DC Field | Value | Language |
dc.contributor.author | Schmidt, P. | |
dc.contributor.author | Born, J. | |
dc.contributor.author | Bommes, D. | |
dc.contributor.author | Campen, M. | |
dc.contributor.author | Kobbelt, L. | |
dc.date.accessioned | 2023-02-17T11:35:16Z | - |
dc.date.available | 2023-02-17T11:35:16Z | - |
dc.date.issued | 2022 | |
dc.identifier.issn | 0167-7055 | |
dc.identifier.uri | http://osnascholar.ub.uni-osnabrueck.de/handle/unios/65496 | - |
dc.description.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. | |
dc.description.sponsorship | German Research Foundation within the Gottfried Wilhelm Leibniz programme; Deutsche Forschungsgemeinschaft (DFG) [IRTG-2379]; European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (AlgoHex) [853343]; Projekt DEAL; Excellence Strategy of the Federal Government; Lander; We thank Anton Florey, Alexandra Heuschling, Dorte Pieper, Joe Jakobi, and Philipp Domagalski for testing and contributing to the development of TinyAD. This work was partially funded by the German Research Foundation within the Gottfried Wilhelm Leibniz programme and partially funded under the Excellence Strategy of the Federal Government and the Lander, as well as by grant IRTG-2379 of the Deutsche Forschungsgemeinschaft (DFG). D. Bommes has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (AlgoHex, grant agreement No 853343). Open access funding enabled and organized by Projekt DEAL. | |
dc.language.iso | en | |
dc.publisher | WILEY | |
dc.relation.ispartof | COMPUTER GRAPHICS FORUM | |
dc.subject | Computer Science | |
dc.subject | Computer Science, Software Engineering | |
dc.title | TinyAD: Automatic Differentiation in Geometry Processing Made Simple | |
dc.type | journal article | |
dc.identifier.doi | 10.1111/cgf.14607 | |
dc.identifier.isi | ISI:000864660300011 | |
dc.description.volume | 41 | |
dc.description.issue | 5 | |
dc.description.startpage | 113 | |
dc.description.endpage | 124 | |
dc.contributor.orcid | 0000-0002-3190-1341 | |
dc.contributor.orcid | 0000-0002-8917-3674 | |
dc.contributor.orcid | 0000-0003-2340-3462 | |
dc.identifier.eissn | 1467-8659 | |
dc.publisher.place | 111 RIVER ST, HOBOKEN 07030-5774, NJ USA | |
dcterms.isPartOf.abbreviation | Comput. Graph. Forum | |
dcterms.oaStatus | Green Published | |
local.import.remains | affiliations : RWTH Aachen University; University of Bern; University Osnabruck | |
local.import.remains | web-of-science-index : Science Citation Index Expanded (SCI-EXPANDED) | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.orcid | 0000-0003-2340-3462 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | CaMa281 | - |