Computer Experiments Flashcards
What do we mean by a computer experiment?
- A lot of science is done by computer modelling (in silico)
- These models (simulators) often consist of a number of Partial Differential Equations (PDE’s) that are solved numerically.
- Such simulators are often computationally very expensive
Deterministic Computer Experiments
- These simulators are usually deterministic (same input => same output)
- There are a number of inputs to the simulator (parameters, initial conditions, boundary conditions)
What types of uncertainty exists in Simulators
- Uncertainty in the underlying science
- Uncertainty in the solution of the equations (the discretisation etc)
- These two are known as structural uncertainty
- Uncertainty in the inputs
Whats a emulator
- Run our simulator in a designed experiment to span the input space
- Use a Gaussian process to model the simulator output as a function of its input
- The GP model is known as an emulator
- Because emulators are fast they enable us to do calculations that impossible with the simulator
- They also include an estimate of their own uncertainty
3 appliacations of emulators
Prediction: The emulator is very fast to run so we can quickly predict at new input values
Sensitivity Analysis: How sensitive is the simulator output to a change in an input (or combination of inputs)
Uncertainty Analysis: If we are uncertain about the simulator inputs what does that say about our uncertainty on the outputs
How do we design a set of simulator runs to span input space
Common designs are optimised Latin Hypercubes and quasi-Monte Carlo sequences(Sobol)
What is the Latin Hyper cube
- Decide how many simulator runs you can afford
- Divide each input range into that number of intervals
- Allocate a point to each interval
- Randomly permute across each input
Do Latin Hypercubes fill space on the margins, what about the joints
They fill space on margins but not jointly
