We start in this work the study of the relation between the theory of regularity structures and paracontrolled calculus. We give a paracontrolled representation of the reconstruction operator and provide a natural parametrization of the space of admissible models.
"Paracontrolled calculus and regularity structures I." J. Math. Soc. Japan 73 (2) 553 - 595, April, 2021. https://doi.org/10.2969/jmsj/81878187