# Questions tagged [differential-equations]

A differential equation is an equation that contains at least one derivative.

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### Does probability flow ODE trajectory (in the context of diffusion models) represents a bijective mapping between any distribution to a gaussian?

I have read several papers about diffusion models in the context of deep learning. especially this one As explained in the paper, by learning the score function (∇log(𝑝𝑡(𝑥))) ,probability flow ode ...
• 101
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### How can I coefficients for a model of n linear differential equations in n unknowns

I have (a lot of) time series data, to which I wish to fit a system of n linear differential equations in n unknowns, where by "fit" I mean to find coefficients on the unknowns in a way that ...
• 3,157
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### Lotka-Volterra ordinary differential equation model to describe oscillations in a single observed entity

Background The Lotka-Volterra model is the starting point for any model of ecological dynamics. It can be described as a set of two ordinary differential equations (ODEs) with varying complexity. ...
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### How can we efficiently find the fourth moment of a Poisson distribution?

Suppose we have $X\sim \textrm{Poisson}(\lambda)$ and we know that moment generating function $M(t)=\mathbb{E}(e^{tX})$. How do we use the moment generating function property $M^k(0)=\mathbb{E}(X^k)$ ...
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1 vote
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### Neural ODE and Adjoint method

I am trying to understand the paper NeuralODE which is very interesting. I get the general idea and the proof they give about the dynamics of the adjoint are fairly simple. They define a network $f$, ...
1 vote
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### Efficiently sample from a limit set given a differential equation?

Given a dynamical system of many variables, described by an ordinary differential equation, is there some way to use machine learning to efficiently sample from the limit set (or maybe more accurately ...
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### Partial Differential Equation approach for ridgeplot

I have a series of probability density functions (pdfs) such that I can create a ridge plot with them evolving in time. Is it possible to know the intermediate function in between two of the functions ...
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• 1,590
1 vote
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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 ...
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