# Deep Learning Regressors of Surface Properties from Atomic Force Microscopy Nanoindentations
## 1 Introduction  
The last few decades have brought significant advancements in the field of nanotechnology at various levels. Several areas of research have greatly benefited from these improvements, with the study of materials at their nanoscale being substantially leveraged. Atomic force microscopy (AFM) is one of the main techniques responsible for these studies [1]. Urging from the need for visualizing and manipulating materials at their lower scale, this method was established in the late 20 th century, following the concept of scanning probe microscopy [2]. It is based on a small probe, usually consisting of a cantilever with a tip that can have several geometries attached to its end. From the interaction of the probe with the sampled surface, whether involving contact or not, the target properties can be inferred [3, 4, 5]. Despite being a well-established method, there are still some challenges associated with AFM, particularly those arising from the contact between probe and sample. It has been shown that uncontrolled forces in constant-height contact mode can be reduced by magnetic actuation [6], while difficulties in determining the shape of the tip can be overcome using blind tip reconstruction methods [7, 8]. Correctly identifying the contact point also remains one of the main challenges in AFM, prompting the development of diverse methods to refine this process [9, 10]. High-resolution and three-dimensional images of the surface topography at the nanoscale can be generated by measuring the topographic height through the probe-sample interaction [11]. The height measurements not only allow for the reproduction of such images but they are also the basis for obtaining the roughness and other surface characterization parameters [12]. Furthermore, due to its wide range of operating modes, one can obtain nanomechanical properties that contribute to understanding the behaviour of materials at increasingly smaller scales. This is the case of AFM nanoindentations, which consist in approaching the probe towards the sample and indenting it for a defined threshold, followed by withdrawing the probe until it detaches from the sample or reaches its original position. Along this ramp cycle, the deflection of the probe cantilever is recorded as a function of the probe's displacement, which can later be translated into force-indentation (F-I) curves. By fitting these curves with appropriate contact models, the target material properties are finally obtained. Furthermore, if there is knowledge about the location in the sample where each F-I curve was obtained, it is possible to create surface maps for each measured property [13; 14; 15]. Regarding approach curves, they play a crucial role in inferring the elastic modulus of the sample and can be fitted with the models developed by [PERSON] [16] or [PERSON] [17]. On the other hand, retraction data offer essential insights on its adhesion properties [18; 19; 20], which are particularly relevant in low-stiffness materials, such as biological cells, where they play a major role in processes such as cell proliferation and migration, and sudden changes in these properties can lead to diseases such as cancer [21; 22] or osteoporosis [23; 24]. Since during the retraction stage, adhesion forces between both surfaces are predicted to have a higher impact in the experiments, an Hertzian-based analysis is no longer precise enough, so other models must be employed. Amongst them are JKR (Johnson-Kendall-Roberts) and DMT (Derjaguin-Muller-Toporov) [25; 26], which represent two extreme cases in adhesive interaction: while DMT is valid for hard samples, large tip radius and low adhesion forces, JKR meets the specific features of this work, since it is applicable for soft samples, small tip radius and high adhesion forces [27]. Another field that has witnessed remarkable advancements in recent times is artificial intelligence (AI) and its subset of machine learning (ML), taking advantage of the exponential increase in computational power.