Glossary

Key terms

  • Extreme Response Distribtuion (ERD): Distribution of the largest response experienced over a timeframe. e.g distribution of the largest reponse a windturbine will experience in 20 years of operatation.

  • period: A sample of the environment for the timeframe of interest. e.g 20 years worth of samples of the env dist.

    • n_periods The number of these periods.

    • period_len: the number of samples require to create timeframe of interest.

      • e.g timeframe is 1 year, and env samples are for 1 day, then period_len=365.25

  • environment distribution (env_dist):

Dimension Notation:

The ax stack (ax, botorch, gpytorch, pytorch) comprises of a number of libraries, each with their own notation. As axtreme interacts with differrent parts of this stack, it is useful to know the different conventions. axtreme uses botorch tensor notation unless otherwise specifiec.

Botorch tensor notation.

key terms that we make use of that we should define:

  • Dimension convension used by (botorch)[https://botorch.org/api/models.html#botorch.models.gp_regression.SingleTaskGP]

    • X: input data

    • batch_shape: (*b) batch shape. Varying number of dimensions (including 0)

    • n: input points.

    • m: target/output dimensionality

    • d: dimensionality of input points.

  • Optimisation:

    • q: number of candidate points optimised jointly.

    • t: number of points passed to optimise in parrallel (not optimised jointly)

  • The dimension convension used by gpytorch

    • (..., b1 x ... x bk): batch shape

    • n: input points.

    • t: target/output dimensionality

    • d: dimensionality of input points.

TODO

Glossary task to be added

Explain how:

  • Multitask in gpytorch can be used with SingleTaskGP