Explaining topics of 🤖 Machine Learning & 🌊 Simulation with intuition, visualization and code.
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Hey,
welcome to my channel of explanatory videos for Machine Learning & Simulation. I cover topics from Probabilistic Machine Learning, High-Performance Computing, Continuum Mechanics, Numerical Analysis, Computational Fluid Dynamics, Automatic Differentiation and Adjoint Methods. Many videos include hands-on coding parts in Python, Julia, or C++. The videos also showcase the application of the topics in modern libraries like JAX, TensorFlow Probability, NumPy, SciPy, FEniCS, PETSc and many more.
All material is also available on the GitHub Repo of the channel: github.com/Ceyron/machine-learning-and-simulation
Enjoy :) And please leave feedback.
If you liked the videos, feel free to support the channel on Patreon: www.patreon.com/MLsim
If you want to make a one-time donation, you can do so via PayPal: paypal.me/FelixMKoehler
Sure 😃 He is an example using finite differences (btcs scheme) with a PetSc solver: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-oqxPyRZKOu4.html and an example using FEniCs: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-QpA7E4YHbyU.html
Cool, is there an example or code for discrete accompanied CFD shape optimization using automatic differentiation, like SU2, but the instructional version?
Thanks for the comment 😊 From the back of my head I do not have anything right away, but I remember that SU2 had quite extensive documentation. So there could be educational examples as well. You could also check resources on FEniCs and Openfoam. Best of luck 🤞
Hi. I am having a question regarding the use of Leibniz rule. When you formulate the problem as a constrained optimization with ODE constraint, you take the total derivative of the Lagrangian with respect to the parameter \theta. By the Leibniz rule, you brought the derivative d/d\theta inside the integral, but when you brought it inside, it should become a partial derivative wrt \theta, is it not?
I think it is worth drawing a distinction between vectorization and parallelization in jax computation. Vectorization takes SISD(Single Instruction Single Data) to SIMD(Single Instruction Multiple Data) while Parallelization takes it to MIMD( Multiple Instruction Multiple Data). To do parallelization in jax you would need to use sharded parallel or for simpler cases pmaps. This is a good showcase of how vmaps and vectorization in jax works.
Thanks a lot for the kind comment 😊 I'm glad you liked the showcase. I would agree partially. There are multiple flavors of parallelization available within JAX, vectorization (via jax.vmap) is one of them. Parallelization just means that multiple calculations are executed simultaneously (en.m.wikipedia.org/wiki/Parallel_computing).
Jax is awesome, i prefer Jax ecosystem to Pytorch ecosystem. Even if Jax is more complex to understand compared to Pytorch, it is highly rewarding. In particularly, in Reinforcement Learning when the envs are mainly into the CPU while your NN is into the GPU.
@@MachineLearningSimulation i fall in love with Jax even i am still learning (just three weeks ago i began ). It is more complex i expected but you have the feeling to have superpower.
You provided a very comprehensive introduction and hands-on experience with LBM. The level of clarity and neatness is awesome! Great job! It was a real pleasure to watch content with this level of quality. In this particular case, 'LBM' should be read as 'Lovely-Baked Manual'!
Hey! Thanks for the videos. Just wondering if you could do a short career talk on the SciML skills needed to get into a place like Pasteur labs ;) . I would like to get specific at something. Cheers!
Great video Felix! Could you also make a video on how to compute the lyapunov exponents from time series data? I am currently using the Eckmann algorithm in nolds package, but I dont really have a good conceptual understanding of what's going on under the hood.
Hello! Shouldn't the u advection term for u-momentum equation be udu/dx = 0.5(d(u^2)/dx) and not d(u^2)/dx? (Or if you modify the terms using continuity equation the other term will turn into d(uv)/dx?).
Great content as always! Although, I wonder if you plan on making FEniCSx content anytime soon? YT is practically devoid of a simple guide on the library and I cannot figure it out for the life of me.
Thanks a lot <3 I have the Julia videos a bit on hold at the moment, but I plan for a series on fundamental finite difference simulation of PDEs, which will be Julia-Python side-by-side.
Thanks :) Yeah, the functional approach is the most straightforward. I would also probably use it for a quick implementation, but the class-based approach will turn out beneficial in the next videos. Just in terms of the interface, it shows how close the MLP emulator will be to the RK4 simulator.
