AIEC FCAL Simulation Q-Learning

Overview

It has been difficult to find correlations between the LED amplitudes for FCAL blocks and existing pi0-based calibrations. We are limited by the amount and type of information in the experimental data. One possible way to gain insight is to simulate the model we assume for the FCAL LED responses and see if a model can be trained to extract the configuration parameters.

Here is the currently assumed model:

$A(i,t)=g_{i,t}^{-1}\omega _{i}\alpha _{t}R_{i,t}$

i	block number
$t$	time (could be be actual time or run number)
$A_{i,t}$	Amplitude of ADC readout for block i at time t
$g_{i,t}$	Gain of block i at time t
$\omega _{i}$	Optical coupling of block i (no time dependence)
$\alpha _{t}$	Amplitude of LED pulser (no block dependence)
$R_{i,t}$	Radiation damage (integrated) to block i at time t. (assume to be "1" for now)

Setup

1. Simulation should stat with small, but configurable sample of blocks. Say, 50.
2. Simulation should sample a set