Instant Prediction of Moire Superlattice Relaxation in Twisted Bilayers of Transition Metal Dichalcogenides Using Different Neural Network Architectures

The relaxation of moiré superlattices in twisted bilayers of transition metal dichalcogenides (TMDs) has been modeled using a set of neural-network (NN)-based approaches. The physical system considered is described by a small number of parameters (layer properties, twist angle, type of solution (straight or twirl)); thus, the number of input parameters for the NN should be small. Principal Component Analysis demonstrates that 99.99% of the information describing the structure is provided by 7 parameters. We implemented and compared several NN architectures, including (i) an interpolator combined with an autoencoder, (ii) an interpolator combined with a decoder, (iii) a direct generator mapping input parameters to displacement fields, and (iv) a physics-informed neural network (PINN). Among these, the direct generator architecture demonstrated the best performance, achieving machine-level precision with minimal training data. Remarkably, once trained, this simple fully connected network is able to predict the full displacement field of a moiré bilayer within a fraction of a second, whereas conventional continuum simulations require hours or even days. This finding highlights the low-dimensional nature of the relaxation process and establishes neural networks as a practical and efficient alternative to ab initio approaches for rapid modeling and high-throughput screening of 2D twisted heterostructures.