Machine Learning Enables Real-Time Waveform Decomposition for Dual-Readout Calorimetry

This paper demonstrates that machine learning models can effectively separate Cherenkov and scintillation signals in dual-readout calorimeters at lower sampling rates with FPGA-compatible latency, offering a practical real-time alternative to traditional template fitting for future Higgs factory detectors.

The Gist

Imagine you are trying to listen to a duet where two musicians are playing at the exact same time. One musician (the Cherenkov light) plays a very short, sharp "ping" that happens instantly. The other musician (the scintillation light) plays a long, slow, fading hum that lasts for a while.

In the world of particle physics, scientists use special crystals to catch these "notes" from subatomic particles. To understand what the particle was, they need to figure out exactly how much of the "ping" and how much of the "hum" were in the mix. This is called Dual-Readout Calorimetry.

Here is the problem: In the future, these particle detectors will be so busy that they will produce a massive flood of data. If they try to record every single tiny detail of the sound wave (the waveform) to separate the two musicians, the data stream will be so huge it will clog the system, like trying to download a movie in 4K resolution over a dial-up connection.

The Old Way: The Slow, Careful Detective
Traditionally, scientists have used a method called Template Fitting. Imagine a detective who has a library of perfect recordings of the "ping" and the "hum." When a new, messy recording comes in, the detective tries to mathematically adjust the volume of the perfect recordings until they match the messy one.

• The Catch: This detective is very thorough but very slow. They have to do complex math for every single recording. If the recording is low-quality (low sampling rate), the detective gets confused and makes mistakes. To get good results, they need a super-fast, high-definition recording, which creates that massive data flood problem.

The New Way: The AI Musician
This paper introduces a new approach using Machine Learning (ML). Instead of a slow detective, they trained a compact AI (a neural network) to listen to the messy recording and instantly guess the volume of the "ping" and the "hum."

• The Magic: The AI is like a seasoned musician who has heard thousands of these duets. Even if the recording is fuzzy or low-quality (low sampling rate), the AI can still tell the difference between the sharp "ping" and the slow "hum" almost instantly.

What the Paper Found
The researchers tested this AI on three different types of crystal "instruments" (BGO, BSO, and PWO), each with different sound characteristics:

1. Speed vs. Quality: The AI could work with recordings that were much lower quality (lower sampling rates) than the old detective method. Even with a "fuzzy" recording, the AI was just as accurate as the detective was with a "crystal clear" recording.
2. One Size Fits All: They trained one single AI model on a mix of different particle energies (from weak to strong). This one model worked perfectly across the board, meaning they don't need to retrain it for every new situation.
3. Fitting in the Pocket (FPGA): The most exciting part is that the AI is small and efficient enough to be built directly into the detector's electronics (specifically, a chip called an FPGA). This means the detector can do the "listening" and "separating" right at the source, before the data even leaves the machine. This drastically cuts down the amount of data that needs to be sent out.

The Bottom Line
The paper proves that by using a smart, compact AI, we can separate these two types of light signals much more efficiently than before. This allows future particle detectors to be "smarter" at the source, handling massive amounts of data without getting overwhelmed, which is crucial for the next generation of particle colliders.

Technical Summary

1. Problem Statement

Dual-readout calorimeters are a leading technology for future high-energy physics experiments (e.g., FCC-ee) because they simultaneously measure Cherenkov (C) and scintillation (S) light. This dual measurement allows for event-by-event correction of the electromagnetic fraction, significantly improving hadronic energy resolution.

However, extracting these two components from a composite signal presents significant challenges:

• Signal Overlap: Cherenkov light is prompt, while scintillation light has a slower, crystal-dependent decay. Separating them requires analyzing the temporal shape of the waveform.
• Data Rate Bottleneck: Traditional template fitting methods require high sampling rates (e.g., 3.125 GHz) to accurately resolve the waveform shape. At high-luminosity colliders, reading out full waveforms at these rates generates prohibitive data volumes and power consumption.
• Computational Cost: Template fitting involves iterative minimization (e.g., Simplex/MIGRAD algorithms), which is computationally expensive and incompatible with real-time processing in front-end electronics.
• Performance Degradation: Reducing the sampling rate to save bandwidth causes template fitting performance to degrade rapidly, as the waveform becomes under-constrained for multi-parameter optimization.

The paper addresses the need for a real-time, low-latency, and bandwidth-efficient method to decompose these waveforms directly in the front-end electronics (Edge Machine Learning).

2. Methodology

The authors propose replacing conventional template fitting with compact Deep Neural Networks (DNNs) deployed on Field-Programmable Gate Arrays (FPGAs).

