Using Differentiable Physics for Self-Supervised Assimilation of Chaotic Dynamical Systems

Reviewer 1: The authors propose a deep learning “data assimilation” framework based on ensemble KF. The work seems well-formulated and solid. Some of the results are a bit inconclusive, but I think the other advantages of the proposed method is a strong selling feature, and comparable performance to the non-differentiable methods is sufficient for contribution.

I think a concrete motivating example would have helped me to follow the technical arguments. This might not be needed for a reader familiar with the data assimilation literature, but for me, being very familiar with traditional bayesian recursive estimation, it was challenging for me to connect what I know about that to the problem at hand.

Reviewer 2: The contribution presents a solution, called Amortized Assimilation, for ““state estimation in high-dimensional chaotic dynamical systems””. As far as I understand, the problem is to predict the next state in a noisy system by emulating the dynamics with a differentiable model implemented by a neural network. The problem is phrased as a self-supervised task from sequences of noisy observations.

Strengths:

Clarity: well written and well-positioned paper within the domain of application. The formulation is clear, even for a non-expert.
Orthogonal, multi-disciplinary effort: even though I don’t think this is exactly within the scope of the workshop, it might be interesting for the AI community to foster conversations and collaborations with researchers from the physical sciences, and learning from the problems and methodologies encountered in those scenarios.
Soundness: to the best of my knowledge, the experimental setup and formulation is sounds.

Limitations:

Context: the paper could do a better job contextualizing this contribution within the field of AI. It is not entirely clear to me what types of problems these models could represent in a traditional AI domain. Does this have to do with rendering? AR/VR applications? Or is this exclusively applicable to physical science domains? Geoscience is used as an example application domain, and the chosen tasks look quite abstract. For what I can tell, this setup is designed for forecasting tasks for noisy chaotic systems, which I don’t necessarily see as having a direct link to the topics of this workshop. What would be the equivalent to the ““next available observation”” in the context of the topics that are of interest in this venue?

Notes:

I cannot comment on the novelty of the approach as I am not at all familiar with the specific sub-domain. How do you reconcile no loss of accuracy between the self-supervised and the supervised formulation?
are the results in tables 1 and 2 RMSEs? If so, please specify in the caption. I’m surprised not to see some error bars associated with these numbers, to actually measure whether any of these methods is statistically significantly better than the others.