Ticket #145 (new task)
add optimal uncertainty quantification capabilities
Reported by: | mmckerns | Owned by: | mmckerns |
---|---|---|---|
Priority: | major | Milestone: | mystic-0.3a |
Component: | mystic.solvers | Keywords: | |
Cc: |
Description
add optimal uncertainty quantification capabilities
Change History
comment:2 Changed 5 years ago by mmckerns
update the "examples3" code in the UQ branch with the OUQ design of experiments code
comment:3 Changed 4 years ago by mmckerns
- Type changed from idea to task
need improvement on naming conventions used for measures...
comment:4 Changed 4 years ago by mmckerns
Taken directly from from email from Tim Sullivan...
I think that this is a good opportunity to make the mystic structures reflect the mathematics, an investment of time and thought that should pay off in the long run.
"point_mass" / "dirac_measure"
- weight: a scalar, although in advanced implementations we could have vector-valued measures, in which case "weight" would be an array. Suggest default weight = 1.0, for a unit Dirac mass.
- position: an array. More generally, should be able to slot in any data type here: could have measures on the real line (position is a scalar), measures on Euclidean n-dim space (position is a length n array), measures on matrices...
"discrete_measure"
- corresponds to the sum of finitely many point_mass objects with compatible (same-dimensional) position arrays
- weights: a list of the weights of the constituent point masses
- positions: a list of the positions of the constituent point masses
- support: the subset of the positions for which the associated weight is non-zero. Perhaps have a tol here.
- get_center_of_mass: \sum_{i} w_{i} x_{i}, where the w_{i} are the weights and the x_{i} are the positions
- set_center_of_mass: ...
- get_expect(f): when f is a function that takes arrays of dimensionality = dimensionality of the positions of the point masses, returns \sum_{i} w_{i} f(x_{i}).
- set_expect(f): ...
- get_max(f): returns the maximum of f(x_{i}) among x_{i} in positions
- get_ess_mas(f): returns the maximum of f(x_{i}) among x_{i} in support
- get_min(f): returns the minimum of f(x_{i}) among x_{i} in positions
- get_ess_min(f): returns the minimum of f(x_{i}) among x_{i} in support
- set_max(f) ...
"discrete_product_measure"
- corresponds to the measure-theoretic product of finitely many discrete measures (the "marginals")
- should be declared by listing the marginal discrete_measure objects in a list, as we do now
- weights
- positions
- support
- center_of_mass: the list/array whose kth entry is the center_of_mass of the kth marginal
- get_expect(f), set_expect(f), get_max(f), set_max(f)...
- ...
Note: See
TracTickets for help on using
tickets.
fairly stable (in the UQ branch)... but needs work on interface and merge into trunk