Monte Carlo Simulation

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A Monte Carlo simulation is a randomly evolving simulation. In this video, I explain how this can be useful, with two fun examples of Monte Carlo simulations: The first model shows how pi can be determined with Monte Carlo sampling, and in the second part of the video we will take a look how animations can be rendered with Monte Carlo path tracing.
If you want to see another Monte Carlo simulation in action, check out this video:
• Entropy Explained with...
If you want to support my channel, subscribing, liking and sharing is an amazing help. Thank you! :) If you feel like this video added value to your life and you want to support MarbleScience even more, please consider becoming a patron.
/ marblescience
Chapters:
00:00 What are Monte Carlo simulations?
01:01 determine pi with Monte Carlo
03:01 analogy to study design
04:56 back to Monte Carlo
05:57 Monte Carlo path tracing
08:51 summary
There is also a text version of this video on my website:
marblescience.com/blog/monte-...
You can also find me at:
/ tobiasllemke
/ marblescience

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Опубликовано:

18 май 2024

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Комментарии : 1,3 тыс.

@MarbleScience 3 года назад

If you want to support my channel, subscribing, liking and sharing is an amazing help. Thank you! :) If you feel like this video added value to your life and you want to support MarbleScience even more, please consider becoming a patron. www.patreon.com/MarbleScience

@priceandpride 2 года назад

You are incredibly handsome

@freeenergyeducationinterna1086 2 года назад

04:30 The law of large numbers is bullshit. If it were true, no one would have been surprised by the election of Harry S. Truman to the office of president of the USA.

@sofiaramos154 2 года назад

When are you making more videos? :( I absolutely loved this one!

@JorgeBrown 10 месяцев назад

I've done two out of your three suggestions. I liked and I subscribed. Now, I have to think to whom I'm going to send it. What if I send randomlly to my friends list? 😄👍🏼

@MarbleScience 10 месяцев назад

@@JorgeBrown no objections from my side 😄

@DS-kv3og Год назад

You are a mathematician harry

@jglaab 3 года назад

literally hypnotized by how clean that marble animation was. This channel feels like a massive hidden gem!

@ikesau Год назад

yeah it's really good. though the scale with the cylindrical container on it should have been circular 🙈

@dave_ 3 года назад

Nice Video and even better Animation!

@MarbleScience 3 года назад

Thanks!

@AlesZvolanek 3 года назад

:DDD

@dogefugger6960 3 года назад

Ich habe Grade dein Video über die Atemübungen gesehen und jetzt dieses Video und du bist einfach hier in den Kommentaren. (Hab vorher noch nie ein Video von dir gesehen)

@m3hdim3hdi 3 года назад

No! Nice animations even better video

@Retronix21 8 месяцев назад

so ein macher was machst du denn hier :D

@omaramakhtari7600 3 года назад

I ended up here randomly, was not disappointed. Your accent is great, material delivery was clear and concise, the animation was solid, and video length was perfect. Keep up the good work, this channel will go far!

@professortrog7742 3 года назад

Did you drop in during a montecarlo simulation ?

@AndoMusicChannel 3 года назад

Why does this comment sound like a good teacher’s feedback? :)

@theevilmonk1472 3 года назад

@@AndoMusicChannel LOOOL exactly my reaction!

@sadbadmac 3 года назад

@@AndoMusicChannel Because it's constructive, not just another meme.

@arturofernandez6592 3 года назад

Randomly... not really

@FranciscoBerkemeier 3 года назад

This was fantastic. As a mathematician I've always found Monte Carlo simulation to be a tremendously powerful tool, mainly due to its simplicity. To see that you start the video by saying precisely that is truly wonderful :) Keep it up!

@factChecker01 3 года назад

I don't know if I would say that Monte Carlo simulation is so simple as I would say that analytic methods get surprisingly complicated with the slightest modification of the standard examples.

@reiniernn9071 3 года назад

I thought mathematicians were nearly always exact....but those who study physica will enjoy this kind of methodes. (Unless you're specialized in statistics....).

@jakobohler9057 3 года назад

After watching this vid: This channel has to have more than 1million subscribers... .

@rpyrat 3 года назад

After watching the first few seconds: subscribed

@JMan-24 3 года назад

Very clever!

