Kirill Zubov

Zygote.gradient failed with CubaCuhre and batch !=0

1

```julia using Quadrature, ForwardDiff, FiniteDiff, Zygote, Cuba f(x,p) = sum(sin.(x .* p)) lb = ones(3) ub = 3ones(3) p = [1.5,2.0,3.0] prob = QuadratureProblem(f,lb,ub,p; batch=0) sol = solve(prob,CubaCuhre(),reltol= 1e-4,abstol= 1e-4,maxiters=100)[1]...

CubaVegas, CubaSUAVE, CubaDivonne: Julia has exited

2

For small values of `abstol`, `reltol`, `maxiters`, we get the exit error in `solve` for CubaVegas, CubaSUAVE, CubaDivonne. ```julia using Quadrature, Cuba f(x,p) = sum(sin.(x .* p)) lb = ones(2)...

Quadrature.jl don't support GPU with batch != 0

1

While there is no required algorithms that would support vectorization (batch! = 0) and work with GPU ```julia CUDA.allowscalar(false) chain = FastChain(FastDense(2,inner,Flux.σ), FastDense(inner,inner,Flux.σ), FastDense(inner,inner,Flux.σ), FastDense(inner,inner,Flux.σ), FastDense(inner,1)) initθ = initial_params(chain) |>gpu...

```julia using Quadrature, ForwardDiff, FiniteDiff, Zygote, Cuba f(x,p) = sum(sin.(x .* p)) lb = ones(2) ub = 3ones(2) p = [1.5,2.0] prob = QuadratureProblem(f,lb,ub,p) solve(prob,VEGAS(),reltol=1e-6,abstol=1e-6,maxiters =1000)[1] function testf(p) prob =...

Integrate NeuralOperator and NeuralPDE

4

Couple of strategy/scenarios 1) train-to-train model - train a sub-class of PDEs with NeuralOperator - transfer learning pre-trained prediction from NeuralOperator problem to PINNs - PINNs training with pre-trained model...

Support compound expressions for integrand

2

```julia @parameters t @variables i(..) Di = Differential(t) Ii = Integral(t in DomainSets.ClosedInterval(0, t)) ``` it is only processing a simple expression with the variable of NN ```julia Ii(i(t)) ```...

create a bunch of tests covering the parser to keep track of that the symbolic part is working correctly MWE ```julia @parameters x @variables u(..) Dx = Differential(x) eq =...

DiffEqOperator has a lot of good convergence tests for pde. It would be nice to cover with this tests NeuralPDE. https://github.com/SciML/DiffEqOperators.jl/tree/master/test/MOL

As the next step in the development of the symbolic representation of geometry of PINNs is follow tasks: - [ ] ConstrainedEquation #176 - [ ] polar coordinates - [...

General plot recipe

3

it would be convenient to have one general method for plot of solution. ```julia NeuralPDE.plot(phi, res) ```