Article
Engineering, Mechanical
P. L. Green, L. J. Devlin, R. E. Moore, R. J. Jackson, J. Li, S. Maskell
Summary: This paper discusses the optimization of the 'L-kernel' in Sequential Monte Carlo samplers to improve performance, resulting in reduced variance of estimates and fewer resampling requirements.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Mathematics, Applied
Nikolaj T. Mucke, Benjamin Sanderse, Sander M. Bohte, Cornelis W. Oosterlee
Summary: In the context of solving inverse problems in physics using Bayesian inference, a new approach called Markov Chain Generative Adversarial Neural Network (MCGAN) is proposed to reduce computational costs. By training a GAN to sample from a low-dimensional latent space and incorporating it into a Markov Chain Monte Carlo method, efficient sampling from the posterior distribution is achieved, replacing the need for high-dimensional priors and expensive forward mappings. The proposed methodology converges to the true posterior in Wasserstein-1 distance and sampling from the latent space is weakly equivalent to sampling in the high-dimensional space.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Chemistry, Multidisciplinary
Miad Boodaghi, Sarah Libring, Luis Solorio, Arezoo M. Ardekani
Summary: This study used Bayesian inference to determine the light attenuation and diffusion coefficients of Rhodamine 6G in breast cancer spheroids, finding minimal variation in diffusion coefficients across different types of spheroids but significant differences between tumorigenic and nontumorigenic breast cancer cells. The methodology presented allows researchers to determine diffusion in spheroids and separate transport and drug penetration changes from biological resistivity, showing evidence of cell packing in self-assembled spheroids through agreement between spheroid radius, attenuation coefficient, and diffusion coefficient.
JOURNAL OF CONTROLLED RELEASE
(2021)
Article
Engineering, Multidisciplinary
Dhruv Patel, Deep Ray, Assad A. Oberai
Summary: Inverse problems are common in various fields of science and engineering, and Bayesian inference provides a principled approach to overcome their ill-posed nature. This work presents a novel method for efficient and accurate Bayesian inversion using deep generative models. The method effectively tackles the curse of dimensionality and limited prior information, and produces accurate results with reliable uncertainty estimates.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Tiangang Cui, Xin T. Tong, Olivier Zahm
Summary: Markov chain Monte Carlo (MCMC) methods are important algorithms in Bayesian inverse problems. Likelihood-informed subspace (LIS) methods can improve the efficiency of MCMC methods by utilizing the low-dimensional structure of the underlying problem. However, existing methods assume Gaussian priors and are not suitable for sparse problems. To address this limitation, we propose a prior normalization technique and integrate it with several MCMC methods.
Article
Engineering, Electrical & Electronic
Pierre Palud, Pierre-Antoine Thouvenin, Pierre Chainais, Emeric Bron, Franck Le Petit
Summary: This article focuses on a challenging class of inverse problems that arise in practical applications. The forward model is a complex non-linear black-box with potentially non-injective outputs spanning multiple decades. The observations are subject to both additive and multiplicative noises as well as censorship. The main objective of this work is to provide uncertainty quantification alongside parameter estimates using an adapted Bayesian approach and an MCMC algorithm to deal with the multimodal posterior distribution.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2023)
Article
Statistics & Probability
Lewis J. Rendell, Adam M. Johansen, Anthony Lee, Nick Whiteley
Summary: In order to conduct Bayesian inference with large datasets, it is beneficial to distribute the data across multiple machines. By introducing an instrumental hierarchical model and using an SMC sampler with a sequence of association strengths, approximations of posterior expectations can be improved and the association strength can be adjusted accordingly.
