Variational Bayesian Experimental Design for Geophysical Application

Dominik Strutz & Andrew Curtis

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Design experiments to answer specific scientific questions

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• What information is provided by the experiment ?

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• How can experimental design be done efficiently ?

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prior information

posterior information

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information gain (data, design) =

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prior information

posterior information

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information gain (data, design) =

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prior information

posterior information

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information gain (data, design) =

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prior information

posterior information

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excepted information gain (design) =

average over all data plausible according to prior information

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prior information

posterior information

-

excepted information gain (design) =

average over all data plausible according to prior information

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prior information

posterior information

-

excepted information gain (design) =

average over all data plausible according to prior information

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prior information

posterior information

-

excepted information gain (design) =

average over all data plausible according to prior information

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prior information

posterior information

-

excepted information gain (design) =

average over all data plausible according to prior information

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prior information

posterior information

-

excepted information gain (design) =

average over all data plausible according to prior information

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A quantity to assess the quality of an experimental design

prior information

posterior information

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average over all data plausible according to prior information

excepted information gain (design) =

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inverse problem

inverse problem

prior distribution

prior samples

data samples

forward function

forward function

forward function

forward function

posterior distributions

inverse problem

EIG

sample from prior

calculate information gain

experimental design

inverse problem

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inverse problem

inverse problem

prior distribution

prior samples

data samples

forward function

forward function

forward function

forward function

posterior distributions

inverse problem

EIG

sample from prior

calculate information gain

experimental design

inverse problem

Variational Methods

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data samples

posterior distributions

inverse problem

Variational Methods

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data

Mixture Density Network

data samples

posterior distributions

inverse problem

Variational Methods

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data

Mixture Density Network

data samples

posterior distributions

inverse problem

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Design experiments to answer specific scientific questions

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CO₂ injection

CO₂ Interrogation

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CO₂ Interrogation

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fluid properties

saturated rock properties

seismic properties

CO₂ Interrogation

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CO₂ Interrogation

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CO₂ Interrogation

reflection coefficient

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CO₂ Interrogation

reflection coefficient

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CO₂ Interrogation

reflection coefficient

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CO₂ Interrogation

reflection coefficient

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CO₂ Interrogation

reflection coefficient

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CO₂ Interrogation

reflection coefficient

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CO₂ Interrogation

reflection coefficient

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CO₂ Interrogation

reflection coefficient

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CO₂ Interrogation

reflection coefficient

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CO₂ Interrogation

reflection coefficient

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CO₂ Interrogation

including data uncertainty

reflection coefficient

reflection coefficient

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CO₂ Interrogation

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CO₂ Interrogation

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CO₂ Interrogation

+25% EIG

Compared to heuristic:

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CO₂ Interrogation

+25% EIG

+8% EIG

Compared to heuristic:

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CO₂ Interrogation

+25% EIG

+8% EIG

+8% EIG

Compared to heuristic:

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Visit my website (dominik-strutz.github.io) for further updates and contact information

For more information see our recently published preprint

We can design experiments to answer specific scientific questions

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• Machine learning enables calculating the expected information gain efficiently

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• Specialised designs provide more information on specific scientific questions