HydroGEM: Simulation & Data Quality Models

• HydroGEM is a dual-purpose framework that combines physics-informed hydrodynamic simulations for GEM detectors with machine learning for hydrological data quality control.
• The high-energy physics model uses finite-element methods to simulate charged particle transport, avalanche gain, and discharge probabilities with empirical calibration.
• The hydrological model employs a TCN–Transformer architecture to detect anomalies in continental-scale streamflow sensor networks, significantly improving detection F1 scores and reconstruction error.

HydroGEM refers to distinct, domain-specific computational and machine learning models, each named “HydroGEM,” developed for simulation and data quality control in two principal scientific contexts: (1) hydrodynamic simulation of GEM (Gas Electron Multiplier) detectors for high-energy physics, and (2) foundation modeling for continental-scale streamflow sensor data quality control in hydrology. The models share no conceptual lineage beyond their adoption of hybrid, modular, and physically-grounded numerical architectures.

1. Hydrodynamic Modeling of GEM Detectors

In high-energy and nuclear instrumentation, HydroGEM designates a family of axisymmetric finite-element hydrodynamic solvers for simulating charged particle transport, avalanche gain, and space-charge effects within GEM-based gaseous detectors (Rout et al., 2021, Rout et al., 2020). The core dynamical system is governed by Eulerian drift–diffusion–reaction equations for electrons and ions, self-consistently coupled to Poisson’s equation for the evolving electrostatic field:

• Electron continuity:

$$\frac{\partial c_e}{\partial t} + \nabla \cdot [ -D_e \nabla c_e + u_e c_e ] = R_e$$

• Ion continuity:

$$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$

• Poisson equation and electric field:

$$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$

The source terms $R_e, R_i$ combine ionization, attachment, and local photoionization:

$$S_e = [\alpha(E) - \eta(E)] |u_e| c_e, \quad S_{ph} = \xi \, QE_{gas} \, \mu \, \Psi_0$$

with $\alpha(E)$ (Townsend) and $\eta(E)$ (attachment) field-dependent coefficients extracted from Magboltz simulations for Ar–CO$_2$ (70:30) mixtures.

Photoionization is included via a diffusive approximation for photon transport:

$$-\nabla \cdot (c \nabla \Psi_0) + a \Psi_0 = \delta S_e$$

where parameters are derived from CO$_2$ cross-sections.

2. Initial Conditions, Boundary Conditions, and Detector Geometry

HydroGEM models primary ionization induced by particles—e.g., 5.6 MeV $$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$0 particles (Geant4-driven) and 5.9 keV Fe$$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$1 X-rays (HEED)—projecting simulation outputs into an axisymmetric 2D mesh representing a single GEM hole. For realistic event-by-event variability, primaries are radially distributed following a Gaussian spread (mean $$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$2 mm) and sampled in drift $$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$3-position. The electrode configurations reflect operational devices: single and triple GEM stacks under specified voltage gradients and gap dimensions. Axisymmetry treats only the central hole explicitly; lateral holes are approximated via equivalent circular channels and scale factors, introducing $$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$4 systematic uncertainty.

Boundary conditions include:

• Dirichlet voltages for GEM and drift electrodes.
• "Open" (absorbing) conditions for gas–metal interfaces and "no-flux" for dielectric (Kapton) surfaces.

Seed clusters are initialized above the GEM foil with spatial spreads matched to Monte Carlo benchmarks (e.g., $$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$5 for Fe$$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$6).

3. Numerical Implementation and Computational Performance

HydroGEM is implemented as a multiphysics finite-element system in COMSOL, leveraging domain-specific solvers:

• "Transport of Dilute Species" for charge drift–diffusion.
• "Coefficient Form PDE" for photon transport.
• "Electrostatics" for Poisson’s equation.

Time integration employs COMSOL’s built-in BDF implicit solver. Meshes are heavily refined ($$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$7–$$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$8 μm) at GEM rim regions; coarser elements span gas gaps. Typical run times (8-core workstation): 15–45 min for avalanche and 90–210 min for discharge/streamer formation in axisymmetric triple-GEMs; 3D variants are more costly by orders of magnitude (Rout et al., 2020).

The model’s computational speed and inherent parallelism allow extensive parameter studies, including voltage dependencies, gap configurations, and incident particle type.

4. Physics Results: Avalanche, Gain, and Discharge Probabilities

HydroGEM reproduces the statistical nature of gain and discharge in GEMs:

• Energy resolution: For single GEMs, simulated $$\frac{\partial c_i}{\partial t} + \nabla \cdot [ -D_i \nabla c_i + u_i c_i ] = R_i$$9 matches experimental data (21–24%), rising to 30–35% for triple GEMs as a function of $$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$0 and mean gain $$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$1 (Rout et al., 2021).
• Discharge probability ($$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$2): Simulated $$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$3 shows a rapid S-curve rise above voltage thresholds (e.g., $$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$4 for $$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$5 V in single GEMs, saturating to $$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$6 at higher gain). For triple-GEMs, qualitative behavior—threshold, voltage asymmetry registry, and “U-shaped” minimum with voltage offset—is captured, but absolute $$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$7 is overestimated, suggesting potential underestimation of thresholds or exclusion of mitigating microphysical effects (Rout et al., 2021).

