This mini-symposium will emphasize a range of Kernel and machine learning-based approaches, which can be applied to the solution of partial differential equations (PDEs) in science and engineering. Contributions dealing with practical applications are encouraged, such as in mechanics, civil engineering, aeronautics, bio-medicine, transport and sensing of pollutants, materials design and processing, remote sensing, non-destructive evaluation, meta-models for high-dimensional problems, etc. Papers on other subjects related to the themes of this symposium are also welcome.