A Physics Informed Convolutional Neural Network for Simulating Carbon Nanotube Wires in Infinite Spatial Dimensions and Arbitrary Frequency

We introduce a Physics-Informed Convolutional Neural Network (PI-CNN) that can infer the current density distribution in carbon nanotube (CNT) wires of random shape for any signal frequency within a predefined range. CNTs, known for their superior electrical, thermal, and mechanical properties, hold promise for various applications in electronics, energy storage, and materials science. However, accurately modeling their behavior under varying conditions has been a challenge due to the computational limitations of traditional methods, including high memory requirements and latency. Our PI-CNN architecture uses a multi-pathway approach that combines a Convolutional Neural Network, a Residual Network, and a Fully Connected Network. Our approach has two benefits. First, by using data-driven learning with physics-based constraints, we allow the PI-CNN to self-learn within appropriate guardrails. Second, our approach allows the PI-CNN to learn in infinite spatial dimensions as well as a functionally infinite number of non-spatial dimensions. This is an improvement over other neural operator architectures that can only learn the spatial mapping between an input and output image. We trained the PI-CNN for 300 epochs using a dataset of simulated CNT wire cross-sections in the frequency range of 1THz to 4 THz, along with the embedded Maxwell’s equations in the Residual Network. During validation, we found that the PI-CNN was able to generalize to unseen scenarios. Additionally, the PI-CNN uses very little memory and, for output images of resolution 512 x 512, has an inference time of only 20 seconds on a CPU.