Develop optimal adaptive sampling for improved Conley–Morse models

Develop a theoretically justified adaptive experimental-design method that determines how additional data should be sampled from initial learned models and their Conley–Morse graphs in order to produce improved latent dynamical models.

Background

The paper proposes modifying the data through adaptive experimental design: iteratively collecting data, learning latent dynamics, and computing Conley–Morse graphs. This is intended to improve the quality and rigor of the dynamical information obtained from the latent representation.

The unresolved issue is how to choose additional samples optimally using the information contained in an initial collection of learned models and Conley–Morse graphs. The authors explicitly formulate this as a question about sampling strategy.

References

The second is to choose the size of the follow-up sample as a function of the initial evidence, jointly determining whether and how to collect additional data.

— When is statistical evidence strong enough? Using hypothesis tests to value data collection  (2609.09544 - Epanomeritakis et al., 8 Sep 2026) in Section Conclusions; see also Section Endogenous precision of the follow-up experiment

In other words, given the results from an initial set of models, how should one sample additional data to produce an improved set of models?

— Characterizing High-dimensional Dynamics by Combinatorial-Topological Methods on a Latent Space  (2609.01509 - Bailon et al., 1 Sep 2026) in Section 5, Discussion and open questions, paragraph beginning “The third option”