Orca: Neural Operators for Causal Reasoning in Continuous Time

Research Question and Approach

Traditional Structural Causal Models (SCMs) are designed for static variables and struggle with systems that evolve continuously over time, contain feedback loops, or are sampled at irregular intervals. The authors introduce Orca (Operator-based Reasoning for Causal Analysis), a framework that leverages neural operator learning to model these dynamic systems. By treating each node in a causal graph as a continuous function of time, Orca learns the mechanisms governing these nodes as maps between function spaces. This approach ensures that the model is resolution-invariant, meaning it can be trained and evaluated on different sampling grids without losing causal consistency.

Methodology

Orca represents each causal mechanism as a deep-set operator that takes the history of parent nodes as input. To ensure the model respects the causal structure, it enforces the temporal priority principle—the requirement that a cause must precede its effect. The model is trained by minimizing prediction error on observed data, using a weighted sum of parent embeddings to approximate the integral of parent trajectories. This architecture allows Orca to handle cyclic dependencies, as the unrolled temporal dependencies form a directed acyclic graph, and enables the inference of latent noise variables necessary for counterfactual reasoning.

Main Findings and Significance

In experiments using synthetic continuous-time data, Orca successfully recovers ground-truth dose-response curves and counterfactual trajectories. The authors demonstrate that naive approaches—such as static SCMs that ignore time or neural operators that ignore the causal graph—produce biased estimates. Orca’s ability to learn mechanisms that are independent of the specific measurement grid makes it a robust tool for longitudinal data analysis in fields like medicine, climate science, and economics, where data is often sparse or irregularly sampled.