TinyAD: Automatic Differentiation in Geometry Processing Made Simple

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Date
2022
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Journal ISSN
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Publisher
The Eurographics Association and John Wiley & Sons Ltd.
Abstract
Non-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.
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CCS Concepts: Mathematics of computing --> Automatic differentiation; Mathematical software; Computing methodologies --> Mesh models

        
@article{
10.1111:cgf.14607
, journal = {Computer Graphics Forum}, title = {{
TinyAD: Automatic Differentiation in Geometry Processing Made Simple
}}, author = {
Schmidt, Patrick
and
Born, Janis
and
Bommes, David
and
Campen, Marcel
and
Kobbelt, Leif
}, year = {
2022
}, publisher = {
The Eurographics Association and John Wiley & Sons Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/cgf.14607
} }
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