Marrying Causal Representation Learning with Dynamical Systems for Science
This work addresses the gap between theoretical causal representation learning and practical applications in dynamical systems, enabling more robust and interpretable models for scientific domains like climate science.
The paper tackles the challenge of applying causal representation learning to real-world dynamical systems by integrating identifiable methods from causal representation learning with scalable differentiable solvers from dynamical systems, resulting in explicitly controllable models that isolate trajectory-specific parameters for downstream tasks like out-of-distribution classification and treatment effect estimation, with successful application to a wind simulator and real-world climate data.
Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of any successful real-world application. At the same time, the field of dynamical systems benefited from deep learning and scaled to countless applications but does not allow parameter identification. In this paper, we draw a clear connection between the two and their key assumptions, allowing us to apply identifiable methods developed in causal representation learning to dynamical systems. At the same time, we can leverage scalable differentiable solvers developed for differential equations to build models that are both identifiable and practical. Overall, we learn explicitly controllable models that isolate the trajectory-specific parameters for further downstream tasks such as out-of-distribution classification or treatment effect estimation. We experiment with a wind simulator with partially known factors of variation. We also apply the resulting model to real-world climate data and successfully answer downstream causal questions in line with existing literature on climate change.