Glossary¶

Key terms¶

Extreme Response Distribution (ERD): Distribution of the largest response experienced over a timeframe. e.g. distribution of the largest response a wind turbine will experience in 20 years of operation.
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 required to create the timeframe of interest.
  - e.g. timeframe is 1 year, and env samples are for 1 day, then period_len=365.25
problem space: Refers to the input variables and responses before any transforms/standardization have occurred. For example ax.ModelBridge operates in the problem space because it takes raw/untransformed x value and produce raw/untransformed y values.
model space: Refers to the input variables and responses after transforms/standardization have occurred. Typically \(x\) inputs are scaled to unit hypercube, and y values are standardized. For example ax.Model (found at ModelBridge.model.surrogate.model) operate in this space.

Dimension notation¶

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

Botorch tensor notation¶

See for example: (SingleTaskGP)[https://botorch.readthedocs.io/en/latest/_modules/botorch/models/gp_regression.html]

Dimension convention:
- 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
Optimization:
- q: number of candidate points optimized jointly
- t: number of points passed to optimize in parallel (not optimized jointly)

gpytorch notation¶

Dimension convention:
- (..., b1 x ... x bk): batch shape
- n: input points
- t: target/output dimensionality
- d: dimensionality of input points