Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [neural-odes]

8 questions
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What are the practical uses of Neural ODEs?

"Neural Ordinary Differential Equations", by Tian Qi Chen, Yulia Rubanova, Jesse Bettencourt and David Duvenaud, was awarded the best-paper award in NeurIPS in 2018 There, authors propose the NeuralODE, which is a method that fuses concepts of…
Firebug
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Is my understanding of neural ODE correct?

Given an ode $$\dot x = F(x(t))$$ The neural ODE model introduced in the paper: "Neural Ordinary Differential Equations" uses a neural network to model the solution of this ODE, i.e., $$x(t) = G(x(0))= \int_0^\infty F(x(t)) dt$$ then the neural ODE…
Fraïssé
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Recommnedation for books and material for solving differerntial equations through neural networks

I was going through some past and recent papers on using neural networks for solving ordinary and partial differential equations. One of the fascinating papers that inspired a flurry of papers is https://arxiv.org/pdf/1711.10561.pdf. I was looking…
sajjad veeri
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Are Hopfield networks useful?

Hopfield networks have been introduced to me multiple times as a "biologically plausible" (at least relatively speaking) neural network architecture. My read on this is that they are not necessarily useful for machine learning so much as they are a…
user291435
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Latent updates in Neural ODEs

I have read "Neural Ordinary Differential Equations" by Chen and coworkers and find it extremely interesting (https://arxiv.org/pdf/1806.07366.pdf). There is one caveat that I seem to be missing though: In standard ODEs (physics, math etc.) there is…
yuno
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What is the exact definition of the adjoint state in Neural ODE's?

i am reading the famous article named “Neural Ordinary Differential Equations” by David Duvenaud (2018) I have come across this definition of the adjoint state (page 2): $$a(t) = \frac{\mathrm dL}{\mathrm dz}(t)$$ I don't understand what this…
sosamm
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Neural ODEs gradient calculation for multiple time steps

I was reading the paper on Neural ODEs (here) and was wondering if anyone could offer some insight on calculation of the gradient of the loss function. If we are only considering 2 time points, $t_0,t_1$, I understand how the adjoint method works.…
secondrate
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Can neural ODEs "fit" an ODE from just measurements?

The neural ODE technique, to my knowledge, presents a neural network based way of solving ODEs efficiently, which implies it needs an ODE and an initial value in order to construct the evolution over time. Does the technique still apply if I wish to…
HighVoltage
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