Xenon Signal Denoising via Supervised, Semi-Supervised, and Unsupervised Models

This study demonstrates that supervised, semi-supervised, and unsupervised machine learning models can effectively denoise simulated single-phase liquid xenon time projection chamber signals to achieve energy resolutions of approximately 1% or better, offering a promising path toward enhancing the sensitivity of neutrinoless double beta decay searches.

The Gist

The Big Picture: Listening for a Whisper in a Storm

Imagine you are trying to hear a single, tiny whisper (a subatomic particle event) in the middle of a massive, roaring hurricane (electronic noise).

This paper is about a team of scientists at Lawrence Livermore National Laboratory who are building a super-advanced "noise-canceling headphone" for a giant particle detector called nEXO. This detector is made of liquid Xenon and is designed to catch a very rare event called Neutrinoless Double Beta Decay. Finding this event would be a massive breakthrough in physics, proving that neutrinos are their own antiparticles and helping us understand why the universe exists.

The problem? The detector is so sensitive that the "whisper" of the particle is often drowned out by static. The scientists wanted to use Artificial Intelligence (AI) to clean up the signal, but they faced a tricky problem: How do you teach an AI to remove noise if you don't have a perfect "clean" recording to compare it to?

The Three AI Strategies

The researchers tested three different ways to train their AI, using a "Supervised," "Unsupervised," and "Semi-Supervised" approach. Here is how they work, using a Music Studio analogy:

1. The Supervised Model (The "Perfect Reference" Student)

• The Setup: Imagine a music student who has a recording of a song played perfectly (the "Clean" signal) and a recording of the same song played through a broken speaker with static (the "Noisy" signal).
• The Training: The student listens to both, learns exactly what the static sounds like, and practices removing it until the noisy version matches the clean one.
• The Result: This model worked the best. It achieved an energy resolution of less than 1%.
• The Catch: In the real world, scientists never have the "perfect clean" recording. They only have the noisy data. So, while this proved the AI could work, it wasn't a realistic solution for actual experiments.

2. The Unsupervised Model (The "Guessing Game" Student)

• The Setup: Now, imagine the student only has the noisy recordings. They have never heard the clean song. They have to guess what the song should sound like just by listening to the static and trying to smooth it out.
• The Training: The AI tries to find patterns in the noise itself. It learns that "noise" is random and "signals" are structured. It tries to average out the chaos without ever seeing the truth.
• The Result: It did okay, but not great. The resolution was around 1.5%. It struggled because without a "truth" to aim for, the AI sometimes got stuck in a local loop, thinking it was doing a good job when it was actually distorting the signal.

3. The Semi-Supervised Model (The "Rough Draft" Student)

• The Setup: This is the clever compromise. The student has a rough, blurry sketch of the song (a simulation that is almost right but has some errors) and the noisy real recording.
• The Training:
  1. First, the AI learns from the rough sketch to get the general idea of the song.
  2. Then, it switches to the real noisy data to fine-tune the details, correcting the mistakes in the sketch using the real-world data.
• The Result: This was the big winner. Even though the "rough sketch" (the simulation) was very inaccurate (up to 55% wrong in some tests), the AI still managed to clean the signal almost as well as the perfect student. It achieved a resolution of ~1%.

Why This Matters: The "Crystal Clear" Breakthrough

The paper compares these AI methods to old-school math tricks (like the "Trapezoidal Filter," which is like trying to clean a muddy window with a squeegee). The old methods were okay, but the AI methods were like using a high-tech laser to remove the dirt without scratching the glass.

• Old Methods: The "Trapezoidal Filter" gave a resolution of 4.5%.
• AI Methods: The best AI models got down to ~1%.

Why does 1% vs 4.5% matter?
In particle physics, energy resolution is like the sharpness of a camera.

• If your camera is blurry (4.5% resolution), a rare event (the whisper) looks like a smudge that could be anything. You might miss it or mistake background noise for a discovery.
• If your camera is sharp (1% resolution), that rare event pops out clearly against the background. It turns a "maybe" into a "definitely."

The Takeaway

The most exciting part of this paper isn't just that AI works; it's that AI works even when you don't know the perfect answer.

The scientists proved that you don't need a perfect simulation of the universe to build a great noise filter. You just need a "good enough" guess (a simulation) and some real data to refine it. This opens the door for the next generation of particle detectors to be much more sensitive, potentially allowing us to finally hear that cosmic whisper and unlock the secrets of the universe.

In short: They taught a computer to clean up a messy signal by letting it learn from a "rough draft" and then fine-tuning itself on the real thing, proving that you don't need perfect knowledge to get perfect results.

Technical Summary

1. Problem Statement

The paper addresses the challenge of improving energy resolution in neutrinoless double-beta decay ($0\nu\beta\beta$) searches, specifically for the proposed nEXO experiment using a single-phase liquid xenon time projection chamber (TPC).

• The Core Issue: Electronic noise in charge collection channels introduces uncertainty in measuring the total charge of an event. Since energy resolution is directly proportional to charge resolution, noise degrades the experiment's sensitivity to rare $0\nu\beta\beta$ events.
• The Challenge: Traditional denoising algorithms (e.g., trapezoidal filters) are limited. Furthermore, while machine learning (ML) offers promise, a critical bottleneck exists: perfect "clean" ground truth data is unavailable in real experiments. All experimental data contains noise.
  • Supervised learning requires paired clean/noisy data, which usually relies on simulations that may not perfectly match reality (sim-to-real gap).
  • Unsupervised learning requires no clean data but often struggles with convergence and achieving optimal performance compared to supervised methods.
• Goal: To develop and evaluate ML denoising algorithms that can significantly reduce noise and improve energy resolution ($\sigma_E/E$) under varying levels of knowledge about the true signal (perfect simulation, imperfect simulation, or no clean data).

