Concepts

Rationale

This document is to explain key concepts in ERT. The motivation is not to come up with a definition that is globally accepted, but to establish a domain language for communication between ERT developers. In other words, explain the ERT community’s perspective on related concepts. Furthermore, the hope is that the same terms can then be used for communication with related development efforts and our users. With this in mind it is important to realise that the text below is not the ultimate truth ™, but a basis for which we can continue our discussions. This will be most valuable if we continuously compare our codified data models, as well as our communication with users (through dialog and user interfaces) towards these concepts. And it might very well be that it is the below concepts that needs to be matured further.

A second motivation for writing this is that as soon as ERT is exposing a concept via its interface, that being through a configuration file, an API or a graphical user interface there is at least one formal perspective of what this concept is. To ensure a coherent user and developer experience it is beneficial that different entities reasoning about a concept have a unified perspective. It is not about being correct, it is about being relevant and coherent.

Ensembles and their evaluation

Forward model

The task of the forward model is to deterministically simulate the behaviour of the model under study. In ERT a forward model is considered a black box function. This yields the benefit of extremely flexible modelling at the cost of low ability to reason about the forward model, its internal data flow and to build tooling on top of it. Furthermore, an ERT forward model is today implemented as a sequential list of scripts that are executed in the same disk area such that data from one script can be dumped on disk and picked up by the next job. More on the current and future data model and run environment of the forward model can be found in the The forward model.

Template model

ERT’s domain is to facilitate modelling work under uncertainty. In particular, multiple of the input variables to the forward model have an uncertainty attached to them. We call these variables the parameters of the model and let each parameter be represented by a probability distribution. The model we obtain by combining the forward model and parameter distributions is referred to as the template model. Notice that the template model is not a deterministic model any more, but a model that tries to capture the uncertainty of your current knowledge.

Realisation

The drawback of the template model is that depending on the forward model it might be very difficult to simulate. We can however, by sampling all of the parameters from their corresponding distributions, turn the template model into a realisation. The realisation consists of the forward model fm together with its input variables x. Observe that in a realisation x consists of only deterministic variables and is hence much easier to simulate and reason about than the template model.

Ensemble

As the name hints towards, ERT’s approach to studying a template model, is to create an ensemble of realisations. In particular, an ensemble is a list of realisations. The idea is that with a sufficiently large ensemble the uncertainty of the template model is represented by the ensemble.

Evaluating an ensemble

Recall that a realisation consists of a forward model fm together with input x. An observant reader might have realised that this, together with the assumption that the forward model is deterministic, is sufficient to get hold of the responses (output) of the forward model in this realisation. This process of applying the forward model on the input to retrieve its response y = fm(x) is coined to evaluate a realisation. And similarly, if one evaluates all of the realisations in an ensemble we say that we evaluate the ensemble. This separation between input data together with the method we want to apply on it and the result might seem artificial at first. But the truth is that in real life (as real as it gets on a computer at least) evaluations fail. One can think of it as evaluating a realisation will with high probability give you y = fm(x), but you might also get a failure (None). Since this is an inherent part of our domain we need to be able to communicate and reason about it as a first class citizen of our problem domain.

Realisation response

The response y = fm(x) computed by successfully evaluating a realisation is referred to as the realisation response. Since the forward model is assumed to be deterministic the response of a realisation will be the same each time the evaluation is successful.

Ensemble response

By evaluating an ensemble you will obtain an ensemble response. An ensemble response contains the realisation responses for all of its realisations; fm(x) for all of the successful realisations and the failure state None for each of the failed realisations. By reevaluating an ensemble multiple times one obtain multiple ensemble responses. Notice that the realisation response of a successful realisation is always the same in the different ensembles. Hence, one can merge two ensemble responses in a natural way to obtain a merged ensemble response where all realisations that was successful in at least one the two ensembles evaluations will be successful in the merged ensemble response.