Kirill Zubov

and with adapt derevative. the coolest thing in adaptive der that we are not limited by the accuracy of the derivative algorithm ```julia @parameters t x @variables u(..), Dxu(..) O1(..)...

@killah-t-cell we going to update the doc so I will add the example together with the update.

look like just outdated code after update and it is just need add couple new parameter to build_loss_function.

https://github.com/SciML/SciMLBenchmarks.jl/pull/355 I fixed allen_cahn. Not sure about the results of the prediction. @francescocalisto could you please check how much iteration is needed and etc. Also, other scripts in PINNErrorsVsTime need...

@mohsenhos look it https://github.com/SciML/NeuralPDE.jl/issues/387

complex numbers are not supported but interesting why `bcs = [Dx(u(-1,y)) ~ 1im ,...]` isn't failed.

@killah-t-cell since the solution is split into intervals: x domains = {[x0, x1], ... [xi,xi+1], ..., x9,xend]}. so the initial condition is known only at x0, and at the x_i,...

There is need two functions for two predicted variable. ```julia function create_bcs(t_domain_,f_bound,E_bound) t_0, t_e = t_domain_.left, t_domain_.right if t_0 == 0.0 bcs = [f(t_0,x,v) ~ 1/(v_th * sqrt(2π)) * exp(-v^2/(2*v_th^2)),...

Yeah, it is a sort of data-driven method in the article. The main point here is that LSTM should be the most suitable NN for predicting time-dependent PDE in generally.

Only it is a continuous solution, not discrete, sort of like `res.y(x)` where x in domain_x