Fig. 10: The non-intrusive reduced basis method for the physics-based machine learning framework.

Black arrows indicate the information flow from an input binary image to an output binary image. The figure shown corresponds to the chip with a rock pattern chip with an input size of 512 × 512 pixels. A similar construction approach is used for a chip with a uniform pattern, with an input size of 256 × 256 pixels. a Trained decoder from the Convolutional Autoencoder (CAE) model, used to augment existing segmented images for the construction of the non-intrusive reduced basis (NI-RB) model. b Trained encoder from the CAE model, used to reduce the dimensionality of input images. c Combined latent space of the CAE model and time. d Reduced basis coefficients obtained via Proper Orthogonal Decomposition (POD) on the Lattice–Boltzmann solutions. e Basis functions obtained via POD on the Lattice–Boltzmann solutions.