Laws tutorial

This tutorial provides simple examples on how to create learnable and non learnable laws and how to inject them into the iceflow model.

Let's say we have followed the classical workflow from ODINN, shown in the Forward simulation and Functional inversion tutorials. When we declare the Model type, we can specify the laws that we want to use in the iceflow model. Here we will briefly show how to do it. For more details you can check the Understanding the Law interface section.

Learnable laws

Learnable laws are laws that can be trained using a regressor. They are used to map input variables to a target variable in the iceflow model. In ODINN, we have implemented several learnable laws that can be used in the iceflow model.

using ODINN

# Dummy parameters, only specifying the type of loss function to be used
params = Parameters(UDE = UDEparameters(empirical_loss_function=LossH()))
nn_model = NeuralNetwork(params)

A_law = LawA(nn_model, params)

model = Model(
    iceflow = SIA2Dmodel(params; A=A_law),
    mass_balance = TImodel1(params; DDF=6.0/1000.0, acc_factor=1.2/1000.0),
    regressors = (; A=nn_model)
)

The LawA law is a learnable law that maps the long term air temperature T to the creep coefficient A. It is defined as a neural network that takes as input the long term air temperature T and returns the creep coefficient A. The parameters θ of the neural network are learned during the inversion process, by minimizing the loss function given some target data (for this case the ice thickness).

Non learnable laws

Non learnable laws are laws that are not trained using a regressor. They are used to map input variables to a target variable in the iceflow model, but they do not have any learnable parameters.

Here is a quick example also drawn from the Functional Inversions tutorial. We define a synthetic law to generate the synthetic dataset. For this, we use some tabular data from Cuffey and Paterson (2010).

using ODINN

params = Parameters() # dummy parameters

A_law = CuffeyPaterson()

model = Huginn.Model(
    iceflow = SIA2Dmodel(params; A=A_law),
    mass_balance = TImodel1(params; DDF=6.0/1000.0, acc_factor=1.2/1000.0),
)

In this ice flow model, the ice rigidity A is defined by the CuffeyPaterson law, which is a non-learnable law that maps the long term air temperature T to the creep coefficient A.

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