Monte Carlo Geometry Processing
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- Опубликовано: 28 авг 2022
- How can we solve physical equations on massively complex geometry? Computer graphics grappled with a similar question in the 1990s, leading to the widespread adoption of Monte Carlo methods for photorealistic image generation. This talk explores how Monte Carlo can also be used to solve a broader class of equations appearing in science and engineering, using the so-called "walk on spheres method" and recent extensions developed at Carnegie Mellon University.
The talk was originally given by Keenan Crane at the Oberwolfach Research Institute for Mathematics on August 22, 2022. It is based primarily on two papers:
1. Sawhney & Crane, "Monte Carlo Geometry Processing: A Grid-Free Approach to PDE-Based Methods on Volumetric Domains" - www.cs.cmu.edu/~kmcrane/Projec...
2. Sawhney, Seyb, Jarosz, Crane, "Grid-Free Monte Carlo for PDEs with Spatially Varying Coefficients" - cs.dartmouth.edu/wjarosz/publ... 
Кино
babe wake up, a new keenan crane lecture just dropped
Mr. Crane you present complex data extremely well. Even to non academics. This is my new technical ASMR as a 3D artist. Thank you.
As someone who spent 2 years of PhD juggling probability and finite element method texts, this method is simply amazing. I was always a fan of grid free methods. This marks an amazing new approach in that field. I just hope that some of these methods become mainstream sometime in near future.
Numerical methods is one of the most boring subjects to learn, yet you managed to make it quite interesting. Great work!
I nearly cryed by this perfect video. It gives me a projected hope to keep up with the current papers trend as an undergrad. Thank you so much!
This is worth paying by tax, privatly and by our own spare time!
I think Monte Carlo Geometry Processing is an amazing breakthrough for geometry processing field. And it is easier to implement from scratch!
I think that's a very amazing thing that relates PDE back to SDE, I love it so much and hope to work on the things more.
Thank you so much for such a clear and exhaustive video on the deep connection between diffusion process and geometry!
You have an excellent talent of explaining
Thx for the lecture on this MC geometry processing that I was always wanna take time to digest.
Such an exceptional use of geometry.
Outright awesome! Great presentation, it seems simple as you explain it
This could have saved me some time with some volumetric clouds in the past. It will save me time in computing convex collisions and much more in the future. Thank you so much for such a clean work and explanation!
Keenan, your betrayal of meshes will not be forgotten, nor forgiven.
This video is related to your two recent papers? After watching this video, I should read those papers too! Thank you for the video!
Any recommendations for learning more stochastic calculus? I’d love to understand that Feinman Kak equation at the heart of things here.
I'd love to hear your thoughts on how this would handle transient cases. I only have an intermediate understanding of numerical methods, so I'm not sure how time history data would persist through time steps in this method. Could you populate the internal space with a ton of source terms that reflect the previous time step's state? And if so would this cause error accumulation?
awsome work! could you tell what softwares you use to visualize these wonderful renderings?
Would this supercede the diffusion used in the Vector Heat Method? Since the given vectors to interpolate would be considered point sources / boundaries in WoS?
Absolutely amazing video! Subscribed.
Where can I read more about Monte Carlo Geometry Processing in regards to MD sims or perhaps homology modeling? It'd be interesting to leverage this work towards my dissertation in structural biology.
Do you have a link/title for the path planning work from Ryan Schmidt you referenced at the very end? I'm having trouble finding it.
Can this method be used to solve the eigenmodes of an optical fiber?
Can this be used for navigation & pathfinding? Also Non-euclidean geometry?
Looks like SDF without the tracing
So in Monte Carlo ray tracing the grid is essentially replaced by a cube from which the rays emanate/bounce?
I barely understood anything because I know practically nothing about stochastic calculus. I guess this will be the new thing I rip my hair off trying to figure out.
Wow, impressive. Could this be used for solving Maxwell's equations instead of FDTD?
Theoretically, I would say yes. Light equations are basically Maxwell's equations at it's core.
Very interesting but my brain is unable to grasp most of the things due to lack of prerequisite knowledge
Can you suggest some things
I would suggest searching some names from the video you don't recognize, see what comes up - there are great videos on these topics on RUclips
Also another question: normally MC is embarrassingly parallelisable and can utilise SIMD to run fast on GPUs. Is it true here?
He mentions parallelism as one of the benefits of MC methods in the section starting at 6:30
He mentions that it's embarrassingly parallel in the "propaganda" section at the beginning when he comments on how multiple samples can be merged by just averaging them, and also implicitly when he shows a demo of one of the solvers actually running on a GPU
OH BABBY 50 MINUTES HELL YEAH
Given the quality of the presentation (how well the video supports the audio) you can easily watch it on 1.75x speed.
@@pavolharar why would I do that I like the longer videos
Well, you can watch 1.75 more of them.
I'm pretending to understand something about it ...
I bet you can't find the parametric equation of a hexaflexagon *a real one
Not just 3 strip Mobius strip ask 3blue about me mwhahahaaha
Kac is pronounced like "cots", not "cock"
Thank you. I have asked N people how they pronounce it-and received N different answers!