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Atomic force microscopy (AFM) is a part of the scanning probe microscopy family. It provides a platform for high-resolution topographical imaging, surface analysis as well as nanomechanical property mapping for stiff and soft samples (live cells, proteins, and other biomolecules). AFM is also crucial for measuring single-molecule interaction forces and important parameters of binding dynamics for receptor-ligand interactions or protein-protein interactions on live cells. However, performing AFM measurements and the associated data analytics are tedious, laborious experimental procedures requiring specific skill sets and continuous user supervision. Significant progress has been made recently in artificial intelligence (AI) and deep learning (DL), extending into microscopy. In this review, we summarize how researchers have implemented machine learning approaches so far to improve the performance of atomic force microscopy (AFM), make AFM data analytics faster, and make data measurement procedures high-throughput. We also shed some light on the different application areas of AFM that have significantly benefited from applications of machine learning frameworks and discuss the scope and future possibilities of these crucial approaches. 

We have developed a differentiable programming framework for truncated hierarchical B-splines (THB-splines), which can be used for several applications in geometry modeling, such as surface fitting and deformable image registration, and can be easily integrated with geometric deep learning frameworks. Differentiable programming is a novel paradigm that enables an algorithm to be differentiated via automatic differentiation, i.e., using automatic differentiation to compute the derivatives of its outputs with respect to its inputs or parameters. Differentiable programming has been used extensively in machine learning for obtaining gradients required in optimization algorithms such as stochastic gradient descent (SGD). While incorporating differentiable programming with traditional functions is straightforward, it is challenging when the functions are complex, such as splines. In this work, we extend the differentiable programming paradigm to THB-splines. THB-splines offer an efficient approach for complex surface fitting by utilizing a hierarchical tensor structure of B-splines, enabling local adaptive refinement. However, this approach brings challenges, such as a larger computational overhead and the non-trivial implementation of automatic differentiation and parallel evaluation algorithms. We use custom kernel functions for GPU acceleration in forward and backward evaluation that are necessary for differentiable programming of THB-splines. Our approach not only improves computational efficiency but also significantly enhances the speed of surface evaluation compared to previous methods. Our differentiable THB-splines framework facilitates faster and more accurate surface modeling with local refinement, with several applications in CAD and isogeometric analysis.