Artificial reverberation can be produced either by convolving a signal with a measured room impulse response (RIR) or by synthesizing it with a parametric algorithm such as a Feedback Delay Network (FDN). The former reproduces a captured space faithfully but is costly to run and offers no control over its acoustic properties, while the latter is efficient and editable but hard to match to a specific room. In this paper we bridge the two by fitting a fully differentiable FDN to a measured RIR through gradient descent. The proposed network uses sixteen delay lines at a sampling rate of 48 kHz and trains all of its components jointly, including the delay lengths, the feedback matrix, the early-reflection taps, and a set of attenuation filters that control the frequency-dependent decay.