The problem is not one number

Reservoir simulators are expensive because they solve coupled nonlinear flow through heterogeneous porous media over time. A useful surrogate must approximate those dynamics across permeability contrast, phase movement, pressure support, well controls, and structural complexity. Fast inference is valuable only if the prediction remains faithful to the reservoir response.

That is why a single accuracy number is not enough. A model can look strong on an average field error and still miss water breakthrough, smear a saturation front, underestimate pressure depletion near wells, or fail when a fault changes connectivity. These are not cosmetic errors. They change engineering decisions.

Why reservoir ML needs deployment-grade evaluation

Model comparisons only matter when they reflect operating conditions. Evaluation has to match the actual reservoir task, the failure modes, and the constraints under which a model will be used.

For reservoir simulation, that means benchmarking should not be limited to one smooth permeability field or one convenient split. It should show whether a model generalizes across geological families, fault configurations, grid geometry, well-control regimes, output variables, and prediction timesteps.

Flow Arena is built around that principle: consistent data splits, consistent training protocols, consistent metric definitions, and results broken down by the reservoir conditions that matter to deployment decisions.

What Flow Arena tests

The Flow Arena suite contains two-phase flow problems generated across a controlled matrix of reservoir conditions. The goal is not to make one difficult case; it is to expose how model behavior changes as the physics and geology become less forgiving.

Property model
Channelized and geostatistical permeability fields, so models face both sharp facies boundaries and smoother spatial correlation.
Fault structure
No-fault, zero-throw, and variable-throw cases, testing whether the surrogate can handle barriers, discontinuities, and changing grid geometry.
Well controls
Bottom-hole-pressure and rate-controlled simulations, because boundary conditions change the pressure and saturation response.
Outputs
Pressure and water saturation over time, reported separately so one field cannot hide failure in the other.

How results should be read

The leaderboard is a useful entry point, but it should not be treated as the whole evaluation. rel-L2 gives a stable global ranking, while MRE and MAE expose different error behavior. Per-field results show whether a model is better at pressure than saturation. Per-timestep plots show whether error grows, stabilizes, or spikes around transient events.

The important question is not only “which architecture wins?” It is “under which reservoir conditions does it win, and where does it break?” That is the difference between a model comparison and an engineering evaluation.

Metric definitions

Relative L2
Abbreviated rel-L2 throughout the site. ||pred − true||2 / ||true||2 averaged over test samples. The primary ranking metric: scale-invariant and penalizes large local errors through the L2 norm. All pressure fields use total pressure (bar); saturation is in volume fraction.
MRE
Mean relative error. The subscript identifies the denominator, since published papers disagree on which one to use:
  • MREt1 — per-timestep range (UFNO, Wen 2022). Denominator = max(truet) − min(truet) per timestep. Use for pressure-buildup outputs.
  • MREt2 — per-sample 4D range (Tang 2021). Denominator = max(true) − min(true) over the whole sample.
  • MREabs — per-cell |true| (Badawi 2024). Denominator = |true|. Blows up near zero; not safe for pressure-buildup.
  • MREP_init — initial-pressure normalization. Denominator = Pinit (per-cell PRESSURE_0 on Arena). Use for absolute-pressure outputs.
MAPE / MRPE
Saturation plume metrics, both restricted to the plume mask (cells where saturation deviates from initial by more than 1%):
  • MAPE — Mean Absolute Plume Error: mean(|pred − true|) on plume cells, in saturation units (×100). UFNO paper's MPE.
  • MRPE — Mean Relative Plume Error: mean(|pred − true| / |true|) on plume cells (×100). Badawi 2025 revised MPE.
MAE
Mean absolute error in physical units (bar for pressure, volume fraction for saturation). Directly interpretable but scale-dependent — compare within a field, not across fields.
Per-timestep
Each metric is also reported at every prediction timestep, showing whether error accumulates, stabilizes, or spikes during transient events like water breakthrough or pressure depletion.

Why academic benchmarks are included

The portal also includes reference datasets for CO₂ storage, radial flow, two-phase oil-water flow, and 3D channelized flow. These datasets provide familiar baselines alongside the private Flow Arena cases.

They are not presented as replacements for the Flow Arena matrix. They serve a different role: they calibrate the methodology and show how architectures behave when the dataset, grid, physics, and metric conventions change.

The standard Flow Arena aims for

A reservoir surrogate benchmark should be transparent enough for teams to understand the split, retrain candidate models, recompute the metric, and see why a method succeeds or fails. It should report aggregate accuracy, but not let aggregate accuracy hide local or temporal errors.

One observation from the current results: on Arena's saturation field, FNO3D's mean rel-L² grows from 0.280 on No Fault datasets to 0.425 on Variable Throw — a 1.52× degradation. SegResNet, by contrast, only widens 1.26×. The ranking order doesn't flip — but the gap does, and an aggregate accuracy number would hide it. That spread is the kind of pattern Flow Arena exists to surface.

Bottom line

What matters is not whether a surrogate looks plausible on one example. What matters is whether it remains reliable across the reservoir conditions engineers actually care about.

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