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Detector Inverse Solver (DIS) using a differentiable simulator

February 4, 2023 Machine Learning for Neutrino Oscillation Experiments 2

G (X|Y, 𝜃G)

Inverse Image Solver (DIS)

Input domain of detector simulator

(inaccessible)

Output domain of detector simulator

(e.g. real data)

F (Y|X, 𝜃F)

Differentiable Detector Simulator (DDSim)

and / or

OK, this would be the last slide to describe our ideas. So far, we have focused on the simulator and how to optimize against real data in an end-to-end manner, which can automate calibration analysis. But there are more powerful applications to be enabled, and this slide shows one of them included in our proposal.

This diagram shows two functions F and G. These functions bridge two data domains X and Y, namely the input and output of a detector physics model. The detector physics simulator is this function F, which takes in simulated particle information and outputs the detector-like data. We call this a forward pass.

The inverse pass is this function G which takes in detector data and outputs underlying physics information that would produce the same detector output if forward mapping F is applied. An example of G is a data reconstruction algorithm.

Now, usually G is developed and optimized using simulations where data in the input domain X is available. This potentially bias G and could result in a poorer performance when applied on real data due to discrepancies in the data and simulation. This is particularly problematic when G is a deep learning algorithm which is capable of learning detailed features in data, and this is also a common challenge for neutrino experiments in the U.S. and Japan. To address this challenge, we propose a new paradigm in which G can be optimized directly on real data. Suppose we have a real data which belongs to the domain Y, and we apply G to obtain a corresponding instance in the domain X. Then we apply F and produce a corresponding instance in Y again. We can calculate a discrepancy metric on this and the original data instance in the domain Y, and optimize G to minimize this metric. This can be done because the loss calculated in Y can be back propagated through F as F is differentiable. In principle, this allows G to be optimized using real data. Furthermore, the introduction of F in this optimization process forces G to learn an inverse mapping which respects the forward detector physics model. This is a type of physics-informed machine learning technique. Our team involves leading experts for developing the deep learning application for data reconstruction for neutrino experiments, and we are excited to work on this project. Lastly I would like to mention that this kind of inverse function that unfold the detector effects is particularly impactful for neutrino oscillation experiments where physics strongly depends on comparison of the near and the far data without detector specific effects.

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Differentiable Simulators (DDSims)

February 4, 2023 Machine Learning for Neutrino Oscillation Experiments 3

2) Explicit Physics Parameterization

JAX�
Omar, César

1) Implicit Neural Representation

SIREN�
Junjie, Ryo, �Ryotaro, �Ka Ming

physics model parameters

𝜽

Input

Output

F (x|𝜽)

Optimization target

L ( F (x|𝜽), y)

Approximated gradient

Exact gradient

Gradient-based optimization

Simulation Packages

SimpleSim (César)
WCSim (Ka Ming, Patrick)

Computing (Zhe, Kazu)

(Need help from all!)

Later: real calibration data

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Explicit Physics Parameterization

Great progress switching to JAX!��On the way towards physics parameter fitting → Goal: reproduce SK analysis pipeline

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Optical SIREN Tasks

Simulation Pipeline

Parallelize DataLoader [Junjie]

Scale up to full sample

Investigate simulation artifacts [Ka Ming]

Two 0-pixels (probably dataloader)
Edge effects (e.g. from shotgun sims)�

Sample generation

Analysis and validation [Junjie]

Automate script for checking distribution uniformity and output good/bad

Make wcprod pipeline work on:

HK (EU-) GRID [Ryo]
KEK [César]
IPMU [Patrick]
sukap [Ka Ming]
Debug cedar 30% stalling [Zhe]

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Optical SIREN Tasks

SIREN Development

Complete toolchain and optimization

Loss function definition (type and weighting) [Ryo]
Hyperparameters (# and size of layers, LR): WandB [Ryotaro?]

Needs full dataset, but pipeline can be now
Framework can also be useful for Physics SIREN

Training and performance analysis [Junjie, ?]

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Reconstruction Options

Need to prioritize goals to allocate personpower:

Continue developing fiTQun-like (initial parameter) reconstruction

Followed by intermediate track segment reconstruction

Switch to WatChMaL

Intermediate (track) output from WatChMaL?

Any other ideas? Please write your own pipeline for review in 2 weeks!

E.g. In this Overleaf, Junjie and I have written the current idea

Though Ryo already debunked my segment reconstruction for EM showers
Need some way to incorporate event-by-event stochasticity

Pause development and focus on Optical SIREN

Consider small effort on Physics SIREN with new student(s)