Vol. 14, Issue 4 https://doi.org/10.1214/ss/1009212519	journal	November 1999
Bayesian averaging for ground state masses of atomic nuclei in a Machine Learning approach Mumpower, Matthew; Li, Mengke; Sprouse, Trevor M. Frontiers in Physics, Vol. 11 https://doi.org/10.3389/fphy.2023.1198572	journal	July 2023
A New Mass Model for Nuclear Astrophysics: Crossing 200 keV Accuracy Shelley, Matthew; Pastore, Alessandro Universe, Vol. 7, Issue 5 https://doi.org/10.3390/universe7050131	journal	May 2021
Gaussian Processes for Machine Learning Rasmussen, Carl Edward; Williams, Christopher K. I. The MIT Press https://doi.org/10.7551/mitpress/3206.001.0001	book	January 2005
Probabilistic programming in Python using PyMC3 Salvatier, John; Wiecki, Thomas V.; Fonnesbeck, Christopher PeerJ Computer Science, Vol. 2 https://doi.org/10.7717/peerj-cs.55	journal	January 2016

Similar Records

Model orthogonalization and Bayesian forecast mixing via principal component analysis

Journal Article · Sun Sep 08 20:00:00 EDT 2024 · Physical Review Research · OSTI ID:2440073

Related Subjects

97 MATHEMATICS AND COMPUTING
computational science
information technology
nuclear physics
statistics

Local Bayesian Dirichlet mixing of imperfect models

Citation Formats

References (47)

Similar Records

Related Subjects