Variational Bayesian Experimental Design for Geophysical Application

Dominik Strutz & Andrew Curtis

What information will be provided by an experimental design?

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How do expected data uncertainties affect optimal designs?

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Can experiments be optimised to focus on specific scientific questions?

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How can experiments be designed efficiently?

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prior information

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prior information

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prior information

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prior information

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prior information

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prior information

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prior information

posterior information

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prior information

posterior information

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prior information

posterior information

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prior information

posterior information

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prior information

posterior information

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information gain (data, design) =

prior information

posterior information

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expected information gain (design) =

prior information

posterior information

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average over all data that are plausible according to prior information

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expected information gain (design) =

prior information

posterior information

-

average over all data that are plausible according to prior information

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expected information gain (design) =

prior information

posterior information

-

average over all data that are plausible according to prior information

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expected information gain (design) =

prior information

posterior information

-

average over all data that are plausible according to prior information

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expected information gain (design) =

prior information

posterior information

-

average over all data that are plausible according to prior information

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expected information gain (design) =

prior information

posterior information

-

average over all data that are plausible according to prior information

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expected information gain (design) =

prior information

posterior information

-

average over all data that are plausible according to prior information

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expected information gain (design) =

prior information

posterior information

-

average over all data that are plausible according to prior information

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expected information gain (design) =

prior information

posterior information

-

average over all data that are plausible according to prior information

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expected information gain (design) =

prior information

posterior information

-

average over all data that are plausible according to prior information

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expected information gain (design) =

prior information

posterior information

-

average over all data that are plausible according to prior information

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prior samples

forward function

data likelihood

data samples

experimental design

forward function

forward function

forward function

inverse problem

inverse problem

inverse problem

inverse problem

EIG

calculate information gain

sample from prior

posterior distribution

sample

sample

sample

sample

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prior samples

forward function

data likelihood

data samples

experimental design

forward function

forward function

forward function

inverse problem

inverse problem

inverse problem

inverse problem

EIG

calculate information gain

sample from prior

posterior distribution

sample

sample

sample

sample

Variational Methods

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data samples

inverse problem

posterior distribution

Variational Methods

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data

Mixture Density Network

data samples

inverse problem

posterior distribution

Variational Methods

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data

Mixture Density Network

data samples

inverse problem

posterior distribution

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prior samples

forward function

data likelihood

data samples

experimental design

forward function

forward function

forward function

inverse problem

inverse problem

inverse problem

inverse problem

EIG

calculate information gain

sample from prior

posterior distribution

sample

sample

sample

sample

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prior samples

data samples

sample from prior

EIG

posterior distribution

experimental design

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prior samples

data samples

experimental design

sample from prior

EIG

information of the data likelihood

information of the evidence

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EIG

information of the evidence

information of the data likelihood

data samples

prior samples

sample from prior

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data samples

EIG

information of the evidence

information of the data likelihood

prior samples

sample from prior

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EIG

information of the evidence

information of the data likelihood

data samples

prior samples

sample from prior

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EIG

information of the evidence

information of the data likelihood

data samples

prior samples

sample from prior

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EIG

information of the evidence

information of the data likelihood

data samples

prior samples

sample from prior

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data samples

EIG

information of the evidence

information of the data likelihood

prior samples

sample from prior

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data samples

EIG

information of the evidence

information of the data likelihood

prior samples

sample from prior

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prior samples

data samples

experimental design

sample from prior

EIG

information of the data likelihood

information of the evidence

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prior samples

data samples

experimental design

sample from prior

EIG

information of the data likelihood

information of the evidence

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prior samples

data samples

experimental design

sample from prior

EIG

information of the data likelihood

information of the evidence

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What information will be provided by an experimental design?

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How do expected data uncertainties affect optimal designs?

Effect of the Likelihood Function

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Lomax et al. (2014)

Effect of the Likelihood Function

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damage zone

prior distribution of event locations

Effect of the Likelihood Function

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Effect of the Likelihood Function

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Effect of the Likelihood Function

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What information will be provided by an experimental design?

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How do expected data uncertainties affect optimal designs?

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Can experiments be optimised to focus on specific scientific questions?

CO₂ Interrogation

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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

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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

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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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What information will be provided by an experimental design?

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How do expected data uncertainties affect optimal designs?

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Can experiments be optimised to focus on specific scientific questions?

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How can experiments be designed efficiently?

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Variational Function

EIG

experimental design

update variational function

Variational Function

EIG

update variational function

Variational Function

EIG

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Variational Function

EIG

experimental design

update variational function

Variational Function

EIG

update variational function

Variational Function

EIG

design

update design

design

update design

optimal experimental design

one-step design optimisation

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more stations at higher offsets

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increasing EIG

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computational savings of

at least one order of magnitude

different prior

Conclusions

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• information gain of an experiment can be calculated in different ways

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• effects of the different data likelihoods can be included

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• experiments can be designed to answer specific scientific questions

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• variational methods provide new possibilities of efficiently optimizing experimental designs

Future Directions

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• apply methods to more useful real-world application

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• investigate if focusing on specific questions allows optimal design to
• be more resource efficient,
• to be applied for more complex problems,
• and explore which methods can be used to achieve this.

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• derive heuristics for new sensor types (e.g., DAS, rotational sensors, …)

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• I am open to ideas or collaborations

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Accessibility

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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

github.com/dominik-strutz/GeoBOED

Implementations of all algorithms presented in this talk.

Will be extended and made more user friendly in the future.