Predicting carbon nanotube forest growth dynamics and mechanics with physics-informed neural networks

We develop a physics-informed Transformer framework that predicts the time-resolved growth and collective assembly dynamics of vertically aligned carbon nanotube (CNT) forests. The model embeds relevant mechanics by enforcing physics-informed terms for stick-on-contact, stationary (clamped) CNT roots, and curvature penalties during model training. Ground truth data is generated using a mechanical finite element model (FEM) simulation. The network ingests the nodal coordinates of the CNT ensemble from the two preceding time frames and generates the subsequent nodal configuration through a single forward pass. The Transformer model maintains point-wise displacement errors below 200 nm after 500 predictive steps, which is significantly less than the intrinsic curvature exhibited by CNTs within the forest. The Transformer also preserves 96.8 ± 0.4% of CNT-CNT contacts, and generates CNT forest morphologies whose buckling loads deviate by 500× faster than the FEM simulation while requiring ∼1 GB of memory (compared to ∼38 GB for the FEM), enabling rapid iteration through experimental simulation campaigns.