docs: add description of simulator

docs/source/simulator/index.rst

@@ -2,16 +2,24 @@
 Simulator
 *********
 
-This module hosts functionality for running simulators, as well as some
-simulators used in the landslide community.
+A `simulator` essentially represents a mapping from an input space :math:`\mathcal{X}`
+to an output space :math:`\mathcal{Y}`. More specifically, given a simulator
+:math:`\mathbf{y}=\mathbf{f}(\mathbf{x})`, it maps a :math:`p`-dimensional input
+:math:`\mathbf{x} \in \mathcal{X} \subset{\mathbb{R}^p}` to a :math:`k`-dimensional output
+:math:`\mathbf{y} \in \mathcal{Y} \subset{\mathbb{R}^k}`.
+The mapping :math:`\mathbf{f}` can vary from simple linear equations which can be analytically
+solved to complex partial differential equations which requires numerical schemes such as
+finite element methods.
 
-Currently implemented classes are:
+This module hosts functionality for running simulators, as well as some
+simulators used to model landslide run-out processes. Currently implemented
+classes are:
 
-* :class:`.RunSimulator`:
+* :class:`.RunSimulator`: Serial and parallel execution for simulators defined by the user.
 
-* :class:`.MassPointModel`:
+* :class:`.MassPointModel`: Mass point model for landslide run-out simulation.
 
-* :class:`.Ravaflow24Mixture`:
+* :class:`.Ravaflow24Mixture`: Voellmy-type shallow flow model for landslide run-out simulation.
 
 .. toctree::
    :maxdepth: 1