A. Simulation and Data Generation

• Detector Model: A hybrid dual-readout calorimeter (homogeneous crystal ECAL + sampling HCAL) was simulated using Geant4.
• Crystals Studied: Three representative crystals with distinct decay characteristics were used:
  • BGO: High light yield, very slow decay (dominant 320 ns tail).
  • BSO: Moderate yield, bi-exponential decay.
  • PWO: Fast decay, strong temporal overlap with Cherenkov light.
• Waveform Synthesis: Composite waveforms were generated by convolving photon arrival times (Cherenkov vs. Scintillation) with Single Photon Response (SPR) templates. Noise sources included SiPM dark counts and random time shifts ($t_0$) to simulate timing variations.
• Ground Truth: Each waveform was labeled with the true number of Cherenkov photons ($c$), scintillation photons ($s$), and time offset ($t_0$).

B. Machine Learning Architecture

• Model Type: A compact, fully-connected neural network (FCNN).
• Architecture: Input $\to$ FC(16, ReLU) $\to$ FC(24, ReLU) $\to$ FC(8, ReLU) $\to$ FC(3, Linear).
• Task: Direct regression of parameters $(c, s, t_0)$ from the digitized waveform in a single forward pass.
• Training Strategy:
  • Trained on a combined dataset of electrons and neutral kaons across multiple energies (1, 5, 10, 30 GeV) to ensure energy independence.
  • Loss function: Weighted Mean Squared Error (MSE) with weights $(4.0, 1.0, 0.3)$ to prioritize photon count accuracy over timing.
  • Downsampling: Baseline 3.125 GHz waveforms were downsampled by factors of 10, 20, 50, and 300 (down to 10.4 MHz) to evaluate performance at reduced data rates.

C. FPGA Deployment

• Synthesis: Models were converted to hardware using hls4ml (High-Level Synthesis).
• Optimization: To fit within FPGA resources, the authors applied magnitude-based pruning and Quantization-Aware Training (QAT).
• Quantization: Fixed-point arithmetic was used to eliminate the need for DSP blocks, relying instead on shift-and-add operations.

3. Key Contributions

1. Systematic Comparison: The first rigorous comparison between template fitting and ML for dual-readout waveform decomposition across three distinct crystal types.
2. Low-Rate Superiority: Demonstrated that ML models can achieve comparable or superior accuracy to template fitting at significantly reduced sampling rates (e.g., 10.4 MHz vs. 3.125 GHz).
3. Universal Model: Showed that a single model trained on a wide energy range (1–30 GeV) generalizes robustly without retraining, a critical requirement for collider environments.
4. Hardware Feasibility: Proved that compressed ML models can be synthesized into FPGA firmware with latencies < 25 ns and resource utilization suitable for real-time front-end processing (30k–330k LUTs).

4. Key Results

Performance vs. Sampling Rate

• Photon Count Extraction: At the lowest sampling rate (10.4 MHz), the ML approach achieved a 68th percentile error ($err_{68}$) of ~5% for Cherenkov and Scintillation counts. This performance matched or exceeded template fitting running at the full 3.125 GHz baseline.
• Timing Extraction: While ML at 10.4 MHz could not surpass template fitting at 3.125 GHz (due to fundamental information loss from undersampling), it significantly outperformed template fitting when both were run at the same low rate (10.4 MHz).
• Crystal Specifics:
  • BGO: ML excelled at separating the small Cherenkov signal from the overwhelming scintillation tail.
  • PWO: Despite the severe temporal overlap, ML maintained competitive performance at low rates where template fitting failed.

Resource Efficiency (FPGA)

• Latency: All compressed models achieved inference latencies of 25 ns, compatible with FCC-ee bunch crossing rates.
• Resources:
  • 10.4 MHz models: ~30k LUTs, 213 FFs, 0 DSPs.
  • 312.5 MHz models: ~310k LUTs, ~4k FFs, 0 DSPs.
• Trade-off: The Pareto frontier analysis showed that substantial computational savings are possible by selecting lower sampling rates without sacrificing physics performance.

Generalization

• The multi-energy trained model successfully reconstructed events across the full energy spectrum (1–30 GeV) without degradation, validating its use for unknown beam energies.

5. Significance

This work establishes Edge Machine Learning as a viable and superior alternative to traditional template fitting for dual-readout calorimetry.

• Data Rate Mitigation: By enabling accurate signal extraction at sampling rates 100x–300x lower than currently required, ML drastically reduces the data bandwidth and power consumption of the readout system.
• Real-Time Processing: The ability to perform complex waveform decomposition directly on the detector (on-FPGA) enables "smart" detectors capable of intelligent feature extraction before data leaves the detector.
• Future Impact: This approach provides a practical pathway for implementing dual-readout calorimetry in next-generation Higgs factories (like FCC-ee), where high-luminosity data rates would otherwise make full waveform readout impossible.