Support Vectors Learning for Vector Field Reconstruction

Sampled vector fields generally appear as measurements of real phenomena. They can be obtained by the use of a particle image velocimetry acquisition device, or as the result of a physical simulation, such as a fluid flow simulation, among many examples. This paper proposes to formulate the unstructured vector field reconstruction and approximation through Machine-Learning. The machine learns from the samples a global vector field estimation function that could be evaluated at arbitrary points from the whole domain. Using an adaptation of the support vector regression method for multi-scale analysis, the proposed method provides a global, analytical expression for the reconstructed vector field through an efficient non-linear optimization. Experiments on artificial and real data show a statistically robust behavior of the proposed technique.