@KIWISP 3 года назад

You have an amazing knack for presenting complex stuff in a simple manner. Its not just the storyline or the visuals that are great, the audio part is soft-toned and slow enough, easy to follow.

@markusschoen2051 3 года назад

Thank you! Not easy to find "no-fluff", straight forward explanations these days. Right level of depth and still entertaining!

@TylerMatthewHarris 3 года назад

This is great! Very unique. As a Maya user I appreciate the amount of effort it took to make this. This kind of content is gold and people will find you. Usually when I watch new channels I have critiques but everything about this is damn near perfect. Can't wait for more

@focker0000 3 года назад

As an engineer, I love watching videos explaining various math concepts through different ideas, even though I already learned these concepts quite well. You did a fantastic job. I appreciate all works that make science/math/engineering easy to the grand public!

@brigittetucker1767 3 года назад

It is a brilliant demonstration, also it left me wondering if the robotic arm is connected to the tabletop with the dishes,l guess it could move the dishes slightly,or not?

@ideyaa3640 3 года назад

I needed to understand the Monte Carlo methode for my AI project in the Uni. Your video is amazing! thanks a lot :) The visuals and animations are great.

@Omar-jn9zf 3 года назад

Absolutely fantastic. This is what we call go big or go home. This is astonishing as your 3rd video on RU-vid. Please keep the good work.

@squirrelsaregreat9826 3 года назад

I love those visuals! Simple but they contain everything. :)

@LF1780 3 года назад

Awesome explanation of Monte Carlo simulations! Clear and concise, love it!

@emmanuelagudo4918 2 года назад

I was reading a whitepaper on Project life cycles: and how uncertainty decreases over time (given a set of constraints in the model), and the corresponding increases in cost of change. This animation of Monte Carlo Simulation tool is so beautiful. Thank you!

@walkerstandard2373 3 года назад

Really amazing video, so concise yet explanatory with visuals to boot!

@DesaiAmogh9 3 года назад

I was looking for a quick and simple explanation on Monte Carlo Simulation and thanks to your video it made my job soo much easier!! Amazing video :)

@tedgrove9412 Год назад

I am extremely grateful to live in world where people who are intellectually-gifted are inclined to share their insights to others in an effective, straightforward way.

@vinayzzzful 3 года назад

I haven’t seen anyone explain MC simulations so clearly. Please keep it up and upload videos on more such topics.

@bbnazir 3 года назад

Hi from RU-vid Recommended. Appreciate the production value and quality of content.

@pandalism9513 3 года назад

Great video, did not know monte carlo methods were used for light scattering in diffused surfaces but it makes so much sense!

@rodge4980 8 месяцев назад

Love how the video sections are switched directly on the minute mark.

@mansoorghumro8404 3 года назад

3D animator, learning python, was researching the best way to understand Monte Carlo Simulation. Props for an amazing video overall, crisp animation, no nonsense explanation, and the rendering example just solved too many puzzles bundled in years. Liked and subbed. Thank you very much.

@MarbleScience 3 года назад

Glad it helped :)

@AllemandInstable 3 года назад

Really well explained great visuals nice audio quality this channel is on the right path love it

@avirajbevli7268 3 года назад

Thanks for the amazing content and presentation. This channel is gonna grow for sure!!

@luisewe5488 3 года назад

Amazing work! Hope to see more of it in the future!! :)

@niamhoconnor8986 3 года назад

Never heard anyone explain anything this concise 👏👏👏

@Engiction 3 года назад

Great video man, good explanation and amazing application example

@arunkenta 3 года назад

Channels like these deserve all the subscription for helping students all over the world

@nyanates 3 года назад

I’ve encountered this probably only 3-4 times in my career and every time I need a refresher and am suitably impressed with its elegance and RL applications. Thanks for the simplest explanation and demonstration I’ve seen yet. New subscriber here.

@MarbleScience 3 года назад

Great to hear!

3 года назад

Amazing work and explanation! I think I finally understand the main reasoning to use a Monte Carlo simulation on a given problem. Thanks!

@aritraroy4994 3 года назад

Only 4k view for such an beautiful explanation? Great job man!!

@GhastlyDesigns 3 года назад

Great video and a fantastic explanation! I love the 3D visuals, they look really nice. I’m currently using Monte Carlo simulations to fit molecular simulation boxes to neutron diffraction data.

