Hello. On this week,

we will talk about detector design optimization in high energy physics experiments.

But firstly, let's consider why the design optimization is so important.

From the previous weeks,

we have learned that the detectors in

high energy physics experiments are sophisticated and expensive.

These detectors consist of different parts: tracking system,

Ring Image Cherenkov detector,

electromagnetic and hadronic calorimeters, and muon system.

Each of these parts have thousands of sensors,

which register particles, and measure their momentum and energy.

Layout of these sensors affects precision,

efficiency, and cost of these detectors.

Let's consider several examples.

The first example is the LHCb detector.

This is forward-arm detector and registers particles flying only in one direction.

In this example, particles fly from left to right,

and size of the detector systems also increases in same direction.

This solution allows to detect as much particles as possible,

and reduce the detector cost.

The second example is the CMS detector at CERN.

This is a cilindrical detector and registers particles in all directions.

Let's consider a cross-section of this detector.

This slide shows location and size of different systems of the detector.

For example, there are twelve layers in the tracking system.

But why not five or 20?

How to choose the optimal number or why there are only four layers of the muon chambers?

Probably, it's possible to provide

the same detector performance with smaller number of layers.

One more example is the ATLAS detector at CERN.

It has similar structure as the CMS detector.

This slide shows just overview of the detector.

And if you look closer,

you will find two persons in the figure that help to estimate the detector size.

But, in this example,

we will only consider the ATLAS inner tracking system.

The ATLAS inner tracking system consists of

three different parts of different sensor types.

The system consists of three different parts with different sensor types.

The most inner part has three layers of silicon pixel sensors.

These sensors provide the highest precision of particle track reconstruction.

The middle of this system has four layers of the silicon strip sensors.

And the outer part consists of drift straw tubes.

How can we estimate the number of layers and their locations in the system?

On these questions, we will try to find answers on this week.

Now, let's consider the detector optimization workflow.

The goal of the detector optimization is to

find optimal layout of sensors in the detector.

To do this, an objective function for the optimization must be defined.

This function aggregates key values needed to be optimized: cost of the detector,

track resolution, track reconstruction efficiency,

precision of the momentum and efficiency reconstruction, and so on.

Then, a set of parameters that define the sensor layout

and affect the objective function values must be selected.

And finally, search for the parameters

values correspond to the optimum of the objective function.

For an example, consider a simple tracking system.

The goal of this example is to find optimal geometry of the system.

And this geometry can be defined by the set of shifts between the layers.

A possible objective function is the number of hits per one track.

In your programming assignment for this week,

you will be able to find optimal geometry for this tracking system.

More difficult example is the muon shield optimization in the SHiP experiment at CERN.

The goal of the shield is to deflect as much muons as possible.

The shield consist of eight magnets,

and each magnet is parameterized by seven values.

So, there are 42 parameters to optimize.

The objective function depends on the physical performance of the shield and its weight.

We will consider how the shield was optimized in the next videos.

But, which methods can be used for the detector design optimization?

One of the most popular and the simplest method is grid search.

It defines a grid of the parameter values and

calculates the objective function values for each node in the grid.

The node with the highest or least function value is taken as the optimum.

Consider how it works on a 2D example.

In this example, a function with two parameters is optimized.

For this, the parameter values are divided into the grid.

And the node with the highest function value is considered as the optimum.

However, this method has a range of disadvantages.

The first of them is that grid search is reasonable to use when the number of

parameters is small and the grid size

exponentially grows with number of parameters to optimize.

It became more important when the objective function is expensive to evaluate.

Thus, the grid search requires to large computational resources.

Detectors optimization in high energy physics

requires to run Monte-Carlo simulation of these detectors.

Thus, the optimization in high energy physics requires large computational resources.

On this week, we'll learn about the Bayesian optimization.

Bayesian optimization is a method of finding the optimum of an expensive function.

The goal of the Bayesian optimization is to find the optimum of

the objective function using a small number of function calculations as possible.

But before we'll talk about the Bayesian optimization,

I do like to remind you key properties of

normal distribution and to talk about the Gaussian processes for regression.