2. Methodology

The study utilizes a dataset of $\sim83$ million simulated drift charge detection events from a 32-channel TPC tile. Each event consists of 44,064 dimensions (32 channels $\times$ 1,377 time steps). The noise profile is modeled as colored Gaussian noise ($1/f$ spectrum) with quantization effects.

The authors compare three distinct ML training paradigms using a U-Net architecture (1D convolutions):

A. Supervised Learning

• Data: Paired "clean" (simulation ground truth) and "noisy" (clean + noise) events.
• Model: A U-Net autoencoder trained to minimize Smooth L1 Loss between the prediction and the true signal.
• Rationale: Establishes the theoretical upper bound of performance given perfect signal knowledge.

B. Unsupervised Learning

• Data: Only noisy events (no ground truth available).
• Model: A U-Net trained using Stein's Unbiased Risk Estimator (SURE) loss.
• Technique: Since the noise is colored (not white) and high-dimensional, the authors employ the MC-SURE (Monte Carlo SURE) method. This approximates the divergence term of the SURE loss using Hutchinson trace estimators and finite-difference calculations with random noise probes.
• Challenge: The method struggles with "local minima" (loss basins) and quantization effects, often failing to reach the performance of supervised models.

C. Semi-Supervised Learning (The Proposed Compromise)

• Concept: A two-stage approach designed to mimic real-world experimental constraints where simulations are approximate.
  • Phase I (Supervised): Train on a "distorted" simulation (ground truth modified by a low-pass Gaussian filter to simulate imperfect physics knowledge).
  • Phase II (Unsupervised): Resume training on the exact noisy data (without clean labels) using the SURE loss, initializing weights from Phase I.
• Hypothesis: The supervised phase guides the model toward a better region of the loss landscape, allowing the unsupervised phase to refine the solution using real data characteristics, escaping the suboptimal basins found by purely unsupervised training.
• Distortion Levels: The study tested four levels of signal distortion in Phase I (0.1%, 10%, 30%, and 55% information loss) to test robustness.

D. Baselines

The ML models were compared against:

• Wiener Filter: The theoretical optimal linear filter (requires perfect signal shape knowledge; serves as a bound).
• Trapezoidal Filter: Standard nEXO charge integration method.
• Savitzky-Golay Filter & Visushrink Wavelet Denoising: Conventional signal processing techniques.

3. Key Contributions

1. Multi-Channel Denoising: Unlike previous works focusing on 1D signals, this study denoises 32-channel multivariate time-series data, requiring the model to learn correlations across both time and sensor channels.
2. Semi-Supervised Validation: Demonstrates that a semi-supervised approach can achieve near-supervised performance even when trained on highly inaccurate simulations (up to 55% distortion). This proves that experimentalists do not need perfect simulations to benefit from ML denoising.
3. MC-SURE Implementation: Successfully adapts the MC-SURE method for high-dimensional, colored-noise TPC data, addressing computational feasibility via Hutchinson trace estimation.
4. Performance Benchmarking: Provides a comprehensive comparison of ML vs. traditional methods specifically for $0\nu\beta\beta$ detection, highlighting the limitations of current non-ML techniques.

4. Results

The performance is measured by fractional charge resolution ($\sigma_Q/Q$) and fractional energy resolution ($\sigma_E/E$).

Model Type	$\sigma_Q/Q$	$\sigma_E/E$	Notes
Wiener (Optimal)	0.477%	0.680%	Theoretical limit (not implementable in real time).
Supervised U-Net	0.859%	0.802%	Best ML performance; requires perfect simulation.
Semi-Supervised (0.1% Distortion)	1.014%	0.863%	Near-supervised performance with minor simulation error.
Semi-Supervised (55% Distortion)	2.536%	1.629%	Robust even with very poor simulation approximations.
Unsupervised U-Net	2.773%	1.761%	Struggles to converge to optimal loss basins.
Trapezoidal Filter	4.5%	2.746%	Standard nEXO method.
No Denoising	13.8%	8.230%	Raw noisy data.

• Key Finding: The Supervised model achieves $<1\%$ energy resolution. The Semi-Supervised model achieves $\sim1\%$ resolution even with significant simulation inaccuracies.
• Comparison: All ML methods significantly outperform the Trapezoidal filter (2.746%) and wavelet/Savitzky-Golay methods.
• Unsupervised Limitation: The unsupervised model underperformed ($\sim1.76\%$) due to difficulty escaping local minima in the SURE loss landscape and gradient noise from the MC-SURE approximation.

5. Significance

• Path to Next-Gen Sensitivity: The study proves that ML denoising can push $0\nu\beta\beta$ detectors toward their theoretical sensitivity limits, potentially enabling the discovery of neutrinoless double beta decay.
• Practical Viability: The semi-supervised approach is the most significant contribution for real-world application. It alleviates the "sim-to-real" gap problem, allowing experiments to utilize ML even when their physics simulations are imperfect.
• Methodological Insight: The paper highlights the specific challenges of applying unsupervised learning to high-dimensional, colored-noise physics data, suggesting that hybrid (semi-supervised) approaches are currently the most reliable path forward for particle physics experiments.

In conclusion, this work establishes that machine learning, particularly via semi-supervised strategies, offers a realistic and highly effective path to improving energy resolution in liquid xenon detectors, surpassing traditional signal processing methods by a wide margin.