3 primary components in modeling
 Variable
 Distribution
 Function
Center for Statistics and Machine Learning, Princeton
On Governors, James Clerk Maxwell 1868
\[\text{data} + \text{model} \stackrel{\text{compute}}{\rightarrow} \text{prediction}\]

\[\text{data} + \text{model} \stackrel{\text{compute}}{\rightarrow} \text{prediction}\] 
Work Leah Hirst, Software Engineering Intern and Cliff McCollum.
Tutorial on emulation.
Uncertainty quantification (UQ) is the science of quantitative characterization and reduction of uncertainties in both computational and real world applications. It tries to determine how likely certain outcomes are if some aspects of the system are not exactly known.
Designing an F1 Car requires CFD, Wind Tunnel, Track Testing etc.
How to combine them?
\[ \mathbf{ x}_{t+1} = f(\mathbf{ x}_{t},\textbf{u}_{t}) \] where \(\textbf{u}_t\) is the action force, \(\mathbf{ x}_t = (p_t, v_t)\) is the vehicle state
\[ \mathbf{ x}_{t+1} =g(\mathbf{ x}_{t},\textbf{u}_{t}) \]
\[ f_i\left(\mathbf{ x}\right) = \rho f_{i1}\left(\mathbf{ x}\right) + \delta_i\left(\mathbf{ x}\right), \]
\[ f_i\left(\mathbf{ x}\right) = g_{i}\left(f_{i1}\left(\mathbf{ x}\right)\right) + \delta_i\left(\mathbf{ x}\right), \]
n_initial_points = 25 random_design = RandomDesign(design_space) initial_design = random_design.get_samples(n_initial_points) acquisition = GPyOpt.acquisitions.AcquisitionEI(model, design_space, optimizer=aquisition_optimizer) evaluator = GPyOpt.core.evaluators.Sequential(acquisition)}
250 observations of high fidelity simulator and 250 of the low fidelity simulator
Introduce your own surrogate models.
To building your own model see this notebook.
\ericMeissner{15%}\zhenwenDai{15%}


We need both
Modelling
Inference
log_pdf
draw_samples
PILCO (Deisenroth and Rasmussen, n.d.) is a modelbased dataefficient algorithm that solves the RL problem by the following two step iterative process:
\[ p(y_{t+1}y_t, a_t) \]
Policy after the first episode (random exploration):
Policy after the 5th episode: