Fig. 5. Schematic of the neural networks used for constructive machine learning assisted surrogates.

a Feedforward Neural Network (FNN). the input is constructed by convolution operations, i.e., a combination of sliding Finite Difference (FD) stencils, and, integral operators, for learning mesoscopic models in the form of IPDEs (Eq. (10)); the inputs to the RHS of the IPDE are the features in Eq. (13). b A schematic of the neural network architecture, inspired by numerical stochastic integrators, used to construct macroscopic models in the form of mean-field SDEs.