Model Calibration

Question 1

calibration
- definition
- assumptions
- methods

Answer 1

finding parameters that allow the model to match observations

required for parameters that have physical meaning as well, often from a lack of data

Assumes correct equations, forcing and initial conditions

Methods:
- manual
—- allows for expert judgment
—- slow
—-subjective

• automatic
  —- requires optimisation function (describes goodness of fit like least squares and average relative bias ) and algorithm (finds param to min/max obj func)

Question 2

parameter interaction definition

Answer 2

• concern for automatic calibration
• different parameter sets can achieve about the same results since some have a similar effect
• leads to uncertainty about the best set, also concerns of local optima

Question 3

algorithm options

Answer 3

Downhill simplex
- simplex formed of points in parameter space
- order func value at each point
- calc simple centroid excluding the worst one
- reflect worst point about C
- transformation
—- expansion if reflection better than previous best
—- contraction is reflection now worst point
—- shrink if no improvement with expansion or contraction

Steepest descent
- always finds the local optimum but cant guarantee it is global
- required numerical differentiation since dx is proportional to - f’(x)

Newtons method
- recursive algorithm based on more than 1st derivative
- derivatives found numerically thus Quasi-Newtonian
- requires Hession matrix to generalise to n dimensions
- less steps but more clac/step that steepest descent

Global search
- approximates global optimum
- high accuracy needs high computational effort
- can be combined with random search
—- for accuracy N points sales with m dimensions as N^(m)
—- can be combined with gradient descent

Genetic algorithm steps
- random sample
- calc each individuals goodness of fit
- stop or select best individuals
—- elite = straight to next gen
—- crossover = combination
—- mutation = random alteration, done to some from crossover
- calc the goodness of fit of each individual from the new gen

Question 4

constrained minimization

Answer 4

done using barrier function