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
(2021)
Article
Engineering, Mechanical
Adolphus Lye, Alice Cicirello, Edoardo Patelli
Summary: This tutorial paper reviews the use of advanced Monte Carlo sampling methods in Bayesian model updating for engineering applications, introducing different methods and comparing their performance. Three case studies demonstrate the advantages and limitations of these sampling techniques in parameter identification, posterior distribution sampling, and stochastic identification of model parameters.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Computer Science, Interdisciplinary Applications
Tiangang Cui, Sergey Dolgov, Olivier Zahm
Summary: We propose a novel offline-online method that reduces the computational burden of posterior random variable characterization in statistical learning. This method learns the joint distribution of parameter and observable random variables in a tensor-train (TT) format during the offline phase. Then, in the online phase, it uses order-preserving conditional transport to describe the posterior random variables in real time based on newly observed data. This method relies on function approximation and includes thorough performance analysis, providing improved transport maps for high-dimensional observation and parameter problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Review
Statistics & Probability
Christopher Nemeth, Paul Fearnhead
Summary: MCMC algorithms are considered the gold standard technique for Bayesian inference, but the computational cost can be prohibitive for large datasets, leading to the development of scalable Monte Carlo algorithms. One type of these algorithms is SGMCMC, which reduces per-iteration cost by utilizing data subsampling techniques.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2021)
Article
Mathematics
Samuel Livingstone
Summary: This study investigates the impact of proposal distributions on the ergodicity of the Metropolis-Hastings method, showing that suitable choices can alter the ergodic properties of the algorithm. It is found that allowing the proposal variance to grow unboundedly in the tails of heavy-tailed distributions can establish geometric ergodicity, but the growth rate needs to be carefully controlled to avoid high rejection rates. Furthermore, a judicious choice of proposal distribution can lead to geometric ergodicity in scenarios where probability concentrates on narrower tails, which is not the case for the Random Walk Metropolis.
Article
Computer Science, Artificial Intelligence
Matthew Holden, Marcelo Pereyra, Konstantinos C. Zygalakis
Summary: This paper proposes a new methodology for Bayesian inference in imaging inverse problems using data-driven priors. The methodology learns the prior distribution from training data using generative models and provides rigorous underpinning for Bayesian estimators and uncertainty quantification analyses. The paper also introduces a model misspecification test and a method to identify the dimension of the latent space from training data. Experimental results show the effectiveness of the proposed approach and compare it with other data-driven regularization methods.
SIAM JOURNAL ON IMAGING SCIENCES
(2022)
Article
Computer Science, Theory & Methods
Jeremie Coullon, Robert J. Webber
Summary: The translation introduces a new MCMC sampler for infinite-dimensional inverse problems, based on the affine invariant ensemble sampler adapted to the covariance structure of the target distribution. It is the first time this ensemble sampler has been extended to infinite-dimensional function spaces, resulting in a highly efficient gradient-free MCMC algorithm. This new ensemble sampler is easy to implement and widely applicable, as it does not require gradients or posterior covariance estimates.
STATISTICS AND COMPUTING
(2021)
Article
Ecology
Luiza Guimaraes Fabreti, Sebastian Hoehna
Summary: This study explores different methods for assessing convergence in phylogenetics, including deriving a threshold for minimum effective sample size and converting tree samples into traces of absence/presence of splits for standard ESS computation. The Kolmogorov-Smirnov test is suggested for assessing convergence in distribution between replicated MCMC runs, while potential scale reduction factor is deemed biased for skewed posterior distributions. Additionally, the study introduces a method for computing distribution of differences in split frequencies, highlighting the importance of using the 95% quantile for checking convergence in split frequencies.
METHODS IN ECOLOGY AND EVOLUTION
(2022)
Article
Mathematics, Applied
Ana Carpio, Elena Cebrian, Andrea Gutierrez
Summary: In this work, we propose a computational framework for quantifying uncertainty in shear elastography imaging of tissue anomalies. Bayesian inference is used to find the posterior probability of parameter fields representing the anomalies' geometry and shear moduli. We demonstrate the approach on synthetic tests and obtain statistical information on the anomalies' properties using Markov Chain Monte Carlo techniques. For shapes with low to moderate dimension, ensemble MCMC samplers are suitable, but computationally expensive. For simpler shapes, a fast optimization scheme and linearization around the MAP point are used to approximate the posterior distribution at a low computational cost.
Article
Mathematics, Applied
Richard D. Brown, Johnathan M. Bardsley, Cui Tiangang
Article
Multidisciplinary Sciences
Siyuan Wu, Tiangang Cui, Xinan Zhang, Tianhai Tian
Article
Mathematics, Interdisciplinary Applications
Johnathan M. Bardsley, Tiangang Cui
Summary: This work introduces scalable optimization-based Markov chain Monte Carlo (MCMC) methods for solving hierarchical Bayesian inverse problems with nonlinear parameter-to-observable maps and a broader class of hyperparameters. The algorithmic development is based on the recently developed scalable randomize-then-optimize (RTO) method and integrates RTO into Metropolis-within-Gibbs updates or pseudomarginal MCMC for efficient sampling in hierarchical Bayesian inversion. The integration of RTO and pseudomarginal MCMC provides sampling performance robust to model parameter dimensions, as demonstrated in numerical examples of PDE-constrained inverse problems and positron emission tomography.
