Data?driven diffusion with uncertainties

In a data-driven finite element analysis the experimental data are directly employed as an input for computational analysis, thus evading any state of matter modeling. The essential physical principles, such balance laws and continuity, remain unchanged, do all numerical schemes used in their discretization. addition, uncertainties fluctuations experimentally measured enter simulation. Here is applied to diffusion which common problem with multiple applications like particle exchange, temperature evolution, disease spread or information distribution. governing equations system method derived solution illustrated by simple examples.