Fig. 16: Details on implementing the dynamical scheme.

Overall network architecture and tensorial dimensions of each layer for (a–b) weak scattering and (c–d) strong scattering cases. (a) and (c) show unrolled versions of the architectures in (b) and (d), respectively. (a-b) Weak scattering case: at nth step, n Radon projections \({\boldsymbol{g}}_1,\, \ldots ,\,{\boldsymbol{g}}_n\) create an Approximant \({\boldsymbol{f}}_n^\prime\) by a FBP operation, and a sequence of FBP Approximants \({\boldsymbol{f}}_n^\prime ,\,n = 1, \ldots ,\,N\left( { = 21} \right),\) is followed by an encoder and a recurrent unit. There is an angular attention block before a decoder for the 3D reconstruction \({\hat{\boldsymbol f}}\), (c-d) Strong-scattering case: the raw intensity diffraction pattern \({\boldsymbol{g}}_n,\,n = 1,\, \ldots ,\,N\,( = 42),\) of the nth angular sequence step is followed by gradient descent and the Dynamically Weighted Moving Average (DWMA) operations to construct another Approximant sequence \({\tilde{\boldsymbol f}}_m^{\left[ 1 \right]},\,m = 1, \ldots ,\,M\,( = 12)\) from original Approximants \({\boldsymbol{f}}_n^{\left[ 1 \right]}\). TV regularization is applied to the gradient descent only for experimental diffraction patterns. The DWMA Approximants \({\tilde{\boldsymbol f}}_m^{\left[ 1 \right]}\) are encoded to ξ_m and fed to the recurrent dynamical operation whose output sequence \({\boldsymbol{h}}_m,\,m = 1,\, \ldots ,\,12\), and the angular attention mechanism them into a single representation a, which is finally decoded to produce the 3D reconstruction \({\hat{\boldsymbol f}}\). For both cases, training adapts the weights of the learned operators in this architecture to minimize the training loss function \({\cal{E}}\left( {{\boldsymbol{f}},{\hat{\boldsymbol f}}} \right)\) between \({\hat{\boldsymbol f}}\) and the ground truth object f