@_mar1 3 года назад

So interesting! The flow of the video including the visuals are amazing!

@kylezinho_ 3 года назад

Fantastic video quality! This channel deserves way more subs

@cr7rulz97 3 года назад

Amazing! I was reading a book today that referring to this concept. It's so much clearer now, thanks a ton!

@aakashbava9624 2 года назад

Fooled by randomness?

@SunriseLAW 3 года назад

My father is currently the youngest still-surviving American POW of WW-2. He also worked at RAND Corp., programming early computers. He went to CACI, where he did 'all' of Harry Markowitz's math (Markowitz won a Nobel). Video reminded me of it, thanks for that! My father explained that the Monte Carlo method required lots of 'transactions' to work well. He compared it to a CASINO when we visited Las Vegas: empty and dull until enough people showed up to gamble. He opined that the methodology formed the basis of the modern financial industry, which requires lots of 'transactions' to appear vibrant. In the 1990's he stated that some of the mathematics he wrote and coded at RAND in the early 1960' was still embedded in code modules commonly in use then (and perhaps now as well).

@reji6414 3 года назад

Wow... great

@The_Student2 3 года назад

These animations are unreal and the video quality is amazing.

@forexsanjose6090 9 месяцев назад

Thank you for your patient and well-paced explanation.

@T33K3SS3LCH3N 3 года назад

Great video! Another computer graphics example is Ambient Occlusion, which artificially adds shadows to occluded places that are unlikely to get much light reflected to them, like the corner of a room. Very roughly speaking you can imagine a small sphere around each image pixel, and then you sample a number of random points within that sphere. For each sample point that is "inside" an object, you make the pixel a little darker to simulate occlusion, since that indicates that no light can come from that direction. Usually only a few samples are taken (~8-32 in real time applications like games), so the result is very noisy just like in your lighting example. But this noise is often considered a good thing because you can save the resulting shadows to a seperate image and put them through a smoothing algorithm before applying them to the output screen. The result tends to looks positively organic - reasonbly smooth, but with a bit of visible randomness to it, just like most real life surfaces.

@naivety 3 года назад

Great work on these simulations. I'm looking at Physics graduate programs right now and I've seen "Monte Carlo" thrown around quite a bit. Good to know they just meant "estimates that give good enough answers."

@BrunoMontanhez 3 года назад

That explanation with that animation is pure art. Whoa.

@ryandavis280 3 года назад

Incredible visuals and explanations, thanks!

@Ahsan_Fazal 3 года назад

The production value of this video is AMAZING. Please keep creating content my dude

@MarbleScience 3 года назад

Thank you! Will do!

@Andrew-Andre 3 года назад

This is a really useful concept and is very similar to that used in the colour sampling done using bayer sensors in digital cameras. So long as the pixel count is high enough, the distributed mosaic pattern (or colour filter array) allows for sampling of enough RGB luminance values to fairly accurately interpolate (using demosaicing algorithms) the neighbouring pixel colour. The concept of signal to noise ratios and thresholds for a given task can be applied to just about any situation. You did a great job of explaining this.

@MarbleScience 3 года назад

Interesting! I always love to discover situations where this concept is used, and yes there are really a lot. Thanks for your comment.

@yujingzou1826 3 года назад

Such an incredible video, Monte Carlo simulation is incredibly widely used and important in radiation therapy physics to simulate particles. I am studying it currently and it is so refreshing to think about the concepts in physics with your marble animations! Amazing and thank you!

@khai7519 3 года назад

Vielen Dank, sehr cooles and gut verständliches Video!

@Matyanson 3 года назад

This video is probably gonna blow up in the future. Good luck(68K views now)

@iainmillar1532 3 года назад

2 days later 235k views.... (18 nov 2020)

@Robis9267 11 месяцев назад

1M (10 Jun 2023)

@mehdia5176 2 года назад

Bless you for this clear explanation

@RicardoMontania 3 года назад

Beautifully explained!

@MisterLenor 3 года назад

I really like the style of this video, a good but simple way of explaining things👍 And some really nice animations :)

@MarbleScience 3 года назад

Thanks :)

@adrienferreira4666 3 года назад

@@MarbleScience can you tell me more about how you do them? Is it Blender + Python? Thanks ;)

@igrogro 3 года назад

Incredible job! That's some high quality and very educational content right there. Really hope that your work will be appreciated more :) Thanks

@darlenebennett4891 3 года назад

AKA "I'm too lazy to learn integrals"

@verminr 3 года назад

What a great video! Beautiful graphics and an excellent explanation

@shadsyed943 3 года назад

Excellent presentation. Keep up the good work.

