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DTSTAMP:20260817T171531Z
LOCATION:Hall B5 (1)\, B Block\, Level 5
DTSTART;TZID=Asia/Tokyo:20241203T150800
DTEND;TZID=Asia/Tokyo:20241203T151900
UID:siggraphasia_SIGGRAPH Asia 2024_sess106_papers_1139@linklings.com
SUMMARY:Solving Inverse PDE Problems using Grid-Free Monte Carlo Estimator
 s
DESCRIPTION:Ekrem Fatih Yilmazer (EPFL), Delio Vicini (Google Inc.), and W
 enzel Jakob (EPFL)\n\nPartial differential equations can model diverse phy
 sical phenomena including heat diffusion, incompressible flows, and electr
 ostatic potentials. Given a description of an object's boundary and interi
 or, traditional methods solve such PDEs by densely meshing the interior an
 d then solving a large and sparse linear system derived from this mesh. Re
 cent grid-free solvers take an alternative approach and avoid this complex
 ity in exchange for randomness: they compute stochastic solution estimates
  and generally bear a striking resemblance to physically-based rendering a
 lgorithms.\n\nIn this article, we develop algorithms targeting the inverse
  form of this problem: given an already existing solution of a PDE, we inf
 er parameters characterizing the boundary and interior. In the grid-free s
 etting, there are again significant connections to rendering, and we show 
 how insights from both fields can be combined to compute unbiased derivati
 ve estimates that enable gradient-based optimization. In this process, we 
 encounter new challenges that must be addressed to obtain practical soluti
 ons. We introduce acceleration and variance reduction strategies and show 
 how to differentiate branching random walks in reverse mode.\n\nWe finally
  demonstrate our approach on both simulated data and a real-world electric
 al impedance tomography experiment, where we reconstruct the position of a
  conducting object from voltage measurements taken in a saline-filled tank
 .\n\nRegistration Category: Full Access, Full Access Supporter\n\nLanguage
  Format: English Language\n\nSession Chair: Yonghao Yue (Aoyama Gakuin Uni
 versity)\n\n
URL:https://asia.siggraph.org/2024/program/?id=papers_1139&sess=sess106
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