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That was a rather abrupt end to the lecture, but I think the material was covered well enough.

Amazing, I can't thank you enough.

i got something similar, but this has to work with multi-var calc... so if you define dx as infinitesimal positive, you are saying: dx > 0 and dx*dx -> 0. if you implicitly diff, then you have an operator d[] d[a+b] = d[a] + d[b]. d[a*b] = d[a]*b + a*d[b] then for d[a^b] and d[log_a[b]], the functions are complicated, and don't necessarily handle non-commutative args in general. but if d[a^b] where b is scalar, and d[log_a[b]] where a is scalar, it's easy to define. d[f=a^2 + b^2] = df = 2a da + 2 b db. for df/db: da=0, and db>0, and db*db->0. How does this work on trillion variable calculus?

I am really enjoying your lectures. What program are you using for the notes.

Now that Juno is gone what is the best environment to get all these variable value previews?

Hi Chris, great lectures, thanks to made them public. Which software do you use to write math expressions while presenting the lecture?

So say I have data corresponding to spatiotemporal states like u_i(x,t) where 1<=x<=L and 1<=t<=T and I want some number of iterations of trajectories N so that 1<=i<=N. If I want to store all of the trajectories at every time I should have an array of dimensions size(u) = (N,T,L) so that I can quickly access u_1(x,2) for example. in code it would be u[1,2,:]. ORRR should I reverse the definition so that size(u) = (L,T,N) so u_1(x,2) is given by u[:,2,1]? I'm thinking the latter...

Flashback from my MSc in Physics 12 years ago. Thank you very much for sharing.

Great 💯👍 video 👍📸 thank you 💯💯

what's the name of the program on the left side of the screen?

Amazing video!!! Thank you so much for sharing this. I made my code about x10 times faster just by implementing what Chris says in this first lecture. I didn't know that heap allocation takes so much time. Looking forward to next lectures.

This guy is fantastic, very clear at explaining things. The conclusion was also super encouraging. Thank you.

😱

Glad I chance upon this lecture series because it was very informative! But I can't believe you claim ff8 > ff7 😡

this already super insightful! thank you very much :)

In the "good old days", LaTex was pronounced "lay-techs".

Great explanation on dynamic vs static scheduling! I think that is something that should be part of the manual but it is unfortunately not emphasized enough.

Love the content. Chris Rackauckus is my hero He compared neural nets to Fourier and polynomials bases, but one other basis I wonder about is step functions, which are the basis for boosting. I think those still have the same curse of dimensionality as polynomials and fourier (they don't overcome it like neural nets), but they seem to be fast with a lot of features as well, correct? (I'm thinking xgboost)

What IDE / editor are you using? It looks like it has some useful features.

Great. I have just found this course. It is very interesting. Just is there any notes or notebooks with this course?

Incredible lecture. Thank you for sharing

Dear Sir, how to perform different trajectories at the same time parallely in morris method.. As stated in the primer , P∗ is a k-by-k random permutation matrix in which each row contains one element equal to 1, all others are 0, and no two columns have 1’s in the same position. P∗ gives the order in which factors are moved. How to create a different ordered P* matrix each time for each trajectory

I remember academic discussions in 1994 about how something like a dog catching a frisbee was a neural network solving an ode, which was cool. I think that was when they started engaging on the topic.

I am confused as to why there is a const in front of the a2 array if the values can change. Does this just mean that the size of the array can't change?

extremely helpful for freshman like me! 👍

Ugh the slack notification sound gets me every time haha

Wow this is great, very helpful

Are we going to have a newer edition of this course?! Can't wait for it!

Thanks for organizing the lectures into a playlist now I know how to follow along the roadmap

0:36 Installing Julia 2:40 Setting up an IDE (Atom or VS Code) 9:35 Activate environments 12:55 First .jl script 13:45 Inline help 18:40 PkgTemplates 23:10 Unicode variables and operators 24:30 import, export, and using 26:20 Documentation and further resources

This is absolutely fantastic. Thanks for sharing.

What editor/IDE are you using?

Thanks Chris for the amazing lecture

Amazing lecture again

julia is really great, especially for people coming from matlab. makes me wonder why alot of industry is still using python.

At 14:11 it says that we can improve the fit by increasing the size of the NN, using more training points, or by training for more iterations. Wouldn't the type of loss function used also have an affect on the performance of the learning algorithm? The first thing I was thinking of is that the sum of squared loss we used isn't exactly the best for use in neural networks. If I recall correctly, sum of squared loss is non-convex with respect to the parameters when using tanh activation functions. So optimization over this loss function is going to give suboptimal results. Maybe this is negligible in the case of this problem but I think that using cross-entropy loss or one of it's derivatives would provide better performance.

Tks for this!

Please make a playlists for your neural Odes and differential eqns if you can. You have a lot of hidden gems that needs to be organized

Incredible lecture.

LOL 36m50s... can't redefine function g... no problem, just rename it gg.

This video is FANTASTIC. As someone who is currently learning about compilers and LLVM, this video provides a lot of insight on how many cool things compliers can do.

Can you explain to me why an "experienced programmer" needs to be baby walked through setting up an editor? I am "experienced" enough to know what editors I actually like using (for sure not Atom or VS Code lol) and how to figure out how to use them for any programming language I want.

I think there is some confusion with terminlogies that deserves clarification. Broadcasting, vectorization are being interchanged. Where I come from from (deep learning), broadcasting refers to extending an operation to other dimensions of one of two operands that don't have same shapes. Example: a has shape [4, 1] B has shape [4, 10] Then, broadcasting *allows* adding / multiplying such objects. The rationale is: *a* is a vector, *B* is an array of vectors. The addition is to happen between *a* and *columns* of B resulting in a matrix that looks like *B* with all its columns being equal to *a* + original column value. Vectorization: a function designed to work on scalars, give me a version of it that works fast on vectors by feeding the vectors directly instead of looping over their elements and calling the function just as many times. They might be similar at core, but I have noticed that in some specific fields, the disinction is due.

Thanks for the lecture! By the way I don't quite understand the speed differences between push! and append!. The output is the same, but I suppose the backstage process is different. Regards!

Really good lecture! I have only the question of why the "Stochastic dynamical model" isn't modeled more directly as a Markov Chain?

What is the name of the software being used for typing math equations?

How is julia for making highly concurrent web apps?

excellent explanation

It's important to highlight that KL Divergence is NOT the EMT (Earth movers distance) / OT and its NOT a distance. The EMT analogy is confusing because you are using a commonly employed analogy for EMT and applying it to KL which can implicitly confuse the two concepts for a viewer. There is a relationship between the two, argmin_{p(x,y) \in D(pi_0, pi_1)} KL (p(x,y) || N(x,y, s * I )) as s ->0 this KL becomes the EMT between distributions pi_0 and pi_1 using a squared error cost (Wasserstein distance). Where D(pi_0, pi_1) is the set of distributions p(x,y) with pi_0(x) and pi_1(y) as marginals.

Hi! I don't understand what kind of differential equations can be solved with this iterative process, for example in this case you use the Lorenz System but it can be consider a general approach for any differential equation?