Simultaneous Global Identification of Dynamic and Network Parameters in Transient Stability Studies

Transtrum, Mark K.; Francis, Benjamin L.; Sarić, Andrija T.; Stanković, A.M.

doi:10.1109/pesgm.2018.8586586

Cited by 5 publications

(2 citation statements)

References 5 publications

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“…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.

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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.

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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

“…As advertised, they too show a roughly geometric progression over many orders of magnitude. We will [33], radioactive decay and neural network are taken from [34], quantum wavefunction are taken from [35], diffusion model and Ising model are taken from [29], meat oxidation is from [36], CMB data from [37], accelerator model taken from [38], van der Pol oscillator taken from [39], circadian clock model from [1], SW interatomic potential model from [40], power systems from [41], gravitational model from [42], transmission loss in an underwater environment from [43], and finally H 2 IO 2 combustion model from [44].…”

Section: Local and Global Distancesmentioning

confidence: 99%

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

Quinn¹,

Abbott²,

Transtrum³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Complex models in physics, biology, economics, and engineering are often ill-determined or sloppy: parameter combinations can vary over wide ranges without significant changes in their predictions. This review uses information geometry to explore sloppiness and its deep relation to emergent theories. We introduce the model manifold of predictions, whose coordinates are the model parameters. Its hyperribbon structure explains why only a few parameter combinations matter for the behavior. We review recent rigorous results that connect the hierarchy of hyperribbon widths to approximation theory, and to the smoothness of model predictions under changes of the control variables. We discuss recent geodesic methods to find simpler models on nearby boundaries of the model manifold -emergent theories with fewer parameters that explain the behavior equally well. We discuss a Bayesian prior which optimizes the mutual information between model parameters and experimental data, naturally favoring points on the emergent boundary theories and thus simpler models. We introduce a 'projected maximum likelihood' prior that efficiently approximates this optimal prior, and contrast both to the poor behavior of the traditional Jeffreys prior. We discuss the way the renormalization group coarse-graining in statistical mechanics

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Piecemeal Reduction of Models of Large Networks

Francis

Transtrum

Sarić

et al. 2021

2021 60th IEEE Conference on Decision and Control (CDC)

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Simultaneous Global Identification of Dynamic and Network Parameters in Transient Stability Studies

Cited by 5 publications

References 5 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

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

Piecemeal Reduction of Models of Large Networks

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