Glossary

This glossary defines key concepts used throughout the EnerGNN documentation and library.

Graph & Data Representation

H2MG

Hyper Heterogeneous Multi Graph. The core data representation in EnerGNN. It extends traditional graphs to support complex industrial network topologies:

• Hyper Graph: Edges (Hyper-edges) can connect more than two entities.

• Heterogeneous Graph: Supports multiple types of components (e.g., buses, lines, transformers).

• Multi Graph: Multiple components can be connected to the same set of entities.

Hyper-edge

The fundamental building block of an H2MG. Unlike traditional edges that connect exactly two nodes, a hyper-edge can connect to any number of addresses via its ports.

Address

The interface points between Hyper-edges. In EnerGNN, addresses do not carry numerical features; they only define the connectivity (topology) of the graph.

Port

A named connection point on a Hyper-edge that links it to an Address. All hyper-edges of the same type share the same port names.

Optimization Concepts

Context

Denoted by \(x\). The input data of an optimization problem, represented as an H2MG graph. It typically contains the parameters of the problem (e.g., network topology, physical constraints).

Decision

Denoted by \(y\). The output produced by the GNN model, represented as an H2MG graph. It represents the variables to be optimized or predicted (e.g., phase angles, voltage setpoints, etc.).

Objective Function

A function \(f\) that evaluates the quality of a Decision \(y\) given a Context \(x\) (i.e. \(f(y;x)\)). In EnerGNN, models are trained to minimize this objective function (or its expectation).

Gradient of the Objective Function

A direction of improvement in the decision space for a given Decision \(y\) given a Context \(x\) (i.e. \(\nabla_y f(y;x)\)). This gradient is backpropagated into the GNN model during training, in order to improve the model performance w.r.t. the objective function.

Amortized Optimization

A framework where a model (like a GNN) is trained to predict the solution to an optimization problem directly, rather than solving each instance from scratch using iterative solvers. For a detailed introduction, see [Amos22].

Deep Learning & Framework

Permutation Equivariance

A property of a function where permuting the input (e.g., reordering buses in a power grid) leads to an equivalent permutation of the output. GNNs are by design permutation-equivariant.

Problem

An abstraction representing a single instance of an optimization or learning task. In EnerGNN, a Problem provides the Context, evaluates the Objective Function, and computes its Gradient.

Problem Batch

A collection of Problem instances grouped together for efficient processing. Training a GNN typically involves computing gradients over a batch to stabilize learning and leverage parallel computation (e.g., on GPUs).

Problem Loader

An iterator (implementing the ProblemLoader interface) that yields batches of optimization problems for training or evaluation.

Trainer

The component (Trainer) that orchestrates the GNN training loop, handling back-propagation, optimization steps (via Optax), and evaluation.

References

[Amos22]

Brandon Amos. “Tutorial on Amortized Optimization”. Foundations and Trends in Machine Learning, 2022.