Skip to main content
Loading Explore guides…
Physics Informed Machine Learning · Acedra
Home
Explore
Computer Science
Physics Informed Machine Learning
Sign in to save
Chat
If YouTube asks you to sign in, open the video on YouTube.
Watch on YouTube
Reload player
Transcript
101 segments
Copy
Hide video
0:00
Welcome back. I'm Steve Brunton from the University of Washington and today I'm really excited to start a new lecture series which is a part of a larger uh set of boot camps and short courses on the topic of physics informed machine learning so this is one of the most important topics in all of machine learning because it's really at the intersection of how do you leverage you know existing physical knowledge to improve machine learning systems and how do you use machine
0:30
learning to learn new physics that humans have never written down before okay so um you know the idea of machine learning we talk about this all the time we see the success stories in the news in our daily lives and the pace of progress is really you know astounding in machine learning things that were once only you know uh science fiction are now science fact so this is you know the Mona
0:58
Lisa coming to life from a single still image with machine learning we also have you know uh rapidly advancing generative AI so this is an example of Dolly 2 where you can put in a prompt like guitar monster and it just generates this beautiful image of a monster playing a guitar notice that the guitar is also a monster which I think is kind of cool and although these are absolutely useful
1:24
for things like you know creating new art and graphics and generating text and transla languages all kinds of um you know classic machine learning tasks there is this growing world of how do we use physics inform machine learning for things like designing an entirely new aircraft or a new super material that's going to be used in the engine or in the the wing or the fuselage of this aircraft
1:51
or any of the other um you know engineering and physics tasks that we as humans have things like you know predicting and modeling and understanding fluid uh flows and turbulence which are again important for Designing you know uh aircraft race cars transport ships as well as wind turbines and you know understanding climate change and weather and things like that things like Robotics and
2:18
digital twins uh for autonomy uh and this is just a tiny tiny glimpse of the many many applications of machine learning and physics informed machine learning in particular in engineering and Natural Sciences so if you you know want to be a part of this uh Revolution if you want to change the world if you want to design new super materials that are going to allow us to build better aircraft
2:46
and better wind turbines and um you know better algorithms for robots and understanding things like climate change physics and for machine learning is going to become an essential tool in Your Arsenal in the future so that's what this lecture series is about and this is the overview lecture uh in that series okay so zooming out we've talked about this a lot before that machine learning is essentially the process of building models from data using optimization and regression
3:17
techniques now we've been building models from data with optimization and regression for decades if not centuries if not Millennia as humans so some of our earliest models of the planets were essentially models from observational data that we did some kind of a crude regression uh or optimization to kind of understand those models but today we have much more data it's much more we have much more advanced optimization algorithms and so that's one of the reasons machine learning
3:48
has been advancing so rapidly now that's classic machine learning. What we're interested in talking about today and in this series is Physics Informed Machine Learning which is how do we build physical models from data using those same optimization and regression techniques or at least building on those existing optimization and regression frameworks. So this entire series is focused on this intersection of artificial intelligence and machine learning with physics.
