Quasicrystal Architected Nanomechanical Resonators via Data-Driven Design

From butterfly wings to remnants of nuclear detonation, aperiodic order repeatedly emerges in nature, often exhibiting reduced sensitivity to boundaries and symmetry constraints. Inspired by this principle, a paradigm shift is introduced in nanomechanical resonator design from periodic to aperiodic structures, focusing on a special class: quasicrystals (QCs). Although soft clamping enabled by phononic stopbands has become a central strategy for achieving high-$Q_m$ nanomechanical resonators, its practical realization has been largely confined to periodic phononic crystals, where band structure engineering is well established. The potential of aperiodic architectures, however, has remained largely unexplored, owing to their intrinsic complexity and the lack of systematic approaches to identifying and exploiting stopband behavior. Here we demonstrate that soft clamping can be realized in quasicrystal architectures and that high-$Q_m$ nanomechanical resonators can be systematically achieved through a data-driven design framework. As a representative demonstration, the 12-fold QC-based resonator exhibits a quality factor $Q_m \sim 10^7$ and an effective mass of sub-nanograms at MHz frequencies, corresponding to an exceptional force sensitivity of $26.4$~aN/$\sqrt{\text{Hz}}$ compared to previous 2D phononic crystals. These results establish QCs as a robust platform for next-generation nanomechanical resonators and open a new design regime beyond periodic order.

Local learning for stable backpropagation-free neural network training towards physical learning

While backpropagation and automatic differentiation have driven deep learning's success, the physical limits of chip manufacturing and rising environmental costs of deep learning motivate alternative learning paradigms such as physical neural networks. However, most existing physical neural networks still rely on digital computing for training, largely because backpropagation and automatic differentiation are difficult to realize in physical systems. We introduce FFzero, a forward-only learning framework enabling stable neural network training without backpropagation or automatic differentiation. FFzero combines layer-wise local learning, prototype-based representations, and directional-derivative-based optimization through forward evaluations only. We show that local learning is effective under forward-only optimization, where backpropagation fails. FFzero generalizes to multilayer perceptron and convolutional neural networks across classification and regression. Using a simulated photonic neural network as an example, we demonstrate that FFzero provides a viable path toward backpropagation-free in-situ physical learning.