I believe (but I might be wrong) that are compared the results of two different methods: (a) "algorithmic" where solution(t+1) = algo(solution(t)) and errors accumulate with time steps, vs. (b) based on sufficiently many available pairs (initial_1, solution_1), ...,(initial_N,solution_N), each solution_i a function of time t \in [0,T], a NN (or another gadget) builds a function ALGO(initial)=solution so that the errors in time of solution(t) wrt real_solution(t) are uniform, where real_solution is the real solution for the initial condition initial.