Efficient Interpolation-based Pathline Tracing with B-spline Curves in Particle Dataset

Integration-free Learning of Flow Maps

“…We made a minor modification to the network by removing the ReLU activation function used in the output layer, allowing the model to output negative values. We further compare our method against the recent work by Li et al [29], where the authors showed an improvement over prior work in efficiently interpolating Lagrangian representation to obtain new trajectories. Further, we compare our method with a SIREN [45] that tacks time span on as an additional coordinate, along with particle space-time coordinates (c.f.…”

“…Even though these techniques do not require expensive numerical integration during post-hoc analysis, they are still expensive because of the number of steps required to compute the full trajectory. In the recent work by Li et al [29] they represent the trajectories as Bspline curves and improve the computation time of new trajectories by interpolation between the B-spline control points. Lagrangian representations of flow are attractive as a kind of data reduction, and assuming a sufficientlydense sampling of trajectories, can often be quite accurate.…”

“…4 we present quantitative results comparing our method against different baselines, and in Table 2 we report inference and preprocessing times. Specifically, for the pathline interpolation approach of Li et al [29], preprocessing refers to the time required to fit B-splines, while for Jakob et al [36] this refers to the time required to optimize the CNN for super resolution. For all remaining methods, preprocessing refers to the time required for optimizing to an individual flow field.…”

“…We next evaluate our method on a set of 3D unsteady flows, comparing our method with a SIREN-based flow map [45] as well as the B-spline pathline interpolation technique [29].…”

“…We further compare to the Half Cylinder dataset, a large-scale unsteady flow dataset that cannot be readily stored in memory. We found the pathline interpolation method [29] failed to fit to the data, and thus we limit our comparison to SIREN, please see Fig. 11.…”