4:18
I think too often researchers in the machine learning field kind of forget that we actually have centuries of knowledge of physics we have tons of tons of knowledge of how physical systems actually work, and often times we throw that out when we build these machine learning models. But in the last five or 10 years it started to become more clear that we actually need to incorporate physics into the machine learning process to get the advanced performance we need on really
4:49
complicated systems like in engineering or in natural sciences and biology... things like that. So there's two big aspects that are going to come up over and over again two big themes in this series: one is we can enforce physics into machine learning models we essentially can take known physics or partially known physics, things like symmetries, conservation laws, invariances, things like that... and we can bake those in to our machine learning models to make
5:20
them much more performant. So we can learn better models that generalize better with less training data if we enforce physics into the models. And the flip side of that is we can often and increasingly are are able to use machine learning techniques to discover entirely new physics with our measurement data. So if I have measurement data from galactic motion or a plasma or some biological system, I might be able to use these machine learning methods that are being
5:53
developed in other fields of computer science and I might be able to use those methods to discover new physical models that we've never been able to write down before... that humans haven't been able to discover because of either their complexity or or some other aspect... some complexity of the data. So that's a really exciting aspect too we can start getting things like ordinary and partial differential equations that describe uh really really complex systems that humans
6:22
haven't been able to describe using classical methods okay so those are the two big themes we're going to enforce or bake in physics into the machine learning process and simultaneously often times we're going to use machine learning to discover new physics and we're going to find that these are kind of dual uh problems and here's a really really simple example I like to show just to get us warmed up what do we mean by physics inform form machine learning this is a
6:48
pendulum uh mounted on the wall in my lab and so it's just moving back and forth there's a little uh accelerometer on the tip and a little LED so you can take a video of this and kind of traditional machine learning might take a video of this pendulum and try to use an autoencoder neural network to uh reduce the dimension of this video into a minimal latent State given by this red Vector here such that you can use that minimal State and then recreate the video
7:19
from those very few variables okay we know that this is a low dimensional system we think that this is probably described by you know a variable Theta the angle maybe it's velocity kind of naive machine learning would just you know try to find some coordinates that you can compress this data down to so that you could also then expand it back into the full video whereas physics inform machine learning is trying to do something a little bit more sophisticated we're not just
7:46
trying to learn the coordinates uh to compress this video we're also trying to learn maybe a differential equation for how those coordinates evolve in time something like this equation we know from the the damped pendulum equation and again you can think of this in one of two ways I could either if I knew that this was the equation I could try to bake that into this latent State uh in these these red coordinates here to try to learn the right coordinates um with
8:15
my machine learning model if I baked in this known physics I might be able to do a better job or alternatively I could try to learn this differential equation purely from this measurement data now again zooming into this example we know that there's kind of two key ingredients if we were going to do this using textbook methods the first would be I need to learn a good coordinate system Theta in which I can represent this uh pendulum motion Theta is a lot better than the
8:41
X and Y position of the tip for example and then once I learn that coordinate I want to learn some equations of motion some differential equation that describes how the system evolves in time so that's kind of what we mean by physics and form machine learning often times that means learning the right uh coordinates and Lear learning some governing equations or some physical laws which
9:02
often times are things like differential equations that describe the motion in time okay and again we can either learn that from our data or we can bake some of these elements into our machine learning models. Okay, so we're going to zoom out and we're going to be talking about specifically the stages that go into building a classic machine learning model. I'm going to break this down into five key stages that we typically use to build any machine learning model and then I'm
9:32
going to show you how we can bake physics into each of those five stages. Now this is not 100% accurate... I say you know this is 80-90% accurate, tops... but this is a good kind of guideline for how the process of machine Learning Works that we can use to kind of organize this this lecture Series So the first of five stages in machine learning is essentially deciding on a problem... what are
9:58
we going to model with our machine learning model? So that means deciding on what are the inputs and the outputs? What relationship am I trying to model? So it could be that I have pictures of dogs and cats and I want to build a classifier to label them as dogs or cats... we've decided on a problem of what we're going to model. Stage two: once I've done that I need to gather and curate data training data that I'm going to use to train that model.
