  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.
