Assess reduced state-consistency comparisons for three-dimensional generalization

Determine whether reducing the number of full-state comparisons, potentially to a comparison only at the end of the unrolled trajectory, enables Trajectory-Consistent Network Training to generalize more effectively to three-dimensional reconstruction problems under its computational and memory constraints.

Background

The paper identifies the state-consistency term in Trajectory-Consistent Network Training (TraCTra) as computationally expensive because it requires repeated neural-network evaluations and storage proportional to the number of rollout timesteps and batch size. Consequently, the three-dimensional experiments are formulated primarily as single-trajectory inverse problems, whereas broader training across independent trajectories is demonstrated only for lower-dimensional settings.

The authors suggest reducing the number of full-state comparisons, possibly retaining only a comparison at the end of the unrolled trajectory, as a modification that could make broader three-dimensional generalization feasible. Whether this modification preserves reconstruction quality and enables generalization remains unresolved.

References

We would expect our methods to generalise well in the three-dimensional problems too given broader input data, but this would require some further modifications: one candidate would be to reduce the number of full-state comparisons -- perhaps just at the end of the unrolled trajectory -- which we will explore in future work.

— Learning dynamically consistent flow reconstructions from limited observations  (2608.30909 - Zhu et al., 31 Aug 2026) in Discussion and conclusions, Section 4