10:27
So what data will inform that model, and how do I gather that data? Again in that dogs and cats example I need a bunch of pictures of dogs and cats and I have to decide do I actually have the labels? Do I know which images are dogs and which ones are cats you know that that's my my data curation often one of the most expensive processes uh in this pipeline sometimes this can be you know millions or tens of millions of dollars to get that data set
10:56
Stage three, and this is where a lot of people get excited, myself included, is stage three: you get to design some kind of an architecture So we know what problem we're trying to model, we know the inputs and the outputs that we want to be learning the relationship between... stage three is where we choose an architecture, like a special type of neural network or a SINDy model or an auto encoder... whatever type of architecture
11:23
you choose that because you think that it's going to do a good job of representing that functional relationship between the inputs and outputs. So a lot of work goes into designing custom architectures that are good for specific types of problems. we know that if we want to do image classification we use convolutional neural networks if we want to model time series we use recurrent neural networks and things like that so there's a lot of kind of knowhow in choosing
11:47
the architecture in fact this is an architecture of an auto encoder that is used for compressing the dimension of an input down before expanding it back out okay Stage four: so now we know the problem we have, our data, and we have a candidate architecture we think we might be able to train to model that input output relationship. Stage four is crafting a loss function, some kind of an objective function that tells you if your models did a good job. So usually this includes
12:18
terms like the actual error of the input--output prediction of your neural network or whatever your machine learning architecture is with the actual data you use to train it. And there's all kinds of other loss functions you can add... you can add regularization terms to make your model more sparse or more smooth or things like that. so again steps three and four are where a lot of the modern research in machine learning and in physics machine informed machine learning
12:46
uh exists today okay a lot a lot of research in stages three and four and Step five: once we have our architecture and our loss function we essentially pick some optimization algorithm to train the model. And by training the model, what we mean is we use optimization to tweak the parameters of our architecture to tune and learn the parameters of this architecture to minimize our loss function, averaged over our data.
13:16
This is such an important point I'm going to say this again. So our architecture is some class of functions that you can use to represent the input output relationships you want to to model. So there are essentially parameters of this architecture you can tune... in the case of a neural network it's literally the weights of all of the connections in that neural network... you get to tune those weights to learn some kind of
13:41
input output function, and so we use optimization like the ADAM Optimizer, and many other types of stochastic gradient descent optimization to tune those parameters of your architecture to minimize your loss function averaged over your training data. And that's really the entire process of machine learning. We decide on a problem we collect our data we pick a class of functions we think can represent that input output relationship we call that an architecture like a specific kind
14:13
of neural network we design or craft a loss function that tells us if we did a good job and then we use optimization to tweak the parameters of our architecture to learn those parameters that minimize the loss function averaged over our training data and the reason I lay it out like this in these five stages is because Each of these five stages gives unique opportunities for embedding physics into the process, and in some cases for discovering physics.
14:45
If we have partial knowledge of the physics... if I know that I am trying to model the lift over an air foil or some material property or some robotic arm with joints and linkages, then at each of these stages, each of these five stages, I can embed knowledge of the physics and improve this machine learning process. I can constrain the architecture I can add custom loss functions there are certain
15:10
types of optimizations I can use that will respect this physics more than others and so all of these stages give us unique and Powerful ways of adding physics into the process so we're going to use this diagram to organize the almost this entire kind of uh short you know module or boot camp in this larger lecture Series so we're going to zoom into each of these five examples and we're
15:36
going to look at how uh how to embed physics and extract physics in each of these stages of machine learning so um if you want to learn more about this uh some of this is in a textbook written by Nathan Kutz and myself datadriven science and engineering you can download a free pdf uh of it here and I'm hoping that you know around the time that this video is released there will be other
15:59
resources you know notes on this and things like that uh so check the um video description for more links to resources um that that you can use now again we think a lot about architectures that's one of the kind of exciting things that gets people you know a lot of people get excited by all of the cool architectures you can try on a new uh machine learning task especially in physics
16:24
