propagate uncertainty for non-linear systems - Githubissues

BreakingBytes / simkit

Model Simulation Framework

http://breakingbytes.github.io/simkit/

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propagate uncertainty for non-linear systems #84

Open mikofski opened 8 years ago

mikofski commented 8 years ago

If equations (or systems of equations) are non-linear or implicit, IE: they can't be solved analytically , how will uncertainty be propagated?

Assuming non-linear equations are written as residuals:

EG 1: non-linear function

y = f_nonlinear(x)
propagating uncertainty in forward direction is easy, but what is it in the reverse direction?
to find x given y find the roots of the following equation
F = f_nonlinear(x) / y - 1.0

EG 2: non-linear and implicit

y = f_nonlinear(x, y)
not analytic in forward or reverse directions
to find x given y or y given x find the roots of the following equation
F = f_nonlinear(x, y) / y - 1.0

EG 3: non-linear and implicit with extra terms

y = f_nonlinear(x, y, a, b, c)
to find x given y, a, b, c or y given x, a, b, c find the roots of the following equation
F = f_nonlinear(x, y, a, b, c) / y - 1.0

idea 1

this would be handled by uncertainty wrapper as long as the formula is written to solve the equation
works for a single formula, although the formula may have multiple inputs and outputs

idea 2

what if we want to combine multiple formulas into a system of equations?
use uncertainty wrapper with a new formulas made from the system of formulas as in idea 1