Bayesian calibration for large‐scale fluid structure interaction problems under embedded/immersed boundary framework

Cao, Shunxiang; Huang, Daniel Z.

doi:10.1002/nme.6916

Cited by 6 publications

(11 citation statements)

References 126 publications

(185 reference statements)

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“…Such problems may feature multiple scales, may include chaotic dynamics, or may involve turbulent phenomena; as a result the forward models are typically very expensive to evaluate. Moreover, the forward solvers are often given as a black box (e.g., off-the-shelf solvers [13] or multiphysics systems requiring coupling of different solvers [14,15]), and may not be differentiable due to the numerical methods used (e.g., embedded boundary method [16,17] and adaptive mesh refinement [18,19]) or because of the inherently discontinuous physics (e.g. in fracture [20] or cloud modeling [21,22]).…”

Section: Orientationmentioning

confidence: 99%

“…These expectations are computed by assuming θ n+1 |Y n ∼ ρn+1 and noting that the distribution of (θ n+1 , x n+1 ) is then defined by ( 14)- (15). This corresponds to projecting § the joint distribution onto the Gaussian which matches its mean and covariance.…”

Section: Gaussian Approximationmentioning

confidence: 99%

“…(9). With the extended observation model (15) and the specific choice of Σ ν,n , the analysis step without Gaussian approximation can be written as (23) and hence the density functions ρn+1 and ρ n+1 fulfill Eq. (10).…”

Section: Gaussian Approximationmentioning

confidence: 99%

“…The perturbed observations form of the ensemble Kalman filter [83] is applied to the extended mean-field dynamical system ( 14)- (15), which leads to the EKI:…”

Section: Stochastic Ensemble Kalman Inversion (Eki)mentioning

confidence: 99%

“…To derive a continuous-time limit of the novel mean-field dynamical system (Eqs. (14), (15) and ( 18)) we set γ → ∆tγ, define t n = n∆t and define {z n } by x n = ∆t −1 (z n+1 − z n ). Then θ n ≈ θ(t n ) and z n ≈ z(t n ).…”

Section: Appendix a Continuous Time Limitmentioning

confidence: 99%

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Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems

Huang¹,

Huang²,

Reich³

et al. 2022

Preprint

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We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible, since they typically require O(10 4 ) model runs, or more. Moreover, the forward model is often given as a black box or is impractical to differentiate. Therefore derivative-free algorithms are highly desirable. We propose a framework, which is built on Kalman methodology, to efficiently perform Bayesian inference in such inverse problems. The basic method is based on an approximation of the filtering distribution of a novel mean-field dynamical system into which the inverse problem is embedded as an observation operator. Theoretical properties of the mean-field model are established for linear inverse problems, demonstrating that the desired Bayesian posterior is given by the steady state of the law of the filtering distribution of the mean-field dynamical system, and proving exponential convergence to it. This suggests that, for nonlinear problems which are close to Gaussian, sequentially computing this law provides the basis for efficient iterative methods to approximate the Bayesian posterior. Ensemble methods are applied to obtain interacting particle system approximations of the filtering distribution of the mean-field model; and practical strategies to further reduce the computational and memory cost of the methodology are presented, including low-rank approximation and a bi-fidelity approach. The effectiveness of the framework is demonstrated in several numerical experiments, including proofof-concept linear/nonlinear examples and two large-scale applications: learning of

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Section: Orientationmentioning

confidence: 99%

Section: Gaussian Approximationmentioning

confidence: 99%

Section: Gaussian Approximationmentioning

confidence: 99%

“…The perturbed observations form of the ensemble Kalman filter [83] is applied to the extended mean-field dynamical system ( 14)- (15), which leads to the EKI:…”

Section: Stochastic Ensemble Kalman Inversion (Eki)mentioning

confidence: 99%

Section: Appendix a Continuous Time Limitmentioning

confidence: 99%

See 3 more Smart Citations

Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems

Huang¹,

Huang²,

Reich³

et al. 2022

Preprint

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show abstract

A feature points-based method for data transfer in fluid-structure interactions

Dou

GUO²,

ZHANG³

et al. 2022

International Journal of Mechanical Sciences

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Efficient derivative-free Bayesian inference for large-scale inverse problems

Huang¹,

Huang²,

Reich³

et al. 2022

Inverse Problems

View full text Add to dashboard Cite

We consider Bayesian inference for large-scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible, since they typically require O(104) model runs, or more. Moreover, the forward model is often given as a black box or is impractical to differentiate. Therefore derivative-free algorithms are highly desirable. We propose a framework, which is built on Kalman methodology, to efficiently perform Bayesian inference in such inverse problems. The basic method is based on an approximation of the filtering distribution of a novel mean-field dynamical system, into which the inverse problem is embedded as an observation operator. Theoretical properties are established for linear inverse problems, demonstrating that the desired Bayesian posterior is given by the steady-state of the law of the filtering distribution of the mean-field dynamical system, and proving exponential convergence to it. This suggests that, for nonlinear problems which are close to Gaussian, sequentially computing this law provides the basis for efficient iterative methods to approximate the Bayesian posterior. Ensemble methods are applied to obtain interacting particle system approximations of the filtering distribution of the mean-field model; and practical strategies to further reduce the computational and memory cost of the methodology are presented, including low-rank approximation and a bi-fidelity approach. The effectiveness of the framework is demonstrated in several numerical experiments, including proof-of-concept linear/nonlinear examples and two large-scale applications: learning of permeability parameters in subsurface flow; and learning subgrid-scale parameters in a global climate model. Moreover, the stochastic ensemble Kalman filter and various ensemble square-root Kalman filters are all employed and are compared numerically. The results demonstrate that the proposed method, based on exponential convergence to the filtering distribution of a mean-field dynamical system, is competitive with pre-existing Kalman-based methods for inverse problems.

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Bayesian calibration for large‐scale fluid structure interaction problems under embedded/immersed boundary framework

Cited by 6 publications

References 126 publications

Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems

Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems

A feature points-based method for data transfer in fluid-structure interactions

Efficient derivative-free Bayesian inference for large-scale inverse problems

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