In streamer mode, the model identifies the transition criterion based on the Raether limit (e.g., $$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$8 electrons), representation of positive streamer propagation, and E-field enhancement at peripheries (hundreds of kV/cm at the hole rim), consistent with classical streamer physics (Rout et al., 2020).

Validation versus experimental gain and onset voltage data (Bachmann, Gola, Gasik) yields good agreement after empirical scaling for axisymmetry.

5. Limitations and Extensions of Hydrodynamic GEM Models

The HydroGEM approach is subject to several critical simplifications:

• 2D axisymmetric geometry induces $$\nabla \cdot D = \rho_v, \quad D = \epsilon_0 \epsilon_r E, \quad E = -\nabla V, \quad \rho_v = Q_e (c_i - c_e)$$9 systematic errors; peripheral hole effects are not fully resolved.
• The deterministic, continuum (Eulerian) treatment does not resolve microscopic stochasticity—only upstream Monte Carlo input (primary seeds) modulates ensemble behavior.
• Streamer and discharge are flagged via fixed charge thresholds—full streamer kinematics and emergent breakdown (with e.g., dielectric surface charging, recombination) are not modeled directly.
• The photoionization source uses a diffusive, one-group approximation instead of detailed radiative transfer.

Suggested extensions involve explicit 3D geometries, hybrid kinetic-fluid (PIC-hybrid) schemes, advanced photon transport, and systematic numerical convergence studies.

6. HydroGEM for Continental-Scale Hydrological Data Quality Control

A distinct, similarly named HydroGEM model (“Hydrological Generalizable Encoder for Monitoring”) refers to a foundation network for streamflow anomaly detection and reconstruction at national and continental scales (Haq et al., 16 Dec 2025). This HydroGEM employs a hybrid Temporal Convolutional Network (TCN)–Transformer backbone (14.2M parameters), leveraging self-supervised pretraining on 6.03M time series (from 3,724 USGS sites) and fine-tuning with synthetic anomalies in held-out data.

Key features include:

• Architecture: TCN encoder (residual, 4 blocks, dilation), cosine-retention self-attention Transformer (sliding window $R_e, R_i$0), TCN decoder, and a learned gated skip connection.
• Normalization: Hierarchical three-tier: (1) log transform, (2) site-specific standardization, (3) clipping, with explicit scale embeddings.
• Pretraining: Masked modeling (point, block, periodic, feature masking), with a multi-component loss emphasizing reconstruction ($R_e, R_i$1), temporal gradients, variance, scale, and diversity.
• Fine-tuning: Injection of 11 synthetic anomaly types (e.g., spikes, drift, dropout) with a dedicated detection head (11K parameters) trained by focal loss and additional consistency penalties.
• Performance: On 799-test USGS stations, detection $R_e, R_i$2 (36.3% over Isolation Forest baseline), reconstruction error reduction $R_e, R_i$3. Zero-shot transfer to 100 Canadian sites yields $R_e, R_i$4, demonstrating robust generalization.
• Deployment: Designed for human-in-the-loop quality control, with tiered flagging and explicit uncertainty quantification; outputs are expert suggestions, never direct record replacements.

The development addresses the heterogeneity and scale of national hydrological sensor networks, demonstrating robust cross-national zero-shot capability and alignment with operational seasonal edits.

7. Summary and Comparative Perspective

"HydroGEM" designates both (a) a family of axisymmetric (and optionally 3D) hydrodynamic simulation tools for drift, gain, space-charge, and streamer evolution in GEM gaseous detectors (Rout et al., 2021, Rout et al., 2020), and (b) a TCN–Transformer-based foundation model for robust streamflow sensor anomaly detection (Haq et al., 16 Dec 2025).

In high-energy physics, HydroGEM's primary contributions are its physically grounded, computationally tractable simulation of space-charge feedback, discharge statistics, and the continuum-physical response of microstructured detectors—at a computational scale amenable to parameter sweeps. Its main limitations arise from Eulerian approximations and 2D symmetry assumptions. In hydrology, HydroGEM demonstrably advances scalable, explainable, and transferable quality control of massive sensor networks, with strong empirical performance against competitive baselines.

No direct methodological linkage exists between these two lines, but both exemplify domain-driven, hybrid modeling patterns, combining physics-informed initialization, modular subsystems, and empirical or foundation-model fine-tuning for their respective large-scale scientific challenges.