該研究介紹了一種基于深度神經網絡的基本新方法，以基于已知的物理模型將函數形式擬合到噪聲數據。來自美國橡樹林國家實驗室的Stephen Jesse領導的團隊，提出了一種新的方法，可用來逆向解決問題，可從基于光譜成像數據的最小二乘擬合中提取物理模型參數，并能通過深度學習測定先驗參數而增強提取能力。他們將這種方法應用于從壓電響應力顯微鏡數據中提取簡諧振子參數，并表明通過結合使用深度神經網絡和最小二乘擬合，可以探測比傳統方法低一個數量級的信號響應，接近激發信號的熱限制。作為模型系統，他們演示了從層狀鐵電化合物的帶激發壓電響應力顯微鏡成像中提取阻尼簡諧振子參數。這種使用深度神經網絡的方法是通用的，并且在正向和反向情況下都顯示出它們作為函數近似器的效用，且在嘈雜的環境中工作良好。該文近期發表于npj Computational Materials 5 25(2019)。

Summary

Physical property from noisy data: Deep neural networks

A fundamentally new method based on deep neural networks, to fit functional forms to noisy data based on a known physical model is introduced. A team led by?Stephen Jesse?from the Oak Ridge National Laboratory, USA, demonstrated a novel approach for the inverse problem solution and extraction of physical model parameters from spectral-imaging data-based least-squares fitting augmented by deep learning for determination of priors. They apply this method to the extraction of simple harmonic oscillator parameters from piezoresponse force microscopy data, and show that by using a combination of both deep neural networks and least-squares fitting, they can probe signal responses in regimes an order of magnitude lower than with the traditional means, approaching the thermal limit for the excitation signal. As a model system, they demonstrate the extraction of damped simple harmonic oscillator parameters from band-excitation (BE) piezoresponse force microscopy(PFM) imaging of a layered ferroelectric compound. This approach of using deep neural network (DNN) is general and shows their utility as function approximators in both forward and reverse cases and that they work well in noisy environments. This article was recently published in npj Computational Materials 5 25(2019).

原文Abstract及其翻譯

Deep neural networks for understanding noisy data applied to physical property extraction in scanning probe microscopy (應用深度神經網絡解讀掃描探針顯微鏡中噪聲數據的物理特性)

Nikolay Borodinov,?Sabine Neumayer,?Sergei V. Kalinin,?OlgaS. Ovchinnikova,?RamaK. Vasudevan?&?Stephen Jesse?

Abstract?The rapid development of spectral-imaging methods in scanning probe, electron, and optical microscopy in the last decade have given rise for large multidimensional datasets. In many cases, the reduction of hyperspectral data to the lower-dimension materials-specific parameters is based on functional fitting, where an approximate form of the fitting function is known, but the parameters of the function need to be determined. However, functional fits of noisy data realized via iterative methods, such as least-square gradient descent, often yield spurious results and are very sensitive to initial guesses. Here, we demonstrate an approach for the reduction of the hyperspectral data using a deep neural network approach. A combined deep neural network/least-square approach is shown to improve the effective signal-to-noise ratio of band-excitation piezoresponse force microscopy by more than an order of magnitude, allowing characterization when very small driving signals are used or when a material’s response is weak.

摘要 在過去十年中，掃描探針、電子顯微鏡和光學顯微鏡的光譜成像方法發展迅速，導致大型多維數據集的興起。在許多情況下，將高光譜數據降維到較低維度的材料特性參數，依賴于功能擬合，雖然擬合函數的近似形式是已知的，但函數的參數卻是需要人為確定的。然而，通過迭代方法實現噪聲數據的功能擬合(如最小二乘梯度下降)，常常出現虛假結果，并且對初始猜測值非常敏感。本研究提出了一種利用深度神經網絡方法降維高光譜數據的方法。將深度神經網絡與最小二乘法結合使用，可以將帶隙-激發壓電響應力顯微鏡的有效信噪比提高一個數量級以上，從而可用非常小的驅動信號即可實現表征，或可用很弱的材料響應即可實現表征。

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