@Layput 3 года назад

"It's a type of overtly theoretical concept that can solve incredibly complex problems, which I thoroughly enjoy doing" Nerds have a totally different world.

@lemonade1016 3 года назад

High quality content, I can see you channel growing quickly and eventually to millions of subscribers!!!

@karan4624 3 года назад

I wish the same

@Exbozz 3 года назад

High quality, extremely nice production value, subbing just because of that.

@improcrastinating8063 3 года назад

Wow I didn't look at subscribers until after, I just assumed it was like several hundred thousand at least!

@rocksolid6494 3 года назад

This video has illuminated some more random knowledge paths in my mind to see this concept more clearly.

@aditya4974 3 года назад

Saw first video from your channel today and have already hit the subscribe button! Really cool explanation. Thank you!

@alexhopman163 3 года назад

Can you use a Montecarlo simulation to determine when randomness becomes reliable? Perhaps Defining reliable as 2decimal places. Just curious.

@PabloSanchez-qu6ib 3 года назад

I imagine you can continue the simulation until it wanders as little as you need.

@samarthhawaldar9931 3 года назад

From the law of large numbers, you can make predictions about the standard deviations. It mostly goes as ~1/√N where N is the number of samples

@toomuchtoknowitall 3 года назад

Man, am I glad that Edward Snowden finally found a job

@xyzct 3 года назад

... playing Harry Potter.

@WilcoVerhoef 3 года назад

He looks even more like Ryan Eggold, actor in The Blacklist

@toomuchtoknowitall 3 года назад

@@WilcoVerhoef True again

@toomuchtoknowitall 3 года назад

Tobias (the person in the Video), just in case you’re reading this: I enjoide the whole video, honestly. Were just having a little fun here.

@NoVoiOvi 3 года назад

@@WilcoVerhoef Yeah, was thinking the same.

@sapito515 3 года назад

This was done reaaaalllly nicely, good job man!

@Rx2TF 3 года назад

I'm so glad to have been randomly interested in this and have found this channel as a result.

@basharkhan5161 3 года назад

Why’d I think this vid was hummus recipe

@andrewslater6846 3 года назад

Oh my gosh same!!

@trapezius77 3 года назад

I thought it was chickpeas too and that's why clicked on the video!

@MIDO2802 3 года назад

😂

@MycroftDev 3 года назад

I finally did it!!!! I FOUND WALDO!!! 😭

@basedyoshi7253 3 года назад

He looks like Mr. Beast dressed as waldo

@Vamavid 2 года назад

Awesome video! I had come across "Monte Carlo simulation" several times while reading rendering papers. Now to get an understanding of "stochastic".

@oldrockhopper3652 3 года назад

Fantastic explanation of the Monte Carlo simulation concept.

@epiccollision 3 года назад

So that’s what “default hair” looks like in real life...neat.

@aldoileanumeliber 8 месяцев назад

😂

@karan4624 3 года назад

People who disliked this video have a soul, but no hole!

@SuperNova153 7 месяцев назад

Wonderful explanation! I've read so many papers that use Monte Carlo simulations to analyze results but I never really knew what that meant. Thank you for your intuitive approach to explaining the concept, this was very clear.

@ananashrabi3728 3 года назад

This is an amazing video!! Please make more!!

@axlapointe 3 года назад

Did anyone else think he was doing a Monte Carlo simulation with Corn Pops from the thumbnail???

@trapezius77 3 года назад

I thought it was chickpeas LOL

@nastrimarcello 3 года назад

Considering that your viewers are a random representation of the population. Does the like/dislike ratio represent how good or bad your content is?

