Hello everyone! I am trying to include the convolution integral \int_0^tKr(t -\tau)\dot x(\tau)d\tau in my equation and I keep coming up with this error when trying to do NeuralPDE.discretize ERROR: KeyError: key :tau not found Below is a reduced version of my code. using NeuralPDE, ModelingTo…

Similar issue from a few years ago, but doesn’t seem to have a resolution either. [image] Way to write the integral with ModelingToolkit Machine Learning Hi @ChrisRackauckas I tried what you suggested but I am unable to discretize the equation, below is the co…

How WOULD your typical ODE solver be able to handle this type of integral, if the integral couldn’t some how be re-written as a system of ODEs? Because the step the integrator will take is not just dependent on the current state, but also the history of the state — the x(tau) term where tau ranges f…

@mark.garnett I understand the issue you’re pointing out. Looking more into this landed me onto a MATLAB thread that describes a similar equation. In the end they solved it in the ways you described. One of the latest comment chains describes how to rewrite as a coupled ODE under certain conditions…

I don’t know what to do if you can’t re-write the integral-differential equation as an ODE in the context of Modeling Toolkit. You don’t have access to the history of the variables AFAICT, maybe some of MTK devs have an idea of how. I ran into this situation where the problem was heat diffusion int…

[image] mark.garnett: You don’t have access to the history of the variables AFAICT It seems like you do. Here is an example from NeuralPDE of solving an integro differential equation. [Screenshot 2026-07-10 at 12.14.45 PM]

Great! Thank you. I’ll see if I can make it work for the problem I was trying to solve.

Briefly reading through NeuralPDE’s paper , the section describing Integro-Differential Equations gives an answer to how NeuralPDE.jl handles the history problem. “Because the neural network defines the value of 𝑢(𝑥) over all space, one can simply use a quadrature technique, such as those in Quadrat…

How to use a convolution integral with NeuralPDE.discretize

Specific Domains Modelling & Simulations

cmichelenstrofer July 8, 2026, 3:53pm 3

Similar issue from a few years ago, but doesn’t seem to have a resolution either.

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How to use a convolution integral with NeuralPDE.discretize

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