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1. Dynamic reliability of infrastructure networks using augmented Monte Carlo simulation

   Zhou, X.; Duenas-Osorio, L. (September 2022, The 13th International Conference on Structural Safety and Reliability (ICOSSAR 2021-2022))

   Li, J.; Spanos, P. D.; Chen, J. B.; Peng, Y. B. (Ed.)

   Infrastructure networks offer critical services to modern society. They dynamically interact with the environment, operators, and users. Infrastructure networks are unique engineered systems, large in scale and high in complexity. One fundamental issue for their reliability assessment is the uncertainty propagation from stochastic disturbances across interconnected components. Monte Carlo simulation (MCS) remains approachable to quantify stochastic dynamics from components to systems. Its application depends on time efficiency along with the capability of delivering reliable approximations. In this paper, we introduce Quasi Monte Carlo (QMC) sampling techniques to improve modeling efficiency. Also, we suggest a principled Monte Carlo (PMC) method that equips the crude MCS with Probably Approximately Correct (PAC) approaches to deliver guaranteed approximations. We compare our proposed schemes with a competitive approach for stochastic dynamic analysis, namely the Probability Density Evolution Method (PDEM). Our computational experiments are on ideal but complex enough source-terminal (S-T) dynamic network reliability problems. We endow network links with oscillators so that they can jump across safe and failed states allowing us to treat the problem from a stochastic process perspective. We find that QMC alone can yield practical accuracy, and PMC with a PAC algorithm can deliver accuracy guarantees. Also, QMC is more versatile and efficient than the PDEM for network reliability assessment. The QMC and PMC methods provide advanced uncertainty propagation techniques to support decision makers with their reliability problems. 

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2. Fast algorithms using orthogonal polynomials

   https://doi.org/10.1017/S0962492920000045  

   Olver, Sheehan; Slevinsky, Richard Mikaël; Townsend, Alex (May 2020, Acta Numerica)

   We review recent advances in algorithms for quadrature, transforms, differential equations and singular integral equations using orthogonal polynomials. Quadrature based on asymptotics has facilitated optimal complexity quadrature rules, allowing for efficient computation of quadrature rules with millions of nodes. Transforms based on rank structures in change-of-basis operators allow for quasi-optimal complexity, including in multivariate settings such as on triangles and for spherical harmonics. Ordinary and partial differential equations can be solved via sparse linear algebra when set up using orthogonal polynomials as a basis, provided that care is taken with the weights of orthogonality. A similar idea, together with low-rank approximation, gives an efficient method for solving singular integral equations. These techniques can be combined to produce high-performance codes for a wide range of problems that appear in applications. 

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3. On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2

   https://doi.org/10.1073/pnas.2318989121  

   Didier, Gustavo; Glatt-Holtz, Nathan E.; Holbrook, Andrew J.; Magee, Andrew F.; Suchard, Marc A. (January 2024, Proceedings of the National Academy of Sciences)

   The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC’s infinitesimal generator (rate) matrix. Motivated by the derivative’s extreme computational complexity as a function of state space cardinality, recent work demonstrates the surprising effectiveness of a naive, first-order approximation for a host of problems in computational biology. In response to this empirical success, we obtain rigorous deterministic and probabilistic bounds for the error accrued by the naive approximation and establish a “blessing of dimensionality” result that is universal for a large class of rate matrices with random entries. Finally, we apply the first-order approximation within surrogate-trajectory Hamiltonian Monte Carlo for the analysis of the early spread of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology. 

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4. Automated Model Selection with Bayesian Quadrature

   Chai, Henry; Ton, Jean-François; Osborne, Michael A.; Garnett, Roman (January 2019, Proceedings of the 36th International Conference on Machine Learning)

   We present a novel technique for tailoring Bayesian quadrature (BQ) to model selection. The state-of-the-art for comparing the evidence of multiple models relies on Monte Carlo methods, which converge slowly and are unreliable for computationally expensive models. Although previous research has shown that BQ offers sample efficiency superior to Monte Carlo in computing the evidence of an individual model, applying BQ directly to model comparison may waste computation producing an overly-accurate estimate for the evidence of a clearly poor model. We propose an automated and efficient algorithm for computing the most-relevant quantity for model selection: the posterior model probability. Our technique maximizes the mutual information between this quantity and observations of the models’ likelihoods, yielding efficient sample acquisition across disparate model spaces when likelihood observations are limited. Our method produces more-accurate posterior estimates using fewer likelihood evaluations than standard Bayesian quadrature and Monte Carlo estimators, as we demonstrate on synthetic and real-world examples. 

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5. PyQMC : An all-Python real-space quantum Monte Carlo module in PySCF

   https://doi.org/10.1063/5.0139024  

   Wheeler, William A.; Pathak, Shivesh; Kleiner, Kevin G.; Yuan, Shunyue; Rodrigues, João N. B.; Lorsung, Cooper; Krongchon, Kittithat; Chang, Yueqing; Zhou, Yiqing; Busemeyer, Brian; et al (March 2023, The Journal of Chemical Physics)

   We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for a simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions. 

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