Dear Fellow Scholars, this is Two Minute Papers with Dr. Károly Zsolnai-Fehér.
If you have been watching this series for a while, you know very well that I love
learning algorithms and fluid simulations. But do you know what I like even better?
Learning algorithms applied to fluid simulations, so I couldn’t be happier with today’s paper.
We can create wondrous fluid simulations like the ones you see here by studying the laws of
fluid motion from physics, and writing a computer program that contains these laws.
However, I just mentioned learning algorithms.
How do these even come to the picture? If we can write a program that simulates the laws,
why would we need learning-based algorithms? This doesn’t seem to make any sense.
You see, in this task, the neural networks can be also applied to solve something that
we already know how to solve. However, if we use a neural network to perform this task,
we have to train it, which is a long and arduous process. I hope to have convinced you
that this is a bad, bad idea. Why would anyone bother to do that? Does this make any sense?
Well, it does make a lot of sense! And the reason for that is that this training step
only has to be done once, and afterwards, querying the neural network, that is, predicting
what happens next in the simulation runs almost immediately. This takes way less time than
calculating all the forces and pressures in the simulation while retaining high quality results.
This earlier work from last year absolutely nailed this problem. Look,
this is a scene with the boxes it has been trained on.
And now, let’s ask it to try to simulate the evolution of significantly different shapes.
Wow. It not only does well with these previously unseen shapes,
but it also handles their interactions really well.
But there was more! We could also train it on a tiny domain with only a few particles,
and then, it was able to learn general concepts that we can reuse to simulate
a much bigger domain, and also, with more particles. Fantastic!
This was a simple, general model that truly is a force to be reckoned with.
Now, this is a great leap in neural network-based physics simulations, but of course, not everything
was perfect there. For instance, over longer timeframes, solids became incorrectly deformed.
And now, a newer iteration of a similar system just came out from DeepMind’s research lab that
promises to extend these neural networks for an incredible set of use cases:
aerodynamics, structural mechanics,
cloth simulations and more. I am very excited to see how far they have come since!
So let’s see how well it does, first, with rollouts, then, with generalization experiments.
Here is the first rollout experiment, so what does that mean, and what are we seeing here?
On the left, you see a verified handcrafted algorithm performing the simulation,
we will accept this as the true data, and on the right, the AI is trying to continue
the initial simulation. But there is one problem. And that problem is that the AI was only trained
on short simulations with 400 time steps, that’s only a few seconds! And unfortunately,
this test will be a hundred times longer. So, it only learned on short simulations, can it manage
to run a longer one and remain stable? Well, that will be tough…but, so far so good…still running.
My goodness, this is really something. Still running and it’s very close to the ground truth!
Okay, that is fantastic, but that was just a piece of cloth. What about interaction with other
objects? Well, let’s see. I’ll stop the process here and there so we can inspect the differences.
Again, flying colors. Loving it.
And, apparently, the same can be said for simulations in structural mechanics, and
incompressible fluid dynamics. Now, that is one more important lesson here - to be able to solve
such a wide variety of simulation problems, we need a bunch of different hancrafted algorithms
that took many-many years to develop. But this one neural network can learn and perform them all,
and it can do it 10 to a 100 times quicker.
And now comes the second half, generalization experiments. This means a simulation scenario
with shapes that the algorithm has never seen before. And let’s see if it obtained general
knowledge of the underlying laws of physics to be able to pull this off. Oh my! Look at
that! Even the tiny piece that is hanging off of the flag is simulated nearly perfectly.
In this one, they gave it different wind speeds and directions that it hadn’t seen before, and not
only that, but we are varying these parameters in time, and it doesn’t even break a sweat.
And hold on to your papers, because here comes my favorite - it can even
learn on a small-scale simulation with a simple rectangular flag, and now,
we throw at it a much more detailed, cylindrical flag with tassels. Surely this will be way beyond
what any learning algorithm can do today. And…okay, come on…I am truly out of words. Look.
So now, this is official. We can ask an AI to perform something that we already know how to do,
and it will not only be able to reproduce similar simulations, but we can even ask things
that were previously quite unreasonably outside of what it had seen, and it handles all these
with flying colors. And it does this much better than previous techniques were able to. And it can
learn from multiple different algorithms at the same time. Wow. What a time to be alive!
Thanks for watching and for your generous support, and I'll see you next time!