Model Card — CHINO v1.0

Model Description

CHINO (CHanneling Instability Neural Operator) is an attention-augmented graph neural operator for predicting reactive infiltration instability in porous media. It maps an initial CO2 concentration field to a predicted field at a later time, capturing the large-scale dynamics of convective fingering in deep saline aquifers.

Field	Value
Model name	CHINO v1.0
Architecture	Attention-augmented MeshGraphNet
License	Apache 2.0
Framework	PyTorch
Parameters	7,409,537

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Intended Use

CHINO is designed for researchers studying:

• Geological carbon capture and storage (CCS)
• Reactive infiltration instability (RII) in porous media
• Convective dissolution of CO2 in saline aquifers
• Neural operator methods for chaotic PDE systems

The model predicts individual realizations of the concentration field, not ensemble statistics. It correctly captures large-scale spatial structure (depth of CO2 penetration, broad convective pattern) but does not reproduce exact finger positions, which are irreducibly stochastic at high Rayleigh numbers.

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Physical Regime

Parameter	Value	Physical interpretation
Rayleigh number Ra	500, 1000, 1577	Buoyancy-driven fingering intensity
Peclet number Pe	317	Advection vs. diffusion ratio
Da_S	1.0	Dissolution sink rate
Da_inj	0.005	CO2 injection rate
Domain	[0,10] x [0,1]	Non-dim. aquifer (500m x 2000m physical)
Grid	200 x 40	MAC staggered finite difference
t_max	2.0	2000 years of geological sequestration

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Architecture

Each of the 6 processor blocks contains three sequential operations:

1. Local edge update (k=8 Moore + stride-4 edges, O(E)): captures fine-scale concentration gradients at finger boundaries.
2. Global self-attention (4 heads x 64 dim, O(N^2)): every node attends to every other node simultaneously, representing the instantaneous pressure coupling of the Darcy-Boussinesq system.
3. Node update MLP: fuses local messages, global attention, and sinusoidal time embedding.

The attention matrix (N=8000 nodes, 4 heads) requires 1 GB of VRAM per forward pass — negligible on modern GPUs.

Node input features (6): c_in, S, x, y, t_in, Ra

Output: c(x,y,t_out) >= 0 (Softplus activation)

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Training

Detail	Value
Total epochs	550
Phase 1 (ep. 1-300)	Standard curriculum, w_phys=0.05
Phase 2 (ep. 301-550)	Resumed, w_phys=0.3
Loss	Anomaly relative L2 (0.7) + full L2 (0.3) + physics + BC
Optimizer	AdamW, lr=5e-4, cosine schedule
Hardware	NVIDIA RTX PRO 6000 Blackwell (95 GB)
Wall time	~13 hours total

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Performance

Metric	Value	Seed
L2 at t=0.5	0.74	Seeds 18-19, Ra=1577
L2 at t=1.0	0.43	Seeds 18-19, Ra=1577
L2 at t=2.0	0.25	Seeds 18-19, Ra=1577

At t=1.0, the model produces visible finger-like spatial structure that corresponds spatially to the dominant fingers in the finite-difference reference. At t=2.0, the broad swept pattern of merged fingers is captured with correct left-right asymmetry.

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Limitations

• Early-time prediction (t=0.5): L2=0.74. Finger nucleation at short times is controlled by sub-grid perturbations and is not predictable deterministically.
• Individual finger positions: Not reproduced. The chaotic nature of the Rayleigh-Taylor instability at Ra=1577 means finger positions are sensitive to initial conditions at scales below the grid resolution. This is a fundamental physical property, not a training failure.
• Out-of-distribution Ra: The model has not been tested above Ra=1577 or below Ra=500.
• 2D only: The current version is trained on 2D simulations. A 3D extension is in development.

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Citation

If you use CHINO, please cite:

@software{hier_majumder_2025_chino,
  author    = {Hier-Majumder, Saswata},
  title     = {CHINO: CHanneling Instability Neural Operator},
  year      = {2025},
  license   = {Apache-2.0},
  url       = {https://github.com/sashgeophysics/CHINO}
}

@article{sun2020geological,
  title   = {Geological Carbon Sequestration by Reactive Infiltration Instability},
  author  = {Sun, Yizhuo and Payton, Ryan L. and Hier-Majumder, Saswata and Kingdon, Andrew},
  journal = {Frontiers in Earth Science},
  volume  = {8},
  pages   = {533588},
  year    = {2020},
  doi     = {10.3389/feart.2020.533588}
}