# Extending NeuroML with LEMS#

As a language, LEMS defines a set of built-in types which can be used together to build more user-defined types. For example, Python defines int, float, str and so on as built-in types, and these can then be combined to define user defined types, classes. An object of a particular class/type can be instantiated by supplying values for the members defined in the class/type.

ComponentTypes in LEMS are similar to classes in Python. They define the membership structure of the type, but they do not specify values for their members. Once a ComponentType has been defined, an instance of it can be created by setting values for its members. This object is referred to as a Component in LEMS.

The NeuroML2 standard is a list of curated ComponentTypes. In cases where the set of ComponentTypes defined in the NeuroML standard is not sufficient for a particular modelling project, new ComponentTypes can be defined in LEMS to extend the NeuroMLv2 standard.

Having definitions in LEMS allows their re-use, and these new ComponentTypes can be submitted for inclusion to the NeuroMLv2 specification to be made accessible to other users.

• Like NeuroML, LEMS files are also XML files.

• Next, like NeuroML, LEMS also has a well defined schema (XSD) that is used to validate LEMS XML files.

• However, also similar to NeuroML, you can use the LEMS Python tools to work with LEMS and do not need to work directly with the XML files.

## LEMS elements#

The list of built-in types provided by LEMS can be seen in the LEMS documentation. As the documentation notes, a ComponentType is the “Root element for defining component types”. It must contain a name, and can extend another ComponentType, thus inheriting its members/attributes. Each ComponentType can contain members of other LEMS types: Parameter, DerivedParameter, Dynamics, Exposure and so on. These are also all documented in the LEMS documentation.

## Example: Lorenz model for cellular convection#

Let us create a new LEMS ComponentType, one that is not neuroscience specific. We will first create it using the plain XML and then see how it can be done using the Python pyLEMS API.

For this example, we will use the Lorenz model for cellular convection [Lor63]. The Wikipedia article provides a short summary of the model, and the equations that govern it:

(1)#\begin{align} \frac{dx}{dt} &= \sigma (y - x) \\ \frac{dy}{dt} &= x (\rho - z) - y \\ \frac{dz}{dt} &= xy - \beta z \end{align}

So we can see here that we have three parameters:

• $$\sigma$$

• $$\rho$$

• $$\beta$$

Next, x, y, and z are the state variables for this model, with initial values x0, y0, and z0 respectively. We also want to be able to observe the values of x, y, and z, so they must be exposed in the LEMS definition.

Let us start with the XML definition of a ComponentType that will describe this model. Each XML file must start with a <Lems> “root node”. This includes information about the version of the LEMS schema that this document is valid against. In this case, we document that this LEMS file should be valid against version 0.7.6 of the LEMS schema.

<Lems xmlns="http://www.neuroml.org/lems/0.7.6"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:schemaLocation="http://www.neuroml.org/lems/0.7.6 https://raw.github.com/LEMS/LEMS/master/Schemas/LEMS/LEMS_v0.7.6.xsd">

<ComponentType name="lorenz1963" description="The Lorenz system is a simplified model for atomspheric convection, derived from the Navier Stokes equations.">

<!-- Parameters: free parameters to be used in the model -->
<Parameter name="sigma" dimension="none" description="Prandtl Number"/>
<Parameter name="beta" dimension="none" description="Also named b elsewhere"/>
<Parameter name="rho" dimension="none" description="Related to the Rayleigh number, also named r elsewhere"/>

<!-- Initial Conditions: also free parameters to be set when creating a Component from the ComponentType -->
<Parameter name="x0" dimension="none"/>
<Parameter name="y0" dimension="none"/>
<Parameter name="z0" dimension="none"/>

<!-- Exposure: what we want to be able to record from the LEMS simulation -->
<Exposure name="x" dimension="none"/>
<Exposure name="y" dimension="none"/>
<Exposure name="z" dimension="none"/>
</ComponentType>
</Lems>


Note that each parameter has a dimension, not a unit. This is because LEMS allows us to use any valid units for each dimension, and takes care of the conversion factors and so on. NeuroML also takes advantage of this LEMS feature, as noted here.

