The workshop aims to unite the theoretical rigor of numerical mathematics, the stochastic analysis of data inaccuracies, and the flexibility and adaptability of machine learning. This interdisciplinary convergence is still in its infancy, and the workshop would initiate a systematic interaction between these communities. By exploring how error estimation, adaptivity, and convergence analysis can inform and enhance machine learning models for PDEs, we hope to lay the foundation for a new generation of hybrid computational surrogate methods that are reliable, data-aware, and numerically robust and efficient. To achieve these goals, the workshop will have several experts in the field give plenary lectures, have a poster session to foster extensive exchange of ideas, and a panel discussion with additional speakers from industry.