I try to use NeuralPDE to solve ODE problem, when I define the system with the separate variable u1(…) and u2(…) it run normally. (The code following)

```
using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimJL
import ModelingToolkit: Interval, infimum, supremum
@parameters t
@variables u1(..), u2(..)
D = Differential(t)
eq = [D(u1(t)) ~ u2(t),
D(u2(t)) ~ 5 - 10*sin(u1(t))-1.7*u2(t)];
import ModelingToolkit: Interval
bcs = [u1(0) ~ -1, u2(0) ~ 7]
domains = [t ∈ Interval(0.0,10.0)]
dt = 0.01
input_ = length(domains) # number of dimensions
n = 16
chain =[Lux.Chain(Dense(input_,n,Lux.σ),Dense(n,n,Lux.σ),Dense(n,1)) for _ in 1:2]
@named pde_system = PDESystem(eq,bcs,domains,[t],[u1(t),u2(t)])
strategy = NeuralPDE.GridTraining(dt)
discretization = PhysicsInformedNN(chain, strategy)
sym_prob = NeuralPDE.symbolic_discretize(pde_system, discretization)
pde_loss_functions = sym_prob.loss_functions.pde_loss_functions
bc_loss_functions = sym_prob.loss_functions.bc_loss_functions
callback = function (p, l)
println("loss: ", l)
# println("pde_losses: ", map(l_ -> l_(p), pde_loss_functions))
# println("bcs_losses: ", map(l_ -> l_(p), bc_loss_functions))
return false
end
loss_functions = [pde_loss_functions;bc_loss_functions]
function loss_function(θ,p)
sum(map(l->l(θ) ,loss_functions))
end
f_ = OptimizationFunction(loss_function, Optimization.AutoZygote())
prob = Optimization.OptimizationProblem(f_, sym_prob.flat_init_params)
res = Optimization.solve(prob,OptimizationOptimJL.BFGS(); callback = callback, maxiters=10000)
phi = discretization.phi
```

However, when I changed the way to define the variable I got the message that “None Sym BasicSymbolic doesn’t have a name”

The code after changing following:

```
using NeuralPDE, Lux, ModelingToolkit, Optimization, OptimizationOptimJL
import ModelingToolkit: Interval, infimum, supremum
@parameters t
@variables (u(..))[1:2]
D = Differential(t)
eq = [D(u(t)[1]) ~ u(t)[2],
D(u(t)[2]) ~ 5 - 10*sin(u(t)[2])-1.7*u(t)[2]];
import ModelingToolkit: Interval
bcs = [u(0)[1] ~ -1, u(0)[2] ~ 7]
domains = [t ∈ Interval(0.0,10.0)]
dt = 0.01
input_ = length(domains) # number of dimensions
n = 16
chain =[Lux.Chain(Dense(input_,n,Lux.σ),Dense(n,n,Lux.σ),Dense(n,1)) for _ in 1:2]
@named pde_system = PDESystem(eq,bcs,domains,[t],[u(t)[1],u(t)[2]])
strategy = NeuralPDE.GridTraining(dt)
discretization = PhysicsInformedNN(chain, strategy)
sym_prob = NeuralPDE.symbolic_discretize(pde_system, discretization)
```

The message causes by the code `sym_prob = NeuralPDE.symbolic_discretize(pde_system, discretization)`

.

Please help me on how to fix it.

Thank you all.