Monte Carlo Geometry Processing

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:

[colejhudson]

babe wake up, a new keenan crane lecture just dropped

[MichaelHalsell]

Mr. Crane you present complex data extremely well. Even to non academics. This is my new technical ASMR as a 3D artist. Thank you.

[mehrdaddowlatabadi]

One of the good lectures I have seen on YouTube so far.

[loukitmyname]

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.

[maxqutekerman]

Numerical methods is one of the most boring subjects to learn, yet you managed to make it quite interesting. Great work!

[choochootraiin]

Thank you so much for such a clear and exhaustive video on the deep connection between diffusion process and geometry!

[晴栩]

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.

[vandang]

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!

[marc-andrepiche]

You have an excellent talent of explaining

[pedroth]

I think Monte Carlo Geometry Processing is an amazing breakthrough for geometry processing field. And it is easier to implement from scratch!

[zwazwezwa]

Outright awesome! Great presentation, it seems simple as you explain it

[fluffy_tail]

Just found this video, it is absolutely stunnign work and your presentation skills are incredible as well

[IvanMorenoPlus]

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!

[AndreaTagliasacchi-ry]

Keenan, your betrayal of meshes will not be forgotten, nor forgiven.

[immowang]

Thx for the lecture on this MC geometry processing that I was always wanna take time to digest.

[sungjuyea]

This video is related to your two recent papers? After watching this video, I should read those papers too! Thank you for the video!

[logo]

Any recommendations for learning more stochastic calculus? I’d love to understand that Feinman Kak equation at the heart of things here.

[meatmanek]

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.

[theoreticalorigamiresearch]

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.

[guangfuwang]

awsome work! could you tell what softwares you use to visualize these wonderful renderings?