Hi, thanks for the great question and for the kind feedback. 😊 Unfortunately, I don't have experience with modeling blood vessels. My first guess would be to decide how the fluid and the wall interact. If it is only the wall deforming, one could apply the movement as a respective Dirichlet boundary condition on the flow field. However, since the domain changes, it might require remeshing (and as such unstructured meshes) if no immersed boundary method is used. Either way, I guess that this might be beyond this simple method I presented in the video.
Thank for the great explanation. However I am wondering why didn’t you add initial value condition in the lagrange function? Only lambda^T * ode has added.
Thanks for the kind comment 😊 This is VS code with the python extension and a dark theme. For this video, I didn't use a notebook, just a plain python file.
That's a great question but I am probably not the best person to answer this since I currently do a PhD in a rather theoretical topic. There might be good resources you can find elsewhere on the internet. My first thoughts are that you need a good understanding of both fluid mechanics and numerical methods (for which I also present the fundamentals on this channel). Beyond that, it is necessary that you understand at least one of the big CAE softwares (either Ansys fluent, siemens starccm+, or openfoam) since most companies don't use their own solver codes. For this, it is also important that you completed projects and gained experience how the entire simulation pipeline (preprocessing, solving, Postprocessing, and interpretation) works. And, unfortunately, there is also some luck involved since these positions are (afaik) in a position of more supply than demand. Hence, it helps to build a publically visible portfolio and a social media/online presence that could help you get noticed. Good luck 🤞
As far as I am aware, PhiFlow should support the addition of obstacles within the domain and also supports rectangular domains. Check out its GitHub page with many cool examples: github.com/tum-pbs/PhiFlow This particular example could get you started: tum-pbs.github.io/PhiFlow/examples/grids/Batched_Smoke.html Since the phiflow 3.0 release, there is support for unstructured meshes but I haven't used it yet myself. You could check this example: tum-pbs.github.io/PhiFlow/examples/mesh/Build_Mesh.html
@@MachineLearningSimulation Thanks for the response. It was really helpful. I am trying to simulate a smoke plume in 2D field with obstacles. I want it to be without buoyancy. Is it possible to do so?
Thank you for the video. I have a question regarding saving historical states. With the jax.vmap, it essentially predicting the full domain in one command, is that correct? I would like to be able to store historical states and then use the historical states in the prediction, but I am not sure how to do it in this configuration. I assume it will consist of performing the operator prediction sequentially, saving the historical state, and then repeating until the end of the domain. Thank you
def loss_fn(model,length, epoch): predictions_list = [] historical_states = jnp.zeros((151, 5)) for i in range(length): trunk_input = jnp.hstack((historical_states[i, :], trunk_inputs_train[i, :])).reshape(1, -1) predictions = jax.vmap(model)(branch_inputs_train[epoch,:].reshape(1, -1),branch_IC_inputs_train[epoch,:].reshape(1, -1), trunk_input) predictions_list.append(predictions) # Update the historical state buffer for the next timestep if i < length - 1: # Ensure we don't update beyond the last index # Shift the historical states left and add the new prediction historical_states = historical_states.at[i + 1, 1:].set(historical_states[i, :-1]) historical_states = historical_states.at[i + 1, 0].set(predictions[0]) predictions_list.append(predictions) predictions_array = jnp.vstack(predictions_list) mse = jnp.mean(jnp.square(predictions_array - outputs_train[epoch, :length])) return mse Something like this, but with no loops, of course.
ffmpeg prompt is not working PS C:\Users\deniz\julia first> ffmpeg -f image2 -framerate 24 -i kolmogorov_%05d.png kolmogorov_animation.gif ffmpeg : The term 'ffmpeg' is not recognized as the name of a cmdlet, function, script file, or operable program. Check the spelling of the name, or if a path was included, verify that the path is correct and try again. At line:1 char:1 + ffmpeg -f image2 -framerate 24 -i kolmogorov_%05d.png kolmogorov_anim ... + ~~~~~~ + CategoryInfo : ObjectNotFound: (ffmpeg:String) [], CommandNotFoundException + FullyQualifiedErrorId : CommandNotFoundException