Now, we can define the dynamics of the model, summarised in the equations above:

        <Dynamics>
<!-- State variables: linked to Exposures so that they can be accessed -->
<StateVariable name="x" dimension="none" exposure="x"/>
<StateVariable name="y" dimension="none" exposure="y"/>
<StateVariable name="z" dimension="none" exposure="z"/>

<!-- Equations defining the dynamics of each state variable -->
<TimeDerivative variable="x" value="( sigma * (y - x) ) / sec"/>
<TimeDerivative variable="y" value="( rho * x - y - x * z ) / sec"/>
<TimeDerivative variable="z" value="( x * y - beta * z) / sec"/>

<!-- Actions to take on the start of a LEMS simulation -->
<OnStart>
<StateAssignment variable="x" value="x0"/>
<StateAssignment variable="y" value="y0"/>
<StateAssignment variable="z" value="z0"/>
</OnStart>
</Dynamics>


Our LEMS file is almost complete. However, notice that we have used sec in the dynamics to denote time but have not yet declared it. We define sec as a constant whose value is defined in the ComponentType itself (and will not be set by us when instantiating a Component of this ComponentType):

        <Constant name="sec" dimension="time" value="1s"/>


Also note that while we have defined this constant, we have not yet defined the time dimension or its units. We can do that outside the ComponentType:

  <Dimension name="time" t="1"/>
<Unit name="second" symbol="s" dimension="time" power="1"/>
<Unit name="milli second" symbol="ms" dimension="time" power="-3"/>


We have defined two units for the time dimension, with their conversion factors. LEMS will use this information to correctly convert all dimensions as required. The NeuroMLv2 standard defines various dimensions and their units in the schema for us to use.

The complete LEMS file will be this:

<Lems xmlns="http://www.neuroml.org/lems/0.7.6"
xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
xsi:schemaLocation="http://www.neuroml.org/lems/0.7.6 https://raw.github.com/LEMS/LEMS/master/Schemas/LEMS/LEMS_v0.7.6.xsd">

<Dimension name="time" t="1"/>
<Unit name="second" symbol="s" dimension="time" power="1"/>
<Unit name="milli second" symbol="ms" dimension="time" power="-3"/>

<ComponentType name="lorenz1963" description="The Lorenz system is a simplified model for atomspheric convection, derived from the Navier Stokes equations.">

<!-- Parameters: free parameters to be used in the model -->
<Parameter name="sigma" dimension="none" description="Prandtl Number"/>
<Parameter name="beta" dimension="none" description="Also named b elsewhere"/>
<Parameter name="rho" dimension="none" description="Related to the Rayleigh number, also named r elsewhere"/>

<!-- Initial Conditions: also free parameters to be set when creating a Component from the ComponentType -->
<Parameter name="x0" dimension="none"/>
<Parameter name="y0" dimension="none"/>
<Parameter name="z0" dimension="none"/>

<!-- Exposure: what we want to be able to record from the LEMS simulation -->
<Exposure name="x" dimension="none"/>
<Exposure name="y" dimension="none"/>
<Exposure name="z" dimension="none"/>
<Constant name="sec" dimension="time" value="1s"/>

<Dynamics>
<!-- State variables: linked to Exposures so that they can be accessed -->
<StateVariable name="x" dimension="none" exposure="x"/>
<StateVariable name="y" dimension="none" exposure="y"/>
<StateVariable name="z" dimension="none" exposure="z"/>

<!-- Equations defining the dynamics of each state variable -->
<TimeDerivative variable="x" value="( sigma * (y - x) ) / sec"/>
<TimeDerivative variable="y" value="( rho * x - y - x * z ) / sec"/>
<TimeDerivative variable="z" value="( x * y - beta * z) / sec"/>

<!-- Actions to take on the start of a LEMS simulation -->
<OnStart>
<StateAssignment variable="x" value="x0"/>
<StateAssignment variable="y" value="y0"/>
<StateAssignment variable="z" value="z0"/>
</OnStart>
</Dynamics>
</ComponentType>
</Lems>


We now have a complete LEMS model declaration. To use this model, we need to create an instance of the ComponentType, a Component. This requires us to set the values of various parameters of the defined model:

<lorenz1963 id="lorenzCell" sigma="10" beta="2.67" rho="28"
x0="1.0" y0="1.0" z0="1.0"/>


Here, we’ve set parameters that result in the chaotic attractor regime. We could also use different values for the parameters—like a class can have many many objects with different parameters, a ComponentType can have also have different Components.

Note that one can also define a Component using the standard constructor form:

  <Component id="lorenzCell" type="lorenz1963" sigma="10" beta="2.67" rho="28" x0="1.0" y0="1.0" z0="1.0"/>


The two forms are equivalent. As with other conventions, either form can be used as long as it is used consistently.

