In the last decade, machine learning, and more specifically deep neural networks, have thoroughly renewed the research perspectives in many fields like Natural Language Processing and Computer Vision. Despite indisputable successes however, the introduction of ML approaches in complex physical systems remains a challenging open issue. This project aims at developing new Machine Learning techniques tailored to the modelling and inference of high-dimensional complex physical systems described by partial differential equations (PDEs), focusing on the paradigmatic KPZ model, describing a rough interface. The internship will be in collaboration between LPTMS and LISN at Paris-Saclay.