Previous generation survey: SDSS
Current generation survey: DES
LSST precursor survey: HSC
We want to solve for the Maximum A Posterior solution:
$$\arg \max - \frac{1}{2} \parallel {\color{Orchid} y} - {\color{SkyBlue} x} \parallel_2^2 + \log p_\theta({\color{SkyBlue} x})$$ This can be done by gradient descent as long as one has access to the score function $\frac{\color{orange} d \color{orange}\log \color{orange}p\color{orange}(\color{orange}x\color{orange})}{\color{orange} d \color{orange}x}$.$\Longrightarrow$ We can see which parts of the image are well constrained by data, and which regions are uncertain.
import tensorflow as tf
import flowpm
# Defines integration steps
stages = np.linspace(0.1, 1.0, 10, endpoint=True)
initial_conds = flowpm.linear_field(32, # size of the cube
100, # Physical size
ipklin, # Initial powerspectrum
batch_size=16)
# Sample particles and displace them by LPT
state = flowpm.lpt_init(initial_conds, a0=0.1)
# Evolve particles down to z=0
final_state = flowpm.nbody(state, stages, 32)
# Retrieve final density field
final_field = flowpm.cic_paint(tf.zeros_like(initial_conditions),
final_state[0])
Thank you !