inform formed machine learning and there is a zoo of possible you know architectures just for neural networks and I want to make an important Point not all machine learning is just neural networks there's a lot of other architectures that are not neural networks that we can use um to learn models from data but even within the realm of just looking at neural networks there is this kind of managerie this this zoo of neural networks and a lot of times what we do is kind of akin to
16:56
uh Alchemy so kind of modern day Al Alchemy where you have a problem and through some combination of intuition maybe reading Reddit posts or seeing what your friend did we have some idea of what types of neural network architectures might or might not work for our problem and then we often end up just trying a bunch of them and sometimes they work and sometimes they don't sometimes you can turn lead into gold metaphorically speaking and sometimes you can't and so one
17:25
of the big pushes of applying machine learning to physical systems where we actually do have some prior knowledge we know a lot about these systems is that maybe we can start also learning principles of how and when different neural network architectures actually are appropriate for a given problem so this is a really really important point you know obviously we want to be doing better engineering and better science and we want to use the best tools at our disposal which
17:53
nowadays you know machine learning is in that tool set but there is another perspective Ive which is by applying machine learning to physical problems where we sometimes know the answer we can learn a lot more about these um machine learning algorithms and models then we would if we just apply it to a system where we don't know the answer things like you know trying to cure cancer okay so if you apply this to systems where you know the answer we might be able to go
18:19
from this Alchemy stage of machine learning to something that more closely resembles chemistry where there's actual principles and organization to when and how to use these building blocks for a particular problem okay um that's something we are very very you know interested in doing as a community there's a ton of effort uh kind of trying to learn these basic principles of machine learning by applying them to physics systems systems where we know the answer and Engineering
18:49
Systems and this is actually one of the main thrusts of this NSF funded AI Institute in Dynamic systems um you can kind of go to the website and Google it or and check it out but there is this NSF funded AI Institute in Dynamic systems which is really focused on trying to understand how can you embed physics into machine Learning Systems how can you use machine Learning Systems to learn new physics to solve engineering tasks in these you know various application domains and
19:18
to go from that kind of alchemy uh model of just you know guess and check and trial and error to something much more principled okay and so this is a collaboration with many many people and it's actually bigger than just this NSF Institute um trying to learn these principles of machine learning okay so really exciting uh field and topic and area and it's a really great time to be a researcher uh stepping into this field because it's you know there's a ton of open problems
19:48
unsolved challenges and you know many many many uh billion dooll Industries can be transformed with these techniques uh in the coming years good okay so uh I'm just going to zoom into these five uh kind of areas of machine learning and talk about examples of how we bake physics in um this is just going to be a very very fast highlevel overview I'm going to have entire videos going into each of
20:15
these sub problems so we're going to have a whole video talking about how you can bake physics into this stage one and stage two and so on and so forth but let's just kind of zoom in at a very high level so the first stage of machine learning is deciding on the problem sometimes this doesn't even go uh it goes unstated you know people take this for granted but this is an important part of
20:36
the machine learning process is picking what you actually think you can model with your data what you want to model um what would be a useful model why do you want to model those are all important questions and fundamentally at the end of the day if you're modeling a physical system like you know a lava lamp or a pendulum or a fluid flow if you're modeling um you know a materials process or or something that is actually physical then you're kind of already doing this this you
21:05
know physics based machine learning it physics is already in the process when you decide that you're trying to model some physical process so for example if I'm going to you know in my machine learning model try to learn the forces on this pendulum you know so we know f equals ma if I try to learn those forces with a machine learning model I'm already baking physics into the process through the problem statement similarly I could try to learn you know a hamiltonian or a lran I
21:36
could try to learn uh a free energy potential or um you know lots and lots of different ways you can you can bake in physics just by setting up the problem in a clever way okay stage two curating the data so what data am I going to use again if the data comes from a physical system inherently you are kind of of embedding physics through um that that data collection and sometimes I joke
22:03
that stage two is kind of the Google way of baking physics into the model because if you the idea is if you collect enough data of the natural world it kind of has to learn physics like FAL Ma and maybe even eventually things like eal mc^2 just to reconcile all of that data that it's collecting but the reason I say that that's like the Google approach is because it's very very expensive that
22:29
relies on having you know nearly infinite amounts of data which often as scientists and Engineers we don't have that luxury so we much much more often have targeted limited kind of narrow data sets that we have to use to learn the physics that extrapolates more broadly okay um and this is kind of subtle again we're going to have a whole video going into this but I want to to briefly mention
