Natural Data Synthesis using AI

In this research endeavor, the objective is to reconstruct the temperature field—chosen as a representative study—drawing from a limited set of noisy measurements reminiscent of genuine experimental scenarios. Pursuant to this, a dictionary-learning methodology is introduced, seeking to identify a sparse amalgamation of dictionary components. Sparse coefficients are ascertained utilizing both basis pursuit and LASSO methodologies, with a subsequent comparative analysis of these optimization constructs. Within the scope of this study, the dictionary is curated leveraging a priori dependable solutions, such as those derived from numerical solvers, in their unaltered state.