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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.

 

Polarized resonant soft X-ray scattering (P-RSoXS) has emerged as a powerful synchrotron-based tool that combines the principles of X-ray scattering and X-ray spectroscopy. P-RSoXS provides unique sensitivity to molecular orientation and chemical heterogeneity in soft materials such as polymers and biomaterials. Quantitative extraction of orientation information from P-RSoXS pattern data is challenging, however, because the scattering processes originate from sample properties that must be represented as energy-dependent three-dimensional tensors with heterogeneities at nanometre to sub-nanometre length scales. This challenge is overcome here by developing an open-source virtual instrument that uses graphical processing units (GPUs) to simulate P-RSoXS patterns from real-space material representations with nanoscale resolution. This computational framework – calledCyRSoXS(https://github.com/usnistgov/cyrsoxs) – is designed to maximize GPU performance, including algorithms that minimize both communication and memory footprints. The accuracy and robustness of the approach are demonstrated by validating against an extensive set of test cases, which include both analytical solutions and numerical comparisons, demonstrating an acceleration of over three orders of magnitude relative to the current state-of-the-art P-RSoXS simulation software. Such fast simulations open up a variety of applications that were previously computationally unfeasible, including pattern fitting, co-simulation with the physical instrument foroperandoanalytics, data exploration and decision support, data creation and integration into machine learning workflows, and utilization in multi-modal data assimilation approaches. Finally, the complexity of the computational framework is abstracted away from the end user by exposingCyRSoXSto Python usingPybind. This eliminates input/output requirements for large-scale parameter exploration and inverse design, and democratizes usage by enabling seamless integration with a Python ecosystem (https://github.com/usnistgov/nrss) that can include parametric morphology generation, simulation result reduction, comparison with experiment and data fitting approaches.

 

Atomic force microscopy (AFM) provides a platform for high-resolution topographical imaging and the mechanical characterization of a wide range of samples, including live cells, proteins, and other biomolecules. AFM is also instrumental for measuring interaction forces and binding kinetics for protein–protein or receptor–ligand interactions on live cells at a single-molecule level. However, performing force measurements and high-resolution imaging with AFM and data analytics are time-consuming and require special skill sets and continuous human supervision. Recently, researchers have explored the applications of artificial intelligence (AI) and deep learning (DL) in the bioimaging field. However, the applications of AI to AFM operations for live-cell characterization are little-known. In this work, we implemented a DL framework to perform automatic sample selection based on the cell shape for AFM probe navigation during AFM biomechanical mapping. We also established a closed-loop scanner trajectory control for measuring multiple cell samples at high speed for automated navigation. With this, we achieved a 60× speed-up in AFM navigation and reduced the time involved in searching for the particular cell shape in a large sample. Our innovation directly applies to many bio-AFM applications with AI-guided intelligent automation through image data analysis together with smart navigation.