@MarbleScience 3 года назад

Haha good question. Actually I observed that the ratio is shifting. Initially the video was mainly found via search. Now the video is mainly found via suggestions on the home screen. The like/dislike ratio was still higher when the video was mainly watched by people who where specifically searching for Monte Carlo sims. So, no viewers are certainly not a random representation of the population, and metrics like the like/dislike ratio depend a lot on what audience the RU-vid algorithm chooses for a video. That is actually a very interesting and tricky optimization problem. The RU-vid algorithm tries to find good videos based on metrics like like/dislike, and at the same time the algorithm influences these metrics by choosing the viewers. (ha I guess I shouldn't spend so much time on comments but I think that's really interesting😊)

@sadbadmac 3 года назад

@@MarbleScience What's your main field of study? I'm just curious because of the language you're using, which could either stem from Pure Mathematics or Computer Science lol Also, please do more videos, using these visualizations. I could imagine that even concepts such as Quantum Mechanics could be better explained with marbles, than by any teacher...

@MarbleScience 3 года назад

I studied chemistry, but I'm PhD student in a computational chemistry group 😉

@SimeonFrank 3 года назад

We use monte carlo to test our GNC algorithms for my university satellite program. Seeing the example of render draws some awesome parallels to the simulation we use, and I will definitely be using your example when explaining our simulation in the future. Awesome video!

@chopper2754 3 года назад

Awesome video! Was always interested in what Monte Carlo simulations are. Great Animations as well! Can't wait to see what other videos you're going to make.

@csmlegend3704 3 года назад

Harry Potter + Mark Zuckerberg = MarbleScience

@lululipes4382 3 года назад

he looks like mr beast if he had continued college

@AChannelFrom2006 3 года назад

He should shave his beard and just leave the moustache.

@Zetsuke4 3 года назад

lol

@a.vanwijk2268 3 года назад

Very interesting. Often you just are taught: this is how MC simulations work. But now I learned that they are a short cut, you don't have to trace all possibilities!

@mikejason3822 3 года назад

Thanks for the short and clear explanation.

@Zi7ar21 3 года назад

AKA "I'm too lazy to learn integrals"

@alexxxO_O 3 года назад

:REAL:

@joemosertv 3 года назад

Not everything can be integrated. Especially in real life...

@SKSCOMEDY 3 года назад

You have no idea what you are talking about. Just because you took an intro to calc class doesn't mean you know how to properly simulate anything. If you disagree tell me how you would even approach this problem using integrals without an absurd amount of computing power

@SKSCOMEDY 3 года назад

@top.of.reddit 5 месяцев назад

Modern graphics simulations will have to disagree with you. Path tracing is impossible without Monte Carlo.

@runnerslow 3 года назад

Congrats man, great video!

@PratikSatpathy97 3 года назад

Thank you! It's crisp and clear. Amazing video making. :)

@stevebusby7331 3 года назад

Dude, this was really good... takes a complex concept and illustrates it with very understandable examples and graphics. Well done.

@maheshsoftware4742 3 года назад

Thanks for your simple explanation...excellent

@MegaJdalton 3 года назад

I love to see the excitement in your explanations! Wonderful example.

@MarbleScience 3 года назад

Thank you! 😃

@barryisland5942 3 года назад

A very well-presented video. Well done, and thanks!

@lumotroph 3 года назад

Excellent explanation! Well made!

@pseudophd1073 3 года назад

The production value in this video is great.

@ilyasyomov378 3 года назад

The quality of videos on that channel is extremely well: explanations are clear and thorough and proper animations play a great deal in illustrating concepts. The world needs content like that, please do more.

@MarbleScience 3 года назад

Glad you like them!

@visheshgoyal3999 3 года назад

love the video! Keep them going! thank you for your help :)

@sammahjoubinia1400 3 года назад

Thank you for this, such an important concept to grasp.

@lucasNinard 2 года назад

Love it, clear, precise but not too much : just the right amount of information for a break, and enough to want to watch the rest :)

@georgewambold 3 года назад

Well done! Great video, looking forward to more.

@itseasy3980 2 года назад

This video production is a gem.

@danielk6537 3 года назад

Thank you for sharing this! Much appreciated

@EpicMCTroll 3 года назад

Love the video! Hope your channel gets way more viewers soon!

@kumarprosenjit9714 3 года назад

Outstanding dude. Keep going. I am an enthusiast but I had no idea of these. Love it.

@jake_runs_the_world 3 года назад

Absolutely brilliant!

@kenlau4649 2 года назад

The marble animations are fantastic, and you in the video are even better.

@logitfau252 3 года назад

love it used Markov-Chain-Monte-Carlo for my master thesis study in the medical field. Made me a bit happy that the youtube algorithm showed me your video :)