A priori determination of the number of sparse measurements for SFR

Determine an a priori rule or criterion for selecting the number of sparse measurement locations M_S to record when applying sparse flow reconstruction (SFR) to reconstruct full-resolution CFD snapshots from temporally down-sampled full snapshots X′ and high-frequency sparse measurements Y, replacing ad hoc selection and enabling principled accuracy–compression trade-offs.

Background

The paper introduces Sparse Flow Reconstruction (SFR), which reconstructs full-resolution, high-frequency CFD snapshots by combining two smaller datasets: temporally down-sampled full snapshots (X′) and high-frequency sparse measurements (Y). While SFR can substantially reduce writing and storage costs, its performance depends on how many sparse measurements are taken and where they are placed.

The authors advocate a pragmatic strategy using many randomly placed sparse measurements for simplicity and scalability, acknowledging that more sophisticated optimization methods exist but are complex to integrate with CFD workflows. However, they explicitly note that this random approach lacks optimality and, crucially, that the number of sparse measurements required is not known a priori, motivating the need for principled selection guidelines.