Rapid Fitting of Band-Excitation Piezoresponse Force Microscopy Using Physics Constrained Unsupervised Neural Networks

Scanning probe spectroscopy generates high-dimensional data that is difficult to analyze in real time, hindering researcher creativity. Machine learning techniques like PCA accelerate analysis but are inefficient, sensitive to noise, and lack interpretability. We developed an unsupervised deep neural network constrained by a known empirical equation to enable real-time, robust fitting. Demonstrated on band-excitation piezoresponse force microscopy, our model fits cantilever response to a simple harmonic oscillators more than 4 orders of magnitude faster than least squares while enhancing robustness. It performs well on noisy data where conventional methods fail. Quantization-aware training enables sub-millisecond streaming inference on an FPGA, orders of magnitude faster than data acquisition. This methodology broadly applies to spectroscopic fitting and provides a pathway for real-time control and interpretation.