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Python tutorials: import tutorial tutorial.run()

Super cool as always. Some feedback to enhance clarity - when writing modules (SpectralConv1d, FNOBlock1d, FNO1d), overlaying the flowchart on the right hand side to show the block to which the code corresponds would be really helpful. I felt a bit lost in these parts.

Thank you so much for this series! It has helped me tremendously to understand how automatic differentiation works under the hood. I was wondering if you plan to continue the series, as there are still operations you haven't covered. In particular, I am interested in how the pullback rules can be derived for the "not so mathematical" operations such as permutations, padding, and shrinking of tensors.

Ich finds geil wie du from scratch das einf mal so dahincodest und dabei super erklärst 😅

Just one observation: the functional unconstrained optimization solution gives you an unnormalized function, you said it is necessary to normalize it afterwards. So what does guarantee that this density, but normalized, will be the optimal solution?? If you normalize it, it will not be a solution to the functional derivative equation anymore. Also, the Euler-Lagrange equation gives you a critical point, how does one know if it is a local minima/maxima or a saddle point?

Excellent work! Thanks a lot for sharing.

Thank you. This is super helpful as an intro to fenics for fluid.

Thank you for the video. Very informative and helps a lot. I have a small question: Why there is no density in the equations? In NS equation it is exist. And one bigger question: Is it possible to include the heat transfer into this code with the same scheme as pressure update, or should be there a different way?

whait if the velocity is not constant and changes with the density(q)??

Exam in 20 minutes, thanks haha

For full accuracy, at 0:15, the distribution of X is actually the distribution of X given Z=z, right?

I love you

Thank you so much for all you great video. What IDE do you use?

Hello I'm a undergraduate student from South Korea. I really appreciate your videos. It helps me a lot on understanding jax and programming. Can I know if this 1D turbulence flow has a name?

Thank you for this wonderful video. Please can you also do another one for a vertical flow for two phase liquid and gas

This dude is always on point ... keep it coming!

how do we know the joint dist?

Very nice video. Truly showing the potential of Julia for sciml! I’m curious have you compared this Julia algorithm with Jax? It seems like much faster than training in Jax. However, I’m also worried about what if I need to construct mlp rather than one layer net which is most common situation in ml? How about high dimensional data rather than 1d data? Does that also increase the complexity to use Julia?

when u say Z is exponential distribution and X is normal distribution, how do u know this? Is this an assumption?

Thank you very much!

Great stuff

Hi this was the most epic explanation I've ever seen, thank you! My question is that at ~14:25, you swap the numerator and denominator in the first term -- why did you do this swap?

Very cool video! The walkthrough write-up of this alternate program of 1D FNO is super useful for newcomers like myself :)

Hi man, awesome videos! a problem, if I may. let's say i have a box or cylinder with fluid(1/2, 3/4). i need is to simulate acceleration on it, input(accelerationXYZ, dt) - return inertia feedback foces on XYZ over time. simple detalisation for 300-400fps. maybe bake center mass beheviour into ML or something. any ideas? Thanks!

Not sure if I'm mistaken or not. In your explanation, the formula is wrong since it's actually suppose to use "ln" rather than "log" For others looking at the math part of the explanation np.log is actually doing ln or Log base e got me confused for a while.

danke! hat bei meinem probablistic ml assignment geholfen!

Great video on explaining even the math concepts, but I stood with a doubt, perhaps a stupid one: In the beggining of the video you had the blue line p(Z|D) = probability of the latent variable Z knowing D data, so events Z and D are not independent right? If I understood correctly, then, at 10:20, you say that we have the joint probability P(Z *intersect* D). I don't think I understood this: how do we know we have that intersect? Is it explained in any prior minute...? Thank you for your attention

Hi .. was looking for JAX tutorials .. found this video and your channel and hence must say THANKS for the nice explanations.

Are you german? Sound very german! Great videos BTW!

10:27 I don't think it is right. Summation is for the whole (q * p/q), and we cannot conveniently apply summation to just q alone.

Great video! I think at 12:10 it should be inner_objective(gd_iterates,THETA) instead of solution_suboptimality. In this case it is still working since the analytical solution is 0.

please make a video series on Graph neural network

Awesome stuff. I am wondering if you can do a similar video for the new neural spectral methods paper?

It would be cool here to show analytically that the maximum likelihood estimated parameter for a Bernoulli is just the sample mean of the data :) I guess autodiff is just performing this procedure numerically?

Really cool stuff, with a clear explanation in 1D, that seems rare. Great work, thanks!

Amazing expectation thank you so much!

Super interesting observation and super clear explanation! Thanks for sharing it with us!

This was very useful!! Thank you so much!! Can you please make a video on how to solve helmholtz pde in BEMPP (boundary element method python package) for acoustic simulations?

太清晰了

glad i found your channel. great explanation👍

writing so ugly...

Do you have the code for this saved? If so, could I have it for reference on my own fluid sim?

Can we also use fenics to solve the nonlinear heat equation, i.e. the case were the diffusivity depends on temperature?

Challenging! Can this video solve the problem of finding dA/dθ in adjoint optimization for min J(x(θ),θ); s.t. Ax=b;😀

6:00 this next step doesn't look correct to me, e.g., if i choose a specific g(u,\theta) = \theta^u, i don't think i would get a sum with these two terms. Am i missing something? The right solution of the derivation of the integrand would have been just \theta^u Your equation peoposes something else

Thanks so much for the video explanation! 😍 My understanding is that both Lagrangian and implicit derivative methods yield the same sensitivity analysis results, right? The Lagrangian approach is more convenient for large linear equation constrained implementations, as it requires only one forward and one backward propagation computation per iteration. In CFD, sensitivity analysis and adjoint optimization are typically implemented using adjoint equations, right?

Do you use fenicsx?

Hello, thank you for the tutorial. It is very helpful. Could you answer a doubt? In the pressure boundary condition, could I do the Homogeneous Neumann everywhere and specify in a node ( any node inside the domain) pressure =0? Therefore, there aren't infinite solution, but one solution with zero in node which was specified.

Thank you very much for these videos; they are incredible and offer the best explanations of these topics that I've found online. I particularly appreciate the format of your introductions, where you succinctly review prior knowledge and clearly define the key question that the video will explore. My understanding of the Dirichlet distribution is that it serves as a prior for probabilities, with each individual probability constrained to the [0, 1] range. I was wondering if you're aware of any methods to impose specific bounds on individual probabilities within the context of the Dirichlet distribution. For example, suppose you had prior knowledge that the probability of it being sunny could never exceed 0.8; you might want to set its range between [0, 0.8]. Of course, the sum of probabilities would still need to total 1. Is there a known approach or modification to the Dirichlet distribution that accommodates this type of constraint? Many thanks for your help!

Excellent