Academic Journal
Differential Walk on Spheres.
| Τίτλος: | Differential Walk on Spheres. |
|---|---|
| Συγγραφείς: | Miller, Bailey, Sawhney, Rohan, Crane, Keenan, Gkioulekas, Ioannis |
| Πηγή: | ACM Transactions on Graphics; Dec2024, Vol. 43 Issue 6, p1-18, 18p |
| Θεματικοί όροι: | Monte Carlo method, Inverse problems, Structural optimization, Stochastic convergence, Partial differential equations |
| Περίληψη: | We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at arbitrary points, without performing a global solve or constructing a volumetric grid or mesh. The method is hence well suited to inverse problems with complex geometry, such as PDE-constrained shape optimization. Like other walk on spheres (WoS) algorithms, our method is trivial to parallelize, and is agnostic to boundary representation (meshes, splines, implicit surfaces, etc.), supporting large topological changes. We focus in particular on screened Poisson equations, which model diverse problems from scientific and geometric computing. As in differentiable rendering, we jointly estimate derivatives with respect to all parameters---hence, cost does not grow significantly with parameter count. In practice, even noisy derivative estimates exhibit fast, stable convergence for stochastic gradient-based optimization, as we show through examples from thermal design, shape from diffusion, and computer graphics. [ABSTRACT FROM AUTHOR] |
| Copyright of ACM Transactions on Graphics is the property of Association for Computing Machinery and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
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| Items | – Name: Title Label: Title Group: Ti Data: Differential Walk on Spheres. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Miller%2C+Bailey%22">Miller, Bailey</searchLink><br /><searchLink fieldCode="AR" term="%22Sawhney%2C+Rohan%22">Sawhney, Rohan</searchLink><br /><searchLink fieldCode="AR" term="%22Crane%2C+Keenan%22">Crane, Keenan</searchLink><br /><searchLink fieldCode="AR" term="%22Gkioulekas%2C+Ioannis%22">Gkioulekas, Ioannis</searchLink> – Name: TitleSource Label: Source Group: Src Data: ACM Transactions on Graphics; Dec2024, Vol. 43 Issue 6, p1-18, 18p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+problems%22">Inverse problems</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+optimization%22">Structural optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+convergence%22">Stochastic convergence</searchLink><br /><searchLink fieldCode="DE" term="%22Partial+differential+equations%22">Partial differential equations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at arbitrary points, without performing a global solve or constructing a volumetric grid or mesh. The method is hence well suited to inverse problems with complex geometry, such as PDE-constrained shape optimization. Like other walk on spheres (WoS) algorithms, our method is trivial to parallelize, and is agnostic to boundary representation (meshes, splines, implicit surfaces, etc.), supporting large topological changes. We focus in particular on screened Poisson equations, which model diverse problems from scientific and geometric computing. As in differentiable rendering, we jointly estimate derivatives with respect to all parameters---hence, cost does not grow significantly with parameter count. In practice, even noisy derivative estimates exhibit fast, stable convergence for stochastic gradient-based optimization, as we show through examples from thermal design, shape from diffusion, and computer graphics. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of ACM Transactions on Graphics is the property of Association for Computing Machinery and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1145/3687913 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 1 Subjects: – SubjectFull: Monte Carlo method Type: general – SubjectFull: Inverse problems Type: general – SubjectFull: Structural optimization Type: general – SubjectFull: Stochastic convergence Type: general – SubjectFull: Partial differential equations Type: general Titles: – TitleFull: Differential Walk on Spheres. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Miller, Bailey – PersonEntity: Name: NameFull: Sawhney, Rohan – PersonEntity: Name: NameFull: Crane, Keenan – PersonEntity: Name: NameFull: Gkioulekas, Ioannis IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 07300301 Numbering: – Type: volume Value: 43 – Type: issue Value: 6 Titles: – TitleFull: ACM Transactions on Graphics Type: main |
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