GridFM

GridSFM is a block-structured discrete neural operator that processes power grids as heterogeneous graphs. Following discrete exterior calculus (DEC) principles, bus quantities (voltage magnitude, angle, nodal injections) are treated as discrete 0-forms on graph vertices, while branch flows are 1-forms on oriented edges. The bus–branch incidence acts as the discrete exterior derivative coupling the two; Kirchhoff’s current law appears naturally as its codifferential. This formulation gives the architecture a coordinate-free, topology-agnostic view of power flow that transfers across grids of different size and connectivity.

A type-aware projection embeds heterogeneous node and edge features into a shared latent space, augmented with a topology-conditioned learned positional encoding. The latent representation is refined by a stack of N blocks, each applying three sub-operations in sequence with residual skips:

1. A per-type global mixer — every node attends to every other node of its type.
2. A topology-aware mixer along the grid’s edges — where node types interact and the grid’s topology enters.
3. A per-type MLP.

Five prediction heads output bus voltage magnitude V, angle θ, generator active dispatch Pg, generator reactive dispatch Qg, and a feasibility verdict with a continuous margin. Branch flows (Pij, Qij) are computed analytically from the predicted bus state via the π-equivalent branch model with off-nominal tap ratio, following the PowerModels.jl polar-AC formulation. This keeps the model on the AC manifold by construction rather than as a soft constraint.

Training Data

GridSFM is trained on ~200 base transmission topologies drawn from three open sources:

• PGLib-OPF — the IEEE PES benchmark library covering networks from hundreds to tens of thousands of buses.
• OPFData — a large-scale AC-OPF dataset derived from PGLib-OPF.
• The msr_* corpus — a 48-state continental-US transmission topology set plus six multi-state regions, built by our open-data pipeline (described below).

Each base topology is expanded via a multi-axis perturbation pipeline that varies, independently and in combination:

Generator merit order — cost coefficients shuffled on 40% of generators, so dispatch learns from physics and cost structure rather than per-grid orderings.

Load profiles — 0.8×–1.5× nominal global scaling with ±10% per-load jitter; a separate high-load variant from 1.1×–1.3× covers the upper-stress tail.

Generator availability — 30% of scenarios contain outages (70% single, 20% double, 10% triple element), weighted by Pmax.

Line ratings — 20% of scenarios derate 10% of branches to 70%–95% of nominal.

Voltage limits — 15% of scenarios tighten Vmin/Vmax on 10% of buses.

A synthetic-infeasibility pipeline generates targeted failure modes — voltage squeeze, thermal bottleneck, angle tightening, DC-thermal congestion — driving a balanced ~50/50 feasible/infeasible training mix. Across all topologies and scenarios, training spans more than half a million labeled samples.

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“On a brand-new grid, as few as ~10 fine-tuning scenarios already produce reasonable cost and dispatch estimates.”

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