The Include element type allows us to modularise our models. In NeuroML based models, we use it to break our model down into small independent reusable files.

### Writing the model in Python using PyLEMS#

While the underlying format for NeuroML and LEMS is XML, Python is the suggested programming language for end users. In this section we will see how the Lorenz model can be written using the PyLEMS Python LEMS API. The complete script is below:

#!/usr/bin/env python3

import lems.api as lems
from lems.base.util import validate_lems

model = lems.Model()

lorenz = lems.ComponentType(name="lorenz1963", description="The Lorenz system is a simplified model for atomspheric convection, derived from the Navier Stokes equations")

lorenz.add(lems.Parameter(name="beta", dimension="none", description="Also named b elsewhere"))
lorenz.add(lems.Parameter(name="rho", dimension="none", description="Related to the Rayleigh number, also named r elsewhere"))

lorenz.dynamics.add(lems.TimeDerivative(variable="x", value="( sigma * (y - x)) / sec"))
lorenz.dynamics.add(lems.TimeDerivative(variable="y", value="( rho * x - y - x * z ) / sec"))
lorenz.dynamics.add(lems.TimeDerivative(variable="z", value="( x * y - beta * z) / sec"))

onstart = lems.OnStart()

beta="2.67", rho="28", x0="1.0", y0="1.0", z0="1.0"))

file_name = "LEMS_lorenz.xml"
model.export_to_file(file_name)

validate_lems(file_name)


As you will see, the PyLEMS API exactly follows the XML constructs that we used before. Running this script, let’s call it LorenzLems.py gives us:

\$ python LorenzLems.py
Validating LEMS_lorenz.xml against https://raw.githubusercontent.com/LEMS/LEMS/development/Schemas/LEMS/LEMS_v0.7.6.xsd
It's valid!


The generated XML file is below. As you can see, it is identical to the XML file that we wrote by hand in the previous section. You will also see that the Python API also provides convenience functions, such as the export_to_file and validate_lems functions to quickly save your model to an XML file, and validate it.

<?xml version="1.0" ?>
<Lems xmlns="http://www.neuroml.org/lems/0.7.6" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.neuroml.org/lems/0.7.6 https://raw.githubusercontent.com/LEMS/LEMS/development/Schemas/LEMS/LEMS_v0.7.6.xsd">
<Dimension name="time" t="1"/>
<Unit symbol="s" dimension="time" power="1" scale="1.0"/>
<Unit symbol="ms" dimension="time" power="-3" scale="1.0"/>
<ComponentType name="lorenz1963" description="The Lorenz system is a simplified model for atomspheric convection, derived from the Navier Stokes equations">
<Parameter name="sigma" dimension="none" description="Prandtl Number"/>
<Parameter name="beta" dimension="none" description="Also named b elsewhere"/>
<Parameter name="rho" dimension="none" description="Related to the Rayleigh number, also named r elsewhere"/>
<Parameter name="x0" dimension="none"/>
<Parameter name="y0" dimension="none"/>
<Parameter name="z0" dimension="none"/>
<Constant name="sec" value="1s" dimension="time"/>
<Exposure name="x" dimension="none"/>
<Exposure name="y" dimension="none"/>
<Exposure name="z" dimension="none"/>
<Dynamics>
<StateVariable name="x" dimension="none" exposure="x"/>
<StateVariable name="y" dimension="none" exposure="y"/>
<StateVariable name="z" dimension="none" exposure="z"/>
<TimeDerivative variable="x" value="( sigma * (y - x)) / sec"/>
<TimeDerivative variable="y" value="( rho * x - y - x * z ) / sec"/>
<TimeDerivative variable="z" value="( x * y - beta * z) / sec"/>
<OnStart>
<StateAssignment variable="x" value="x0"/>
<StateAssignment variable="y" value="y0"/>
<StateAssignment variable="z" value="z0"/>
</OnStart>
</Dynamics>
</ComponentType>
<Component id="lorenzCell" type="lorenz1963" sigma="10" beta="2.67" rho="28" x0="1.0" y0="1.0" z0="1.0"/>
</Lems>


We strongly suggest that users use the Python tools when working with both NeuroML and LEMS. Not only is Python easier to read and write than XML, it also provides powerful programming constructs and has a rich ecosystem of scientific software.

## Examples#

Here are some examples of Components written using LEMS to extend NeuroML that can be used as references.