In this talk, I will show that all higher-derivative effective field theories (EFTs) of vacuum gravity admit a well-posed initial value formulation when augmented by suitable regularising terms. These regularising terms can be obtained by field redefinitions and do not affect the dynamics in the regime of validity of EFT. I will explain how our result applies to the quadratic, cubic, and quartic truncations of the EFT of gravity and to various truncations of a simple EFT of a scalar field. Finally, I will also discuss some numerical results on the non-linear dynamics of this simple scalar field theory.
