PhytoSim Calibration
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PhytoSim Calibration User Guide

The Calibration module can be used to automatically fit a model to measured data. The model can be fitted to the entire dataset or to parts of the data using a moving window approach. Calibration is also sometimes called parameterisation or parameter estimation. An optimization algorithm is used in order to minimize the difference between the model simulations and the measured data by changing model parameter or derived variable initial values. The Calibration module will use the current simulation as configured in the Simulation module to perform the model evaluations.

PhytoSim calibration optimizer variables

Additionally, a confidence information calculation can also be performed giving you an indication of the error of the estimated values and the correlations between the optimizer variables.

Why you will like this module:

  • Automatic calibration: If you recognize following situation, then this module is for you.

      - Let's change this parameter...

      - Ok, now we do a simulation...

      - Let's have a look at the results...

      - Mmm, not quite there yet, let's change the parameter a bit more...

      - Running another simulation...

      - Oh oh, that made it worse...

      - Mmm, maybe I'll change another parameter...

      - ...

  • Confidence information: Obtain estimation errors and the correlation matrix.
  • Compilation free modelling: Immediately start calibrating a changed model.
  • Automatic unit conversions: Differences between model and calibration data units are automatically resolved.
  • Calibration progress visualization: (suspense guaranteed :-))
    • See how your estimated parameters and/or initial conditions evolve during the optimization.
    • Watch how the model simulations get closer to the measured data.
    • Follow the objective value while it creeps closer to zero.

Optimizer Variables

Optimizer variables are model quantities (parameters or derived variable initial conditions) that the optimization algorithm is allowed to change in order to minimize the difference between measurements and simulation. They are allowed to take continuous or discrete values bounded by a minimum and maximum value.

More details in the Calibration User Guide.

PhytoSim calibration optimizer variables

Objective Variables

Objective variables are model components for which measured data is available and which will be used to calibrate the model. The Calibration module uses a weighted sum of squared errors objective value to minimize the difference between the measured data and the simulated values.

More details in the Calibration User Guide.

PhytoSim calibration objective variables

Confidence Information

A confidence information calculation can be performed in order to get an indication of the error of the estimated values and the parameter correlations. The cornerstone of the confidence information is the estimation covariance matrix which is calculated using a nested Richardson extrapolation finite difference approach. Based on the covariance matrix, relative standard errors and the correlation matrix are calculated.

More details in the Calibration User Guide.

Confidence information

Built-in optimizers:

  • Simplex (local search): Also known as the Nelder-Mead method or downhill simplex method or amoeba method. For more information see:

  • Shuffled Complex Evolution (global search): The SCE method is based on a synthesis of four concepts that have proved successful for global optimization: (a) combination of probabilistic and deterministic approaches; (b) clustering; (c) systematic evolution of a complex of points spanning the space, in the direction of global improvement; and (d) competitive evolution. See also Duan et al. (1993).

  • Simulated Annealing (global search): The simulated annealing algorithm models the physical process of heating a material and then slowly lowering the temperature to decrease defects, thus minimizing the system energy. At each iteration (temperature) of the simulated annealing algorithm, a new point is randomly generated in the search space. The extent of the search performed at this point is proportional to the temperature. The algorithm accepts all new points that lower the objective, but also, with a certain probability, points that raise the objective. By accepting points that raise the objective, the algorithm avoids being trapped in local minima and is able to explore globally for better solutions. See also Cardoso et al. (1996).

  • Grid search (global search): Based on the optimizer variable bounds and the number of required intervals a search grid is constructed. At each point of the grid, a model evaluation is performed and the objective evaluated. Strickly speaking this is not a true optimization but it can be useful as a first exploration of the search space.

  • Random search (global search): Not really a search algorithm but generates a number of random samples from the intervals and evaluates the objective value at these points. This algorithm can be useful to quickly scan the optimizer variable space for global minima. Any global optimizer should perform significantly better than this algorithm.

  • Single shot (single evaluation): The objective is evaluated once at the initial values of the optimizer variables.

Dependencies (modules required by this module):

    Can't find the optimizer you are looking for?

    Contact and, if possible, we will be happy to implement it.