[petsc-users] SNES_QN_RESTART_POWELL fails to converge?

[Barry Smith]

  Andrew,
  
    Thanks for your code. I look through the QN code and it seems ok, the one funny thing is that it applies the Powell criteria after the first iterations (before the L-BFGS has properly started) which is why the solution just continues to grow and grow. Essentially with the Powell test it is never starting L-BFSG. I have made two changes 

1)  branch barry/fix-snes-qn-powell/maint that changes the code so that the Powel check is not done until the first full iteration of L-BFGS has been completed. This now gets the ex1_powell.c code to converge (with 18 iterations). Of course waiting for one full iteration of L-BFGS is arbitrary, perhaps 2 is better, I do not know.

2) barry/add-snes-divtol this adds a divergence test to SNES; it was goofy that even though residual norm was increasing without bound the SNES iteration continued to iterate. I added a new convergence test that if the residual grows (default) by 1e4 then the iteration is stopped with a divergence error.

  Thanks for reporting these problems,

  Barry



> On Jul 15, 2016, at 3:14 AM, Andrew Ho <andrewh0 at uw.edu> wrote:
> 
> I've attached two modified versions of ex1:
> 
> ex1_powell.c uses the Powell restart
> ex1_none.c uses no restart
> 
> For the default initial guess (x0 = [0.5,0.5]), both converge just fine. However, for the initial guess x0 = [3.,3.], the Powell solution fails to converge, while None and Periodic both still converge. This is with the "easy" equation set (run without -hard).
> 
> Interestingly enough, the Powell restart still "finishes" in a reasonable number of iterations (7 iterations), but the residual is very large (on the order of 1e254).
> 
> On Thu, Jul 14, 2016 at 5:50 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> 
> > On Jul 14, 2016, at 6:18 PM, Andrew Ho <andrewh0 at uw.edu> wrote:
> >
> > I am trying to solve a simple ionization/recombination ODE using PETSc's quasi-newton SNES.
> >
> > This is a basic non-linear coupled ODE system:
> >
> > delta = -a u^2 + b u v
> > d_t u = delta
> > d_t v = -delta
> >
> > a and b are constants.
> >
> > I wrote a backwards Euler root finding function (yes, I know the TS module has BE implemented, but this is more of a learning exercise).
> >
> > Here is the function evaluation:
> >
> > struct ion_rec_ctx
> > {
> >   PetscScalar rate_a, rate_b;
> >   PetscScalar dt;
> > };
> > PetscErrorCode bdf1(SNES snes, Vec x, Vec f, void *ctx)
> > {
> >   const PetscScalar *xx;
> >   PetscScalar *ff;
> >   ion_rec_ctx& params = *reinterpret_cast<ion_rec_ctx*>(ctx);
> >   CHKERRQ(VecGetArrayRead(x, &xx));
> >   CHKERRQ(VecGetArray(f,&ff));
> >   auto delta = (-params.rate_a*xx[0]*xx[0]+params.rate_b*xx[1]*xx[0]);
> >   ff[0] = xx[0]-params.dt*delta;
> >   ff[1] = xx[1]-params.dt*-delta;
> >   CHKERRQ(VecRestoreArrayRead(x,&xx));
> >   CHKERRQ(VecRestoreArray(f,&ff));
> >   return 0;
> > }
> >
> > To setup the solver and solve one time step:
> >
> > // q0, q1, and res are Vec's previously initialized
> > // initial conditions: q0 = [1e19,1e19]
> > SNES solver;
> > CHKERRQ(SNESCreate(comm, &solver));
> > CHKERRQ(SNESSetType(solver, SNESQN));
> > CHKERRQ(SNESQNSetType(solver, SNES_QN_LBFGS));
> > ion_rec_ctx params = {9.59e-16, 1.15e-19, 1.};
> > CHKERRQ(SNESSetFunction(solver, res, &bdf1, &params));
> > CHKERRQ(SNESSolve(solver, q0, q1));
> >
> > When I run this, the solver fails to converge to a solution for this rather large time step.
> > The solution produced when the SNES module finally gives up is:
> >
> > q1 = [-2.72647e142, 2.72647e142]
> >
> > For reference, when I disable the scale and restart types, I get these values:
> >
> > q1 = [1.0279e17, 1.98972e19]
> >
> > This is only a problem when I use the SNES_QN_RESTART_POWELL restart type (seems to be regardless of the scale type type). I get reasonable answers for other combinations of restart/scale type. I've tried every combination of restart type/scale type except for SNES_QN_SCALE_JACOBIAN (my ultimate application doesn't have an available Jacobian), and only cases using SNES_QN_RESTART_POWELL are failing.
> >
> > I'm unfamiliar with Powell's restart criterion, but is it suppose to work reasonably well with Quasi-Newton methods? I tried it on the simple problem given in this example: http://www.mcs.anl.gov/petsc/petsc-current/src/snes/examples/tutorials/ex1.c.html
> >
> > And Powell restarts also fails to converge to a meaningful solution (solving for f(x) = [1,1], for x0 = [1,1]), but the other restart methods do converge properly.
> 
>    Could you please send the exact options you are using for the ex1.c that both fail and work and we'll see if there is some problem with the Powell restart.
> 
>     Thanks
> 
>     Barry
> 
> >
> > Software information:
> >
> > PETSc version 3.7.2 (built from git maint branch)
> > PETSc arch: arch-linux2-c-opt
> > OS: Ubuntu 15.04 x64
> > Compiler: gcc 4.9.2
> 
> 
> 
> 
> -- 
> Andrew Ho
> <ex1_none.c><ex1_powell.c>