Physics Simulation Just Crossed A Line

Let’s throw two properly dressed armadillos   down into this container. Yowch!  Did you see that? Oh goodness.  I hope they have good health  insurance, because that looked painful. Then, a barbarian ship slides  down the stairs. This guy is   made of 487 thousand tetrahedra. Insane. So how on earth is it  possible to compute all this?  Well, this is a physics program that can compute  how your cloth moves if you do crazy handstands   like this. If only he knew that we are about to  put him into pajamas. Then we are going to throw   these tablecloths down and see these beautiful  complex self-collisions and stacking behavior.   This is a crazy test for these programs  because it creates tons of self-collisions,   but wait…this one keeps every layer  distinct and realistic. Absolutely   amazing. And this is not AI, this  is pure human brilliance. But…how? Well, I’ll tell you the secret  of this program in this video. That would be great, because this can do  incredible things. Just look at this scene   where two fabric strips are pulled in opposite  directions to form a tight knot! The tension   is incredible, and the way the fabric wrinkles  and compresses without passing through itself is   simply beautiful to watch. It handles these  complex frictional contacts so gracefully,   ensuring that the knot tightens  naturally just like in real life. Now hold on to your papers Fellow  Scholars, because this is not only   realistic, but it is fast! So, how fast? This curtain simulation involves 6 million   degrees of freedom. Degrees of freedom refers  to the number of variables the computer has   to solve for. Imagine solving a math problem  with 6 million unknowns! Usually, this would   take an eternity, but this method simulates  one frame in just 6.6 seconds. Mind blown! So how much faster is this  than previous techniques?   Well, up to 66 times faster than C-IPC,   this amazing previous technique that we talked  about 455 videos ago. That’s an exact number. Then, it is 11x faster than PD-Coulomb,   another CPU-based friction method. And  get this - it runs on your processor. Now, you might be thinking: "But Károly,  this runs on the processor. Isn't the CPU   the slow turtle compared to the graphics  card, the GPU for these massive parallel   tasks?”. Excellent question. Well, this  algorithm is so clever that it actually   runs 2.6 times faster than a state-of-the-art  technique that runs on the GPU. That’s like a   minivan beating a Formula 1 car just  because the minivan knew a shortcut! Okay, so how is all this wizardry possible?  How are they doing this? GPUs are meant to be   100s of times faster than CPUs. Yet,  the CPU wins here. How is that even   possible? Dear Fellow Scholars, this is Two  Minute Papers with Dr. Károly Zsolnai-Fehér. To understand this, imagine you are  trying to solve a 10,000-piece jigsaw   puzzle. The GPU approach is like hiring  10,000 ants to solve it. Sounds good,   right? Each ant holds exactly one piece. They are  super fast and all work at the exact same time,   in parallel. Well…this sounds perfect!  But wait, because they are just ants,   they can't see the big picture. They have to  constantly shout at their neighbors, “Hey,   does this fit? And what about this one?" over  and over again. This shouting match is what   scientists call iterations, and for complex  cloth that stretches across the whole screen,   the ants have to shout millions of times to get  the edges of the puzzle to agree with the center.   It works, but man, it takes a lot of yelling.  It’s a bit like your corporate email thread   where you accidentally press reply-all to 10,000  people. But here, everyone does that. Good times! Okay, so that’s not the way. This new paper  proposes a different strategy. Step number one:   fire the ants. Get out of here! Instead,  let's hire 32 puzzle grandmasters - these   represent your CPU cores. The algorithm takes  the giant puzzle and cuts it into 32 large,   separate chunks - this is called  Domain Decomposition. Now,   each grandmaster takes one chunk into a quiet  room and solves it perfectly in a split second. So that means that these are not pajamas.  These colorful pieces of clothing are the   chunks for the domain decomposition.  They look like a patchwork quilt made   by a very mathematically inclined  grandmother. Well done grandma!   The problem has been cut up into many smaller  problems, each of which can be solved very   quickly. But the problem is of course, that  they have to connect. How do we reassemble them? Well, since these are grandmasters,   these people mean serious business. This  means they don't guess. Nope. Instead,   they first agree on the shared edges, and then  instantly solve the rest of their puzzle pieces. So, once the grandmasters finish their parts,  they meet and simply click the 32 big finished   sections together. Because they solved the  hard internal parts perfectly on the first try,   they don't need to have a shouting match.  They just stitch the boundaries together and   go home early. This is genius. Why? Because  it plays into the CPU's strength. You see,   the GPU has an army of ants strategy.  But instead, the CPU can do smart,   heavy lifting on fewer tasks. That is  exactly what we are doing here! Amazing. Okay, so here is how brilliantly  they put this into mathematics.   I’ll explain it in a simple way.  But ,you have to promise that you   won’t close the video. You gotta stay  until the end! Promise? Promise. Okay. This is the original equation from the paper,   but we are a child friendly show  so I’ll truncate it to this one. You see, normally you have to solve for every  single piece of the puzzle at once. The 10,000   ants. That’s a matrix with millions of  rows. Solving these takes insanely long. But this equation says. You know what,  let’s split the variables into two teams. This symbol here, Lambda, is the glue.   It represents the forces holding  the different chunks together.  And this one, XC, represents the corner pieces—the  few crucial spots where the domains touch. These terms here basically say:  "Ignore the million puzzle pieces,   we already know they are perfect. Let's  only solve for the glue and the corners”.  This is what the grandmasters do.  And that is where the brilliance   is. I absolutely love this. So beautiful! Mathematically, this reduces a massive,  impossible problem into a tiny,   easy one that solves the interactions between  the domains. It effectively turns the shouting   match of millions of ants into a polite,  quick handshake between 32 grandmasters. The math actually makes things simpler! This is  beyond amazing. This is the magic of the papers.   This is what makes everything 66 times  faster than a previous technique that   was already amazing. What a time to be alive! And it honestly breaks my heart that almost  nobody knows about this work. This brilliant   paper is sitting there, solving problems 66 times  faster, and the world is just scrolling past it. And this is why I devoted my life to learning and  talking about these papers to you Fellow Scholars.   There are so many hidden gems out  there that no one knows or talks about! You know why? Because apart from very few  cases, Youtube doesn’t recommend this kind   of content. So you can’t make easy money  off of it. That’s it. That’s the reason.   But papers are amazing! John Carmack also picked  up a bit of a paper habit, very proud of him. Way   to go John! So save the snails, save the  beavers, subscribe to Two Minute Papers!