Project Development : Multi-fidelity Modeling for non-linear and multi-valued correlations

Objectives:To develop innovative machine learning tools for the characterization of geophysical properties of the Ocean and its environment. To implement data-driven manifold enbedding and learning with delay coordinates in order to solve the current limitations of Gaussian Process Regressions (GPS) and identify the right intrinsic parameters that could simplify training of the model in presence of complex non-linear and multi-valued data correlation. To investigate the possibility of employing these algorithms for path identification in order to maximize performance of distributed systems.Methodology:We plan to solve the current limitations of Gaussian Process Regressions (GPRs) by expanding the dimensionality of the data- correlation space through the use of time-delay coordinates. The representation of data-correlations in higher dimensional space will enable the application of GPRs in case of complex, non-linear, multi-valued problem. We will employ Manifold Learning through non- linear diffusion maps or multi-dimensional scaling to identify the right intrinsic parameters that could simplify model training.Rationale:Satellite observations and sensors measurements empower oceanographers and engineers with a copious amount of diverse data-sets. Gaussian Process Regressions (GPR) have the potential of leveraging multi-fidelity data-sets to infer predictions of Ocean geophysical characteristics with Uncertainty Quantification (UQ).UQ represents an essential ingredient for planning data acquisition strategies and future measurement campaigns with the ultimate goal to increase the efficiency of prediction tools significantly decreasing costs.Current GPR which break down in case of complex, non-linear, multi-valued correlations between different data sets. The use of time-delay coordinates and data-driven manifold embedding will greatly expand the capabilities of GPRs. The use of time-delay coordinates and data-driven manifold embedding will greatly expand the capabilities of GPRs.