12.9 Gaussian Processes and Neural Networks

Core idea¶

Gaussian Processes and Neural Networks must be treated as a system-level decision rather than an isolated technique. For a floating wind turbine modeled in OpenFAST and with reduced, LPV, and derivative-function surrogates, state what is fixed, what is optimized, what information is available, and what equations define feasibility.

The relevant quantities are high-fidelity $F_H$, surrogate $F_L$, design $p,c$, and model error $e_M$. The chapter-level formulation is

For this section, trace how the choice changes optimization, the active constraints, and the implementable engineering design. A method is useful only when its assumptions are explicit and its result answers the same system question as the baseline.

Engineering interpretation¶

Ask three questions:

1. Which physical, informational, computational, or economic resource changed?

2. Which objective component or active constraint made the change valuable?

3. Does the conclusion survive model, disturbance, initialization, uncertainty, and implementation checks?

A practical action is to validate trajectories. Record units and assumptions before optimization, report component objectives and margins afterward, and verify the result using an independent calculation or higher-fidelity model.

Activity 12.9: quantify gaussian processes and neural networks¶