# Way to write the integral with ModelingToolkit

**URL:** https://discourse.julialang.org/t/way-to-write-the-integral-with-modelingtoolkit/82347
**Category:** Machine Learning
**Tags:** diffeq, pde
**Created:** [June 6, 2022, 9:42pm UTC](https://discourse.julialang.org/t/way-to-write-the-integral-with-modelingtoolkit/82347 "2022-06-06T21:42:36Z")
**Posts on this page:** 1
**Showing post:** 5

<div class="post-metadata">

### Author: ![kaido975](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/kaido975/32/36862_2.png) [@kaido975](https://discourse.julialang.org/u/kaido975)
#### Post date: [June 7, 2022, 5:44pm UTC](https://discourse.julialang.org/t/way-to-write-the-integral-with-modelingtoolkit/82347/5 "2022-06-07T17:44:11Z")

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Hi @ChrisRackauckas I tried what you suggested but I am unable to discretize the equation, below is the code and the error. I am not sure where to pass the parameter x.

```julia
using NeuralPDE, Flux, ModelingToolkit, DiffEqFlux, DomainSets
import ModelingToolkit: Interval

@parameters t, x
@variables u(..)
lambda = -1.5
Di = Differential(t)
Ii = Integral(x in DomainSets.ClosedInterval(0, t))
eq = Di(u(t)) + Ii((t-x)^lambda*u(x)) ~ 1.0
bcs = [u(0.0) ~ 0.0]
domains = [t ∈ Interval(0.0,2.0)]
chain = Chain(Dense(1,15,Flux.σ),Dense(15,1))
initθ = Float64.(DiffEqFlux.initial_params(chain))

strategy_ = GridTraining(0.05)
discretization = PhysicsInformedNN(chain,
                                   strategy_;
                                   init_params = nothing,
                                   phi = nothing,
                                   derivative = nothing)
@named pde_system = PDESystem(eq,bcs,domains,[t],[u(t)])
prob = NeuralPDE.discretize(pde_system,discretization)

```

```julia
ERROR: KeyError: key :x not found

```

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