The lower the energy, the higher the similarity between simulated and reference
density.
+Adaptive force constant scaling
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+To enable a steady increase in similarity between reference and simulated
+density while using as little force as possible, adaptive force scaling
+decreases the force constant when similarity increases and vice versa. To avoid
+large fluctuations in the force constant, change in similarity is measured
+with an exponential moving average that smoothens the time series of similarity
+measures with a time constant :math:`tau` that is given in ps. If the exponential
+moving average similarity increases, the force constant is scaled down by
+dividing by :math:`1+\delta t_{\mathrm{density}}/tau`, where
+:math:`\delta t_{\mathrm{density}}` is the time between density guided simulation steps.
+Reversely, if similarity between reference and simulated density is decreasing,
+the force constant is increased by multiplying by :math:`1+\delta t_{\mathrm{density}}/tau`.
+Note that adaptive force scaling does not conserve energy and will ultimately lead to very high
+forces when similarity cannot be increased further.
+
Future developments
^^^^^^^^^^^^^^^^^^^
(true) Normalize the sum of density voxel values to one for the reference
density as well as the simulated density.
+.. mdp:: density-guided-simulation-adaptive-force-scaling
+
+ (false) Adapt the force constant to ensure a steady increase in similarity
+ between simulated and reference density.
+
+ .. mdp-value: false
+
+ Do not use adaptive force scaling.
+
+ .. mdp-value:: true
+
+ Use adaptive force scaling.
+
+.. mdp:: density-guided-simulation-adaptive-force-scaling-time-constant
+
+ (4) [ps] Couple force constant to increase in similarity with reference density
+ with this time constant. Larger times result in looser coupling.
User defined thingies
^^^^^^^^^^^^^^^^^^^^^