22:54
it so you know for example am I going to take fluid flow Fields as my training data and I'm I am I going to have them at different flow velocities you know that's a very different model if it only has one fluid flow velocity or it has a range of velocities that will change kind of what physics I'm capturing in my model similarly you know if I'd have uh fluid flow geophysical fluid flow this is actually cloud formation uh past Guadalupe Island if I have this kind of data one of the
23:23
things I can do in my data curation process to uh add physics is if I think that the physics doesn't actually depend on you know the angle of rotation or translation if I think that my physics is invariant to some kind of symmetry like translation or rotation I can augment my data with additional copies that are transformed according to that in this case you know rotations in other cases translations that's again a very very common thing people do is that if you know that your
23:57
system has some symmetry or invariance which is another form of physics you can augment that data to kind of have uh to transform your data to have those symmetries and invariance so for example if I'm building a classifier that can tell you know a Prius from a Ford pickup truck and maybe you know other cars and trucks I'm going to take my images of cars and trucks and I might rotate them
24:21
and translate them and scale them because none of that should matter for the classification so I can take my data and augment it it to include those symmetries uh and invariances that we think our model should be uh invariant to good um and again one of the things I'm going to talk about a lot and I've talked about this in previous videos and we're going to zoom into it here is the coordinates typically matter a lot when we're doing uh machine learning on physical systems so
24:50
this is a cartoon uh from M and christon that I really like I use this one a lot that shows these kind of two different coordinate systems systems for the planets and the Sun and the Earth the one on the right this is the geocentric view that is kind of what things look like from our Earth centered perspective and it's really hard to learn physics and models in this coordinate system whereas if we fix the coordinate system and put the Sun at the center it's a lot easier the data
25:17
makes more sense and it's easier to build a model from data so often curating the data means finding the right coordinate system so sometimes we learn that sometimes we kind of force that through prior knowledge of the physics and it makes a huge huge difference in the learning process good uh okay stage three designing an architecture we're going to spend a ton of time here probably you know five
25:41
or 10 hours are going to be dedicated just to all of the different architectures on the market different loss functions for those architectures um again at a mile high we might have things like lran neural networks so if you know that your system has this kind of Oiler lrange equation uh framing if it's a mechanical system like a double pendulum you might use a specific architecture like a lran neural network um so that your system conserves energy important Point almost all of
26:11
these architectures also have a coresponding set of custom loss functions that are needed to train them so stages three and four really do sometimes kind of uh get a little bit mixed okay so this is just one example of a particular structure for a physical system um we also have um one notion of of kind of what is physical is uh parsimony we like our models to be as simple as possible to describe the data but no simpler that's the approach here in our Cindy autoencoder where
26:43
you use an autoencoder to learn a good coordinate system and then you have the sparest model in some class of models that describes the data okay so we're going to use that principle of low dimensional and sparse to promote models that are as simple as possible to describe the data and no simpler this principle of parsimony that's been with us for 2,000 years from you know Aristotle to Einstein that's been one of the ways we've we've kind of measured if a system is physical
27:12
is in its Simplicity and its ability to describe measurement data okay so this is another type of architecture um and then you know this is actually one of my favorite architectures it's it's one of the earlier ones in the modern physics inform formed machine learning era um by Julia Ling and collaborators they were using they were using neural networks to try to predict uh to try to build closure models for for turbulent fluid flows and their architecture is different than
27:43
a standard deep neural network architecture they have this additional auxiliary kind of tenser input layer that allows their Network to be invariant to Galilean Transformations again we know that these fluid flows should be the same you know under certain kinds of rotations and translations and so through a choice of architecture they made it so that their models have to have that kind of uh invariance and they perform way way better than if you don't include
28:13
that into the machine learning process these are just three of like literally hundreds of different types of custom architectures that you can use to imbue certain types of physics into your system now um I was talking to my wife Bing about this earlier and she pointed out when you choose an architecture to be to make your system more physical to make your machine learning model more physical that's something called an inductive bias it's kind of a bias that goes uh
28:44
