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Chris Rackauckas proslijedio/la je Tweet
Pro of academia: I have friends all around the world! Con of academia: My friends are scattered all around the world.
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Chris Rackauckas proslijedio/la je Tweet
In this paper, I describe how Julia and multiple dispatch allow us to propagate arbitrary multivariate probability distributions through any function, accelerated by SIMD or a GPU http://arxiv.org/abs/2001.07625
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Added an example to
#julialang DiffEqFlux README of training a universal neural ODE to a loss of 4e-11@pkofod's Optim.jl and BFGS. Takes about 200 seconds on my laptop so give it a try!#sciml#mlhttps://github.com/JuliaDiffEq/DiffEqFlux.jl#training-universal-differential-equations-with-optims-bfgs …Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi -
For more information on the mathematical background of these data-efficient
#sciml#ml techniques, see the@MIT_CSAIL@MITMath 18.337 course notes. For examples of how to use it in applications, see the 18.S096 course notes. https://github.com/mitmath/18337 https://github.com/mitmath/18S096SciML …Prikaži ovu nitHvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi -
Thanks
@DavidDuvenaud@jessebett@MikeJInnes@oxinabox_frames etc. for sending me down this route into thinking about ML in the context of differential equations. I think white box physics-informed models is an interesting thing that every scientist should be exploring.Prikaži ovu nitHvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi -
In total, we utilize as much prior information about scientific models to utilize ML in an efficient manner. In the context of science, the well-known adage "a picture is worth a thousand words" might well be "a model is worth a thousand datasets." https://arxiv.org/abs/2001.04385
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In our full paper we describe how to accelerate
#climate models 15,000x times through parameterizations automatically derived through universal PDEs, and how 100-dimensional PDEs like Hamilton-Jacobi-Bellman can be reduced to placing neural nets in an adaptive SDE solver.Prikaži ovu nitHvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi -
We have just released an overhaul to our adjoint methods which includes methods like stabilized checkpointing interpolating adjoints that were created specifically to handle some of the universal PDE training problems found in our paper. https://docs.juliadiffeq.org/latest/analysis/sensitivity/#Sensitivity-Algorithms-1 …
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Thus we spent a lot of time making sure the
#julialang code works in this new performance regime of high computational cost but (possibly) small differential equations with small neural networks, lots of scalar operations, high stiffness, etc.Prikaži ovu nitHvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi -
However, going in this direction meant that there were a lot of computational issues we had to solve. For example, while traditional neural ODEs end up usually being stable, a diffusion-advection equation is unconditionally unstable when ran backwards!
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The neural networks are then interpretable since they physical forms of differential equations have meanings. Convolutional neural network representing a PDE with a stencil [1 -2 1] means that the data only has diffusion and no advection. Quadratic reaction predicts regulation.pic.twitter.com/oj0emILRNg
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The idea is to utilize these function approximators to parameterize missing parts of models, and then train them in the scientific context so they only learn "what you forgot to model" or what you simplified out. Tiny neural nets with maybe a 100 parameters will do.
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This is a structure that we call the Universal Differential Equation: a differential equation with embedded universal approximators. Sometimes neural networks, sometimes Chebyshev polynomials, for us it really doesn't matter because they are small approximators.
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Our approach builds upon the work of
@DavidDuvenaud but identifies that the differential equations one works with does not have to be a blackbox, but instead can utilize all of the available scientific models to encode as much prior information as possible.Prikaži ovu nitHvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi -
How To Train Interpretable Neural Networks That Accurately Extrapolate From Small Data. Today we released a new paper that showcases how to do just that using Scientific Machine Learning (
#sciml) techniques to encode non-data scientific information. https://www.stochasticlifestyle.com/how-to-train-interpretable-neural-networks-that-accurately-extrapolate-from-small-data/ …pic.twitter.com/sHrqGZaFy7
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Check out the
#julialang FiniteDiff.jl: it's the next evolution of what was known as DiffEqDiffTools, now generalized to a library for everyone to use. Fast and non-allocating on sparse and structured matrices. Supports GPUs and StaticArrays.https://discourse.julialang.org/t/finitediff-jl-fast-sparse-gradients-jacobians-hessians/32976 …Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi -
Chris Rackauckas proslijedio/la je Tweet
Beginning of the year results for the
#Twitter#Survey so far: What new#Computer#Science#languages excite you the most for#Bioinformatics? http://bit.ly/bioinfocs pic.twitter.com/UhGLq3gPeL
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Ever wondered how to make ODE solvers satisfy conservation laws? Here's an in-depth StackOverflow post on making ODE solvers energy conservative (with
#julialang examples):https://scicomp.stackexchange.com/a/34131/18981Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi -
DifferentialEquations.jl is really close to 1k stars!!!! Help us rally?
#julialanghttps://github.com/JuliaDiffEq/DifferentialEquations.jl …Hvala. Twitter će to iskoristiti za poboljšanje vaše vremenske crte. PoništiPoništi
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