Orca: Neural Operators for Causal Reasoning in Continuous Time

2026-07-30

AI Summary

Traditional structural causal models struggle to represent irregularly observed, feedback-driven, and temporally evolving continuous-time dynamical systems—such as those in physiology, climate, or economics. This work proposes a neural operator–based framework for continuous-time causal modeling, wherein nodes in the causal graph are represented as time-dependent functions. The approach learns mechanisms mapping parent to child nodes through function-space operators, incorporates temporal arrow constraints, and infers latent functional variables to accommodate cyclic dependencies, irregular sampling, and reusable functional exogenous noise. By integrating neural operators into continuous-time causal inference—a first in the field—the method achieves accurate interventional and counterfactual predictions on synthetic data, substantially extending the applicability of causal models to complex dynamical systems.

Abstract

Structural causal models are the standard language for reasoning about interventions and counterfactuals, but they describe static variables, typically measured once, and usually forbid cyclic dependencies. Many systems we care about, such as patients, climates, and economies, instead evolve continuously in time, are observed at irregular time points, and contain feedback loops. We argue that neural operator learning provides a natural foundation for causal reasoning in this setting, and propose Orca, a framework in which each node of the causal graph is a function of time and each mechanism is a learned map between function spaces. We extend existing neural operator architectures to express causal mechanisms: a mechanism computes the function value of a node from its parent nodes by taking several parent functions as input, respects the arrow of time, and treats latent exogenous noise as a function that can be inferred and reused for counterfactuals. We formalize the model class and demonstrate counterfactual reasoning on synthetic continuous-time examples. Code is available at https://github.com/gerritgr/orca

Problem

• structural causal models
• continuous time
• cyclic dependencies
• irregular observations
• counterfactual reasoning

Innovation

• neural operators
• continuous-time causal reasoning
• counterfactual inference
• functional causal models
• irregular time series