unspoken but it highly steers or influences the downstream machine learning process so we're going to talk about inductive biases uh and choices of architectures a bit more later in this section okay good uh moving on so you know item four this is another really really rich area of research is how do you build loss functions that promote models that are more physical in certain ways um we already talked about those sparse models parsimonious models that are as simple as
29:17
possible to describe the data that is Quantified by a term in the loss function the L1 Norm or the l0 norm quantifies sparsity and parsimony so often times you know physics is promoted through additional regularizing terms or loss functions um in your training process probably the most famous example of this is the physics informed neural network or pin um Illustrated here so this is just a standard uh kind of you know deep feed forward neural network used to map some
29:51
inputs like space and time to some outputs like a fluid flow field and normally what I would do is I would just have some loss function that averages you know how accurate is this model over some training data that's kind of the naive way of doing it what the pins does is that from this output data you can actually compute terms in your partial differential equation and you can add your actual physics the partial differential equation that the system should be satisfying as
30:20
another loss term in your loss function so if you know the physics if you know that your system is Divergence free or satisfies The navier Stokes equations or the elastic beam equation whatever the equation is if you know it you can add in a regularizing loss term to your machine learning process and this should dramatically improve the learning performance you can get away with way less data and get much better model performance if you include the physics as a loss function so
30:48
again we're going to have a whole lecture just on this one topic um because it's so important codes and examples and case studies and everything okay the the last step um and this one I think is super important it's not quite as common as stages three and four for embedding physics but it's very very important and we do a lot of work in this um in my lab and in my collaborators groups is using optimization to enforce physics so if I add physics as a term in the loss function that
31:19
is essentially adding the suggestion that we want physics to be satisfied but it's always fighting you know we want low model and we want the physics to be satisfied and they sometimes are dueling objectives so just adding physics as a loss function only kind of promotes physics but it doesn't enforce that physics is satisfied but often with optimization you can constrain um and enforce that your physics is satisfied at a much higher Precision you know at a much um a much more
31:50
stringent type of enforcing of physics so um for example we've done some work in in fluid flow modeling with machine learning and we know that there are certain symmetries and properties like energy is conserved in these incompressible flows and so what I could do is I could build a loss function that has my model error and some constraints that are necessary for this to conserve energy or instead of just having this as a loss function I could do a constrained lease
32:21
squares so that these constraints are satisfied always to numerical Precision by Construction so again if this doesn't make perfect sense right now it's okay we're going to go into depth in each of these topics and have you know at least one video but probably a couple of hours of material on each of these topics but the idea is you can promote if I know some constraints that should be satisfied
32:44
for my system to be physical things like energy conservation or a certain type of symmetry I can either add that in as a term in my loss function but it's not going to go to zero through the optimization process if it's just in my loss function or I can do things like use lrange multipliers or constrained lease squares so that I can change my optimization problem so that these constraints are exactly satisfied uh every you know every time I optimize this function so that's
33:13
something we do a lot um and there are really powerful methods for enforcing physics this way it's a little more involved it gives you better physics imp position but it's also you know more human effort to actually build this into the optim ation function another example um so we're going to find kind of a theme in this lecture series is um we're going to talk a lot about what is physics in the first place what is this physics we're talking about and often times physics manifests
33:43
itself through symmetries okay um I am bilaterally symmetric meaning I have mirror symmetry so if I flip myself in the mirror essentially nothing changes and lots of physical systems have other types of symmetries we've talked about translational symmetry rotational symmetry um this is you know a Quantum potential well with um a hexagonal potential so it has kind of this um interesting symmetry group of uh rotations and Reflections and um I I'll talk about this
34:16
later but there are methods like physics inform DMD where you actually constrain your solution to live on a certain manifold of solutions satisfy that symmetry so this is again going to be a whole probably mini short course all about symmetries and how to bake symmetries into machine learning and how to extract symmetries uh from your data with machine learning huge huge topic very very important and this is going to change how we do machine learning it is currently changing how
34:47
we do machine learning and it's only going to um continue to improve our capabilities in the next 5 10 years okay so those are the five stages those are at least you know five clear opportunities of how to bake physics into your machine learning process now I'm just going to give you a super fast sneak peek of the rest of what you're going to see um at least in the next few hours um so
35:13
