Update README.md

Author: dimitra-maoutsa

README.md

@@ -11,7 +11,7 @@ Link to extended preprint: [http://arxiv.org/abs/2112.05735](http://arxiv.org/ab
 </p>
 
 
-## The main functionality: `DPFC`
+## Main functionality: `DPFC`
 
 To obtain the time dependent control functions create an instance of `DPFC`
 ```python
@@ -28,10 +28,14 @@ where
 -  `reweight`: boolean indicating whether reweighting of forward trajectories is necessary, i.e. when:
    - path constraints are relevant for the problem,
    - the target is a non typical system state and the forward flow will be sampled as a reweighted Brownian bridge,
-- `U`        : function handle representing the path constraints, i.e. <img src="https://render.githubusercontent.com/render/math?math=U(x,t) = ( x - sin(t) )^2"> ,
+- `U`        : function handle representing the path constraints, i.e. <img src="https://render.githubusercontent.com/render/math?math=U(x,t) = ( x - sin(t) )^2"> , for                      pushing the controlled trajectories towards the sin(t) line. Expects two arguments, so even if path constraint is non timedependent add an extra dummy variable                in the argument list, 
 - `dens_est` : idicator determining the method to be employed for the logarithmic gradient (score) estimation. Currently supported:
   - `nonparametric` : for nonparametric sparse kernel estimation, 
 - `reject`   : boolean variable determining whether rejection of backward trajectories failing to reach the initial condition will take place 
                (this is mostly used as an indicator of numerical instabilities - if everything runs smoothly 1 or 2 trajectories need to be deleted, but often none of them
                if more trajectories get deleted, then rerun the computation with more particles N)
-- 
+- `kern`     : the kernel that will be employed for the nonparametric logarithmic gradient estimation of the sampled densities. Currently supported:
+   - `RBF` : radial basis function kernel with lengthscale estimated at every time step from the samples,
+
+- `f_true`   : function handler of system drift function when  the reweighted Brownian bridge functionality for forward sampling is used. In that case, `f` should be supplied with the drift function of the brownian bridge, `U` should be set to the necessary path constraint (see paper), and `reweight` and `brown_bridge` should be turned to True,
+- `brown_bridge`: boolean variable indicating whether the sampling of the forward flow will happen with reweighted Brownian bridge dynamics.