Interaction Networks (IN) are the pioneering Graph Neural Network architecture designed explicitly for learning physical simulations — predicting how objects interact through forces, collisions, and constraints — by decomposing the simulation into a relation model that computes pairwise forces between objects and an object model that updates each object's state based on the net forces acting on it — the first demonstration that neural networks can discover Newton's laws implicitly by observing object trajectories.

What Are Interaction Networks?

• Definition: An Interaction Network (Battaglia et al., 2016) models a physical scene as a graph where nodes are objects (balls, blocks, springs) and edges are relationships (connected by spring, touching, gravitationally attracted). The network alternates between two learned functions: a relation model that computes the effect of each pairwise interaction, and an object model that integrates all incoming effects to update each object's state (position, velocity).
• Relation Model: For each edge $(i, j)$ in the interaction graph, the relation model $phi_R$ takes the states of both connected objects and produces an effect vector: $e_{ij} = phi_R(o_i, o_j, r_{ij})$, where $r_{ij}$ encodes the relationship type (spring constant, collision coefficient). This effect vector represents the "force" or "influence" that object $j$ exerts on object $i$.
• Object Model: For each node $i$, the object model $phi_O$ takes the object's current state and the sum of all incoming effects and produces the updated state: $o_i' = phi_O(o_i, sum_{j} e_{ij})$. This corresponds to Newton's second law — the object's acceleration is determined by the sum of forces acting on it.

Why Interaction Networks Matter

• Physics Discovery: Interaction Networks learn to simulate gravity, springs, collisions, and rigid body dynamics purely by watching trajectories — without being given any equations. The relation model implicitly discovers force laws (inverse-square for gravity, Hooke's law for springs) from data, demonstrating that neural networks can rediscover fundamental physics.
• Generalization: Because the relation and object models are applied uniformly to all edges and nodes, Interaction Networks generalize to scenes with different numbers of objects than seen during training. A model trained on 3-body gravitational systems can simulate 10-body systems without retraining.
• Compositional Physics: Complex physical scenes involve multiple simultaneous interaction types — gravity, contact, friction, springs. Interaction Networks handle this naturally because each edge can have a different relationship type, and the object model integrates all effects regardless of their source.
• Foundation of GNN Physics: Interaction Networks established the blueprint for all subsequent neural physics simulators — GNS (Graph Network Simulator), DPI-Net, and learned mesh-based simulators all follow the same pattern of message-passing for forces followed by node updates for state evolution.

Architecture

Interaction Networks are physics learners — neural networks that discover how things push, pull, attract, and repel each other by observing the world, implicitly rediscovering the force laws that took humanity centuries to formalize.