Schematic of flow matching for posterior estimation with ODISSEO. The training set was generated by sampling i = 0,..., N parameters θⁱ from the prior p(θ) and then forward modeled using ODISSEO to obtain the observation dⁱ ~ p(d | θ). Following the flow described in Sect. 2.4, we sampled t ~ U(0,1) to train a neural network to approximate the vector field v_φ(t, dⁱ, θⁱ). In the lower section, we report a simplified flow matching objective for a 1D case. The neural network is called for different t to regress the vector field that governs the ODE in order to transform the sampling distribution q_t=0 = N(0,I) into the posterior distribution q_t=1 = p(θ | d). Note that in this schematic, we refer to θ₁ described in Sect. 2.4 as θ.