model-json.md

Anatomy of a Model Json File

A model json file contains the description of a model. This description is read by HybridML to generate models and to load previously saved models.

Meta Parameters

• name can be choosen freely
• loss, metrics, optimizer can be choen from the corresponding tensorflow/keras objects.
• Furthermore comments can be added at will.

{
    "name": "my model",
    "loss": "mse",
    "metrics": ['accuracy'],
    "optimizer": "adam",
    "comment": "A comment",
    ...
}

Inputs

• id assigns the input a unique id. The id is used to reference the input in the model.
• size determines how many parameters go into the input. Can be null, if the length is variable.

    "inputs": [
        {
            "comment": "Covariates loaded using flux_datasource.py",
            "id": "cov",
            "size": 8
        },
        {
            "id": "dose",
            "size": 1
        },
        {
            "id": "t",
            "size": null
        }
    ]

Outputs

• outputs name the node connectors from the model that are outputs. These will be used as output for training the model.
• additional_outputs name the node connectors that can be predicted, but are not used for training. These can be used to get the inner state of the model.

    "outputs": [
        "ode_output"
    ],
    "additional_outputs":[
        "k1","k2"
    ]

Nodes

The model is defined as feed forward network. It consists of nodes, which themselves can be models. The nodes are connected with node connectors.

• type determines which type a node has.
• Each type has a unique id which should not contain spaces.
  • The id is used to identify the node when debugging or when showing the model.

1. Blackbox/NeuralNetwork

• "type":"nn"
• inputs is a list of node connectors which are then stacked to form the input for the neural network.
• outputs defines the node connectors that contain the output of the neural net. There are two cases
  1. There is one output: The output has the size of the last layer of the neural network.
  2. There are multiple outputs: The number of the outputs has to mach the size of the last layer of the neural network. The output of the neural network is split to match the node connectors.
• layers is a list of layer objects that form the neural network.
  • size is the size of the layer.
  • activation is the activation function of the layer. All activation functions from tensorflow/keras are possible, such as [tanh,relu,sigmoid]. Setting it to None results in a linear activation
  • kernel_regularizer applies a kernel regularizer to the layer. Possible are L1 and L2. The regularization factor is appended in parenthesis.
  • activity_regularizer is similar to `kernel_regularizer

{
        "id": "BlackBox",
        "type": "nn",
        "inputs": [
            "inp"
        ],
        "layers": [
            {
                "activation": "tanh",
                "size": 10
            },
            {
                "activation": "None",
                "size": 2,
                "kernel_regularizer" : "L1(0.1)",
                "activity_regularizer" : "L2(0.1)"
            }
        ],
        "outputs": [
            "out1",
            "out2",
        ]
    }

2. Arithmetic Expression

• "type" : "arithmetic"
• expression defines an expression to be evaluated.
  • It has the form output = calculation(input) where output is a single new node connnector, that carries the output of the calculation.
  • Possible calculations:
    • +-*/ basic calculations
    • ** powers
    • (a+b)*c parenthesis
    • input[0], all_compartments[:,:,1] slicing. Here the : means keeping the whole dimension and slice only the ones with an actual index.
    • experimental: [[a,b],[c,d]] building multidimensional outputs
    • Generally most things possible in python. This gives great opportunity to break the model.

{
    "id": "expression",
    "type": "arithmetic",
    "expression": "k_out = k_in*1000 + 1.573615e+03"
}

3. Basic Function

Will possibly be deprecated, due doubling functionality with arithmetic expressions

• inputs is a list of node connector inputs.
• outputs is a single new node connector, carrying the result of the calculation
• type Possible types:
  • [addition, multiplication, substraction, average, maximum, minimum, concatenate]

{
    "type" : "addition",
    "inputs" : ["in1", "in2"],
    "output" : "out"
}

4. Linear Ode

This node solves a special case of a linear ode, that is characterized by a system matrix.

• "type" : "linear_ode" implementation of the closed form solution of the ode special case.
• "type" : "casadi_linear_ode" implementation using a general ode solver over casadi/sundials.
• time_series_input the node connector containing the time series for the sample.
• initial_value_input the node connector containing the initial value of the ode for the sample.
• system_matrix an arithmetic expression containing the system matrix.
  • Can be constant or dynamic.
  • Matrix can be written in python style [[a,b],[c,d]] or in matlab style a, b; c, d.
• output single node connector containing the result of the linear ode.
  • Attention The output has one more dimension as other node connectors (samples x time x ode_dimension). When further processed it might be necessary to slice it to get one of the states. This can be archieved through an arithmetic expression layer with the expression: out = ode_output[:,:,2], replacing 2 with the desired state number.

Defining custom nodes

More nodes can be defined. Read (create-json.md)[create-json.md] for reference.