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
(2021)
Article
Mathematics, Applied
Tiangang Cui, Olivier Zahm
Summary: Identifying a low-dimensional informed parameter subspace is a viable way to address the dimensionality challenge in sampled-based solutions to large-scale Bayesian inverse problems. The introduced gradient-based method allows for offline detection of the expensive low-dimensional structure before observing the data, enabling efficient control over the approximation error of the posterior distribution. Sampling strategies are presented to draw samples from the exact posterior distribution using the informed subspace.
Article
Computer Science, Software Engineering
Antoni Musolas, Estelle Massart, Julien M. Hendrickx, P. -A. Absil, Youssef Marzouk
Summary: The paper presents a differential geometric approach for constructing families of low-rank covariance matrices through interpolation on low-rank matrix manifolds, demonstrating its utility in practical applications such as wind field covariance approximation for unmanned aerial vehicle navigation.
BIT NUMERICAL MATHEMATICS
(2022)
Article
Computer Science, Theory & Methods
Tiangang Cui, Sergey Dolgov
Summary: This paper extends the functional tensor-train approximation of the inverse Rosenblatt transport to high-dimensional non-negative functions, develops an efficient procedure for computing the transport, and integrates it into a nested variable transformation framework. The resulting deep inverse Rosenblatt transport significantly expands the capability of tensor approximations and transport maps to handle random variables with complicated nonlinear interactions and concentrated density functions.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2022)
Article
Neurosciences
Lingbin Bian, Tiangang Cui, B. T. Thomas Yeo, Alex Fornito, Adeel Razi, Jonathan Keith
Summary: This study introduces a Bayesian method to characterize latent brain states based on community structure, and demonstrates a new strategy to detect transitions between community structures in BOLD time series. Through in-silico model evaluation and empirical validation using HCP dataset, the results show distinctive community patterns in brain states during working memory tasks.
Article
Mathematics, Applied
Olivier Zahm, Tiangang Cui, Kody Law, Alessio Spantini, Youssef Marzouk
Summary: This paper proposes a dimension reduction technique for Bayesian inverse problems with nonlinear forward operators, non-Gaussian priors, and non-Gaussian observation noise. The likelihood function is approximated by a ridge function, and the ridge approximation is built by minimizing an upper bound on the Kullback-Leibler divergence between the posterior distribution and its approximation. The paper provides an analysis that enables control of the posterior approximation error due to sampling.
MATHEMATICS OF COMPUTATION
(2022)
Article
Statistics & Probability
Tiangang Cui, Xin T. Tong
Summary: The likelihood-informed subspace (LIS) method provides a way to reduce the dimensionality of high-dimensional probability distributions for Bayesian inference. This study establishes a unified framework to analyze the accuracy of dimension reduction techniques and the integration with sampling methods. The results demonstrate the effectiveness and applicability of the LIS method in various scenarios.
Article
Mathematics, Applied
Tiangang Cui, Xin T. Tong, Olivier Zahm
Summary: Markov chain Monte Carlo (MCMC) methods are important algorithms in Bayesian inverse problems. Likelihood-informed subspace (LIS) methods can improve the efficiency of MCMC methods by utilizing the low-dimensional structure of the underlying problem. However, existing methods assume Gaussian priors and are not suitable for sparse problems. To address this limitation, we propose a prior normalization technique and integrate it with several MCMC methods.
Article
Computer Science, Interdisciplinary Applications
Tiangang Cui, Sergey Dolgov, Olivier Zahm
Summary: We propose a novel offline-online method that reduces the computational burden of posterior random variable characterization in statistical learning. This method learns the joint distribution of parameter and observable random variables in a tensor-train (TT) format during the offline phase. Then, in the online phase, it uses order-preserving conditional transport to describe the posterior random variables in real time based on newly observed data. This method relies on function approximation and includes thorough performance analysis, providing improved transport maps for high-dimensional observation and parameter problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Colin Fox, Tiangang Cui, Markus Neumayer
GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS
(2020)
Article
Mathematics, Applied
Johnathan M. Bardsley, Tiangang Cui, Youssef M. Marzouk, Zheng Wang
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2020)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)