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1. Rose: Composable Autodiff for the Interactive Web

   https://doi.org/10.4230/LIPIcs.ECOOP.2024.15  

   Estep, Sam; Ni, Wode; Rothkopf, Raven; Sunshine, Joshua (January 2024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Aldrich, Jonathan; Salvaneschi, Guido (Ed.)

   Reverse-mode automatic differentiation (autodiff) has been popularized by deep learning, but its ability to compute gradients is also valuable for interactive use cases such as bidirectional computer-aided design, embedded physics simulations, visualizing causal inference, and more. Unfortunately, the web is ill-served by existing autodiff frameworks, which use autodiff strategies that perform poorly on dynamic scalar programs, and pull in heavy dependencies that would result in unacceptable webpage sizes. This work introduces Rose, a lightweight autodiff framework for the web using a new hybrid approach to reverse-mode autodiff, blending conventional tracing and transformation techniques in a way that uses the host language for metaprogramming while also allowing the programmer to explicitly define reusable functions that comprise a larger differentiable computation. We demonstrate the value of the Rose design by porting two differentiable physics simulations, and evaluate its performance on an optimization-based diagramming application, showing Rose outperforming the state-of-the-art in web-based autodiff by multiple orders of magnitude. 

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2. MXtalTools: A Toolkit for Machine Learning on Molecular Crystals

   https://doi.org/10.1021/acs.jcim.5c02868  

   Kilgour, Michael; Tuckerman, Mark E; Rogal, Jutta (April 2026, Journal of Chemical Information and Modeling)

   NWe present MXtalTools, a flexible Python package for the data-driven modeling of molecular crystals, facilitating machine learning studies of the molecular solid state. MXtalTools comprises several classes of utilities: (1) synthesis, collation, and curation of molecule and crystal data sets, (2) integrated workflows for model training and inference, (3) crystal parametrization and representation, (4) crystal structure sampling and optimization, (5) end-to-end differentiable crystal sampling, construction, and analysis. Our modular functions can be integrated into existing workflows or combined and used to build novel modeling pipelines. MXtalTools leverages CUDA acceleration to enable high-throughput crystal modeling. The Python code is available open-source on our GitHub page, with detailed documentation on ReadTheDocs.ot Available 

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3. A DifferentiableRay–Wave Framework for HybridRefractive–Diffractive System Modeling and Optimization

   https://doi.org/10.1021/acsphotonics.6c00818  

   Cheng, Jiazhou; Gao, Margaret; Shao, Yixuan; Mao, Chenkai; Milster, Tom D; Fan, Jonathan A (July 2026, ACS Photonics)

   Abstract Hybrid optical systems combining refractive and diffractive optical responses have the potential to support new types of optical behavior, but they are difficult to model and optimize due to the disparate spatial scales and physics exhibited by ray and wave phenomena. In this work, we present a differentiable ray–wave framework for modeling hybrid refractive–diffractive optical systems that operates as a plug-and-play module within standard ray tracing pipelines. Our model uniquely applies to both planar and curvilinear diffractive surfaces and accommodates arbitrary scalar holographic profiles with high spatial frequency responses, with each simulation evaluated at a single wavelength. We analyze ray–wave modeling regimes that optimally account for the spatial frequency properties and spatial curvature of the diffractive surfaces, and we demonstrate the gradient-based end-to-end optimization of hybrid refractive–diffractive systems featuring planar and conformal diffractive surfaces. We anticipate that these modeling capabilities will enable new classes of hybrid optical systems relevant to computational imaging and display applications. 

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4. THB-Diff: a GPU-accelerated differentiable programming framework for THB-splines

   https://doi.org/10.1007/s00366-023-01929-1  

   Moola, Ajith; Balu, Aditya; Krishnamurthy, Adarsh; Pawar, Aishwarya (December 2023, Engineering with Computers)

   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. 

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5. Differentiable Spline Approximations

   Cho, M; Balu, A; Joshi, A; Deva Prasad, A; Khara, B; Sarkar, S; Ganapathysubramanian, B; Krishnamurthy, A; Hegde, C (December 2021, Advances in neural information processing systems)

   The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically require that the machine learning models be differentiable, limiting their applicability. Our goal in this paper is to use a new, principled approach to extend gradient-based optimization to functions well modeled by splines, which encompass a large family of piecewise polynomial models. We derive the form of the (weak) Jacobian of such functions and show that it exhibits a block-sparse structure that can be computed implicitly and efficiently. Overall, we show that leveraging this redesigned Jacobian in the form of a differentiable" layer''in predictive models leads to improved performance in diverse applications such as image segmentation, 3D point cloud reconstruction, and finite element analysis. We also open-source the code at\url {https://github. com/idealab-isu/DSA}. 

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