Accurate Broadband Gradient Estimates Enable Local Sensitivity Analysis of Ocean Acoustic Models

Mortenson, Michael C.; Neilsen, Tracianne B.; Transtrum, Mark K.; Knobles, David P.

doi:10.1142/s2591728522500153

Cited by 2 publications

(1 citation statement)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The vertical axis shows eigenvalues of the Fisher information matrix, scaled by the largest eigenvalue. Cell signaling data from [2], radioactive decay and neural network are taken from [53], quantum wavefunction are taken from [54], diffusion model and Ising model are taken from [38], meat oxidation is from [55], CMB data from [41], accelerator model taken from [56], van der Pol oscillator taken from [57], circadian clock model from [7], SW interatomic potential model from [58], power systems from [59], gravitational model from [60], transmission loss in an underwater environment from [61], and finally H 2 IO 2 combustion model from [62].…”

Section: Local and Global Distancesmentioning

confidence: 99%

Information geometry for multiparameter models: new perspectives on the origin of simplicity

Quinn¹,

Abbott²,

Transtrum³

et al. 2022

Rep. Prog. Phys.

View full text Add to dashboard Cite

Complex models in physics, biology, economics, and engineering are often ill-determined or sloppy: their multiple parameters can vary over wide ranges without significant changes in their predictions. This review uses the tools of information geometry to explore this phenomenon, and the deep relations between sloppiness and emergent theories. We introduce information geometry, the model manifold of predictions whose coordinates are the model parameters, and its hyperribbon structure. These hyperribbons explain why only a few parameter combinations have significant effects on the behavior of complex multiparameter models. We review recent rigorous results using approximation theory to connect the hierarchy of hyperribbon widths to approximation theory, and to the smoothness of model predictions under changes of the system control variables. We discuss recent methods for following sloppy geodesics to find simpler models on the boundary of the model manifold -- emergent theories with fewer parameters that explain the behavior equally well. We discuss a recent `optimal' Bayesian prior which maximizes the mutual information between model parameters and experimental data. This prior naturally favors points on the emergent boundary theories, thus selecting simpler models when they make nearly equivalent predictions. We introduce a `projected maximum likelihood' prior that efficiently approximates this optimal prior, and contrast both to the poor behavior of the traditional Jeffrey's prior. We discuss the way the renormalization group coarse-graining in statistical mechanics introduces a flow of the model manifold, and connect stiff and sloppy directions along the model manifold with relevant and irrelevant eigendirections of the renormalization group. Finally, we discuss recently developed `intensive' embedding methods, allowing one to visualize the predictions of arbitrary probabilistic models as low-dimensional projections of an isometric embedding, and illustrate our method by generating the model manifold of the Ising model.

show abstract

Section: Local and Global Distancesmentioning

confidence: 99%

Information geometry for multiparameter models: new perspectives on the origin of simplicity

Quinn¹,

Abbott²,

Transtrum³

et al. 2022

Rep. Prog. Phys.

View full text Add to dashboard Cite

show abstract

A Fast Multi-Frequency Iterative Acoustic Boundary Element Method Solver Based on a Preconditioned Accelerated Recycling Strategy

Panagiotopoulos,

Desmet,

Deckers

2023

J. Theor. Comp. Acout.

View full text Add to dashboard Cite

Common multi-frequency solution strategies for acoustic systems are either associated with high computational costs or resort to model reduction strategies, which potentially induce considerable approximation errors. In that context, this work proposes a fast multi-frequency solver for acoustic Boundary Element Method (BEM) analyses that combines conventional preconditioners with an accelerated recycling strategy, achieving in that way a fast and accurate iterative solution. Specifically, by approximating both the system and the related preconditioner by individual affine expressions, an upfront Galerkin projection on a global deflation basis is facilitated, therefore enabling the deployment of the accelerated recycling scheme. The latter acts by accelerating the construction of the related deflation projectors, therefore leading to a significantly faster recycling procedure. Finally, the efficiency of the global deflation basis is guaranteed through an Automatic Krylov subspaces Recycling for Deflation (AKR-D) [D. Panagiotopoulos, W. Desmet and E. Deckers, An accelerated subspaces recycling strategy for the deflation of parametric linear systems based on model order reduction, Comput. Methods Appl. Mech. Eng. 403 (2023) 115765] algorithm and thus, the cumulative number of iterations required by an iterative solver within a frequency sweep is drastically decreased. The proposed multi-frequency solver is tested on two industrially relevant examples of an interior and an exterior scattering problem, benchmarked against the traditional solution strategies.

show abstract

Accurate Broadband Gradient Estimates Enable Local Sensitivity Analysis of Ocean Acoustic Models

Cited by 2 publications

References 45 publications

Information geometry for multiparameter models: new perspectives on the origin of simplicity

Information geometry for multiparameter models: new perspectives on the origin of simplicity

A Fast Multi-Frequency Iterative Acoustic Boundary Element Method Solver Based on a Preconditioned Accelerated Recycling Strategy

Contact Info

Product

Resources

About