you know I guess first what I'm going to do is I'm just going to show you kind of a pictoral example of those five stages just so you can see it in a different way and then I'm going to give you a sneak peek uh of some of the things we're going to do you know coming up next so again stage one is setting up the problem so I'm going to give I'm going to walk through a specific example now where the problem I want to solve is model reduction of a fluid flow so problem is I want
35:38
to take a complicated model of a fluid and I want a simpler model of that fluid something that runs faster on a smaller computer so I need some data I need to curate some uh measurement data in this case maybe I have a simulation an expensive simulation of a full complexity you know numerical simulation of a fluid flow so my problem is trying to get a simpler description I start with the high-dimensional data stage three is choosing an architecture so in this case the
36:09
architecture I'm going to choose is this kind of autoencoder architecture because it has the properties I want it goes from high dimension to low Dimension and these low dimensional States Z are chosen so that they are most likely to be able to reconstruct the high dimensional State again and I'm also going to say that I want to be able to learn a dynamical system some differential equation on that low dimensional latent State that's what I mean by model reduction I want to
36:37
take my high dimensional system compress it down to a low dimensional State and learn some Dynamics some differential equation in that low dimensional State it'll be much much faster then to run this simulation maybe in real time and I'll get most of the physics that's happening in this system okay so those are the first three stages stage four is crafting a loss function so we need to build some
37:00
kind of a function that tells me if my model did a good job now remember our architecture is some function that Maps inputs to outputs to do you know the problem to solve the problem we want to solve and it has parameters Theta these parameters are tuning parameters that I can tweak to make this function fit the data okay in this case I have you know my three neural networks each of them has a set of parameters Theta 1 Theta 2 and theta 3 and I can tweak those parameters to make
37:35
this function fit this data better okay and that's Quantified by this loss function what I mean by by a better fit and finally the fifth stage is to optimize over all of those thetas literally to tweak the thetas to minimize the loss function averaged over the training data this is just a restatement of what we've already said but in a slightly different pictoral uh fashion okay okay good so again now we're going to zoom out do a sneak preview of what we're going to see next uh
38:07
in this series so applications and Engineering I think this is a huge one we're going to have lots of case studies and applications looking into how this has actually been used in various use cases and what I'm going to show here is just a small window of the many many applications um that there are and we're going to explore in this series so things like again modeling fluid flows and turbulence um things like shape optimization how do you actually design a wing that has the
38:38
right lift overd drag characteristics and that has the right structural characteristics this is a big multi-objective optimization problem and remember training a machine learning model is also a multi-objective optimization problem so these kind of make sense that they would go together so things like modeling fluid flows maybe designing you know the shape of an aircraft or a car or a wind turbine um designing a material a composite or an alloy that you're going to use
39:07
in these engineering Downstream applications again multiobjective optimization very high-dimensional design space for uh for materials um digital twins so I might have some physical aspect like a robot arm or like an aircraft or a factory floor and I might want some digital representation some Digital model that I can design and optimize over uh like this digital twin here um and then kind
39:34
of just robotics in general Robotics and autonomy is an area that is rapidly uh advancing with new machine learning technology and again this is just a pretty small um you know subset of the applications that there are and that we're going to talk about other examples include drug Discovery protein design um you know and those are systems that are governed by by physics there's physics and how proteins fold and how you know chemistry Works um so you know
40:03
those are also big big applications um other areas things like climate science understanding weather phenomena and patterns and climate Trends again related to turbulence but a very very different context okay tons of applications uh of this um digital twin is really an important concept here when we think about building a machine learning model that is trained from data and has this kind
40:30
of hybrid physics and data driven flavor that's very much what a digital twin is going for it's kind of a living uh model of some complex system like an aircraft or a factory floor or you know a materials uh baking process like a composite baking process where you want this digital uh twin of your physical asset to be as accurate as possible possible you want your model to update as you collect new data so your machine learning models need to be able to update you need to have
41:03
uncertainty estimates of how good that model is or where it's the most uncertain so you can either know if you can trust your model and in you know the best case scenario you know how to go collect more data to improve your model all of those are working towards this notion of a digital twin which in principle should allow us to design to do better engineering design cheaper and faster
41:27
and safer so we're gonna have again a whole short course on digital twin engineering where you know we talk about how do you build these digital twin models and how do you use them for better design uh testing evaluation things like that okay I really like this diagram here from this uh paper by uh captin at all in uh nature computational science and get kind of is a nice representation
41:54
of this kind of Duality between the physical and the digital twin of that physical asset okay so um again physics and for machine learning if you're going to use a digital twin for something like an aircraft it better be you know physical it better have that physics baked into that process okay we're also going to talk about the importance of Benchmark systems so uh most of the progress
42:18
in classic machine learning image Sciences natural language processing things like that a lot of that progress is because we had very good Benchmark problems and data sets that you could use that the community could use to test their methods on so a researcher didn't have to create a benchmark problem and the Machine learning algorithm they could focus their work on the machine learning
42:40
algorithms okay and so increasingly we're finding that we need those kinds of Benchmark problems for Dynamics and control for physics and Engineering problems so I might need you know these static data sets of of our systems um they're not static in the sense the system is evolving in time but once I collect that data the data doesn't change it's a static data set of a dynamical system it
43:06
could be simulated or experimental um but really I want to be you know developing these Benchmark systems for engineering purposes where we're actually trying to manipulate the behavior of the system we actually want to control the fluid with our machine learning model so I need to be able to interact with that simulation and actually close the loop with my machine learning model so we're developing Benchmark problems in that kind of interactive uh control framework as well and
43:36
then ideally we would go you know to actual living cyber physical systems like an actual piece of laboratory equipment that you can train your machine learning model on in real time that's much closer to the kind of digital twin notion that we're going to be getting towards again this is going to be an entire short course on all of the benchmarks that are out there what are the characteristics that you need for a physics and for machine learning Benchmark and so on so this
44:02
is uh an important topic we're going to come back to but we need to be thinking about you know how are we going to test our models and what is the ground truth do we have ground truth in some of these cases um architectures we already talked about the importance of that stage three and really it's architectures and the loss functions we use to train these architectures but We're going to cover a lot of the really important ones... things like ResNets and UNets
44:28
We're going to cover Fourier neural operators and general kind of operator methods. We'll talk about SINDy and Library regression and parsimonious symbolic regression modeling We'll talk about physics informed neural networks, deep operator networks, and a bunch more. This is just kind of a a quick smattering of some of the architectures we're going to look at but we're going to spend a lot of our time doing whole videos or even whole video series diving
44:56
into these really really important topics how do you build these loss functions how do you train these what applications do they work on you know what how do we actually code this up and try it ourselves okay so we're going to really dig into a lot of these applications uh and you can actually take these then and use these to build your own um you know examples and and try this out yourself
45:19
and again um we're going to throughout this entire series revisit this notion of like what is physics in the first Place why do we want to bake physics into our systems why do we need to bake physics into our systems when we try to learn physics from data what does that even mean what are we learning and time and time again we're going to find that things like conservation laws invariances and
45:43
symmetries are some of the ways that we end up uh encapsulating physics so we're going to again see symmetries a lot you know in uh drug Discovery and protein folding there are symmetries fluid flows and mechanical systems uh material systems Quantum systems symmetries are fundamental to physics and so symmetries and conservation laws and invariances are going to keep coming up over and over again also this notion of parsimony or uh Simplicity of the model and in the process
46:15
of doing this we're also going to not lose track of the history uh of Science and the history of physics because that's going to give us a lot of important parallels that we can learn from in this modern machine learning era so the difference between astrology and astronomy what changed the difference between Alchemy and chemistry okay and it really there is a lot of that uh parallel happening today in machine learning and so we can learn a lot from the history of science uh when
46:43
we're doing this kind of new physics and form machine learning okay uh so that's the that's the topic that's the course um physics inform form machine learning we're going to have tons of short uh focused modules on each of these topics um I see this fitting into you know a larger coursework um that we're hoping you know to actually offer for credit uh at University of Washington at some point in the future so you know I hope you enjoy this it's a passion of mine
47:14
it's one of the most important fields of machine learning and this is going to increasingly become uh you know very powerful tool in Your Arsenal to solve real world problems all right thank you you
Here to help you learn
Sign in to keep a private conversation with your course tutor.
Ask me anything about the material…
Sign in to chat