TinyAD: Automatic Differentiation in Geometry Processing Made Simple

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dc.contributor.authorSchmidt, Patricken_US
dc.contributor.authorBorn, Janisen_US
dc.contributor.authorBommes, Daviden_US
dc.contributor.authorCampen, Marcelen_US
dc.contributor.authorKobbelt, Leifen_US
dc.contributor.editorCampen, Marcelen_US
dc.contributor.editorSpagnuolo, Michelaen_US
dc.date.accessioned2022-06-27T16:19:53Z
dc.date.available2022-06-27T16:19:53Z
dc.date.issued2022
dc.description.abstractNon-linear optimization is essential to many areas of geometry processing research. However, when experimenting with different problem formulations or when prototyping new algorithms, a major practical obstacle is the need to figure out derivatives of objective functions, especially when second-order derivatives are required. Deriving and manually implementing gradients and Hessians is both time-consuming and error-prone. Automatic differentiation techniques address this problem, but can introduce a diverse set of obstacles themselves, e.g. limiting the set of supported language features, imposing restrictions on a program's control flow, incurring a significant run time overhead, or making it hard to exploit sparsity patterns common in geometry processing. We show that for many geometric problems, in particular on meshes, the simplest form of forward-mode automatic differentiation is not only the most flexible, but also actually the most efficient choice. We introduce TinyAD: a lightweight C++ library that automatically computes gradients and Hessians, in particular of sparse problems, by differentiating small (tiny) sub-problems. Its simplicity enables easy integration; no restrictions on, e.g., looping and branching are imposed. TinyAD provides the basic ingredients to quickly implement first and second order Newton-style solvers, allowing for flexible adjustment of both problem formulations and solver details. By showcasing compact implementations of methods from parametrization, deformation, and direction field design, we demonstrate how TinyAD lowers the barrier to exploring non-linear optimization techniques. This enables not only fast prototyping of new research ideas, but also improves replicability of existing algorithms in geometry processing. TinyAD is available to the community as an open source library.en_US
dc.description.number5
dc.description.sectionheadersTools and Data
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume41
dc.identifier.doi10.1111/cgf.14607
dc.identifier.issn1467-8659
dc.identifier.pages113-124
dc.identifier.pages12 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.14607
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14607
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.rightsAttribution 4.0 International License
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectCCS Concepts: Mathematics of computing --> Automatic differentiation; Mathematical software; Computing methodologies --> Mesh models
dc.subjectMathematics of computing
dc.subjectAutomatic differentiation
dc.subjectMathematical software
dc.subjectComputing methodologies
dc.subjectMesh models
dc.titleTinyAD: Automatic Differentiation in Geometry Processing Made Simpleen_US
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