[petsc-users] sources of floating point randomness in JFNK in serial
Mark Lohry
mlohry at gmail.com
Thu May 4 07:54:32 CDT 2023
>
> Try -pc_type none.
>
With -pc_type none the 0 KSP residual looks identical. But *sometimes* it's
producing exactly the same history and others it's gradually changing. I'm
reasonably confident my residual evaluation has no randomness, see info
after the petsc output.
solve history 1:
0 SNES Function norm 3.424003312857e+04
0 KSP Residual norm 3.424003312857e+04
1 KSP Residual norm 2.871734444536e+04
2 KSP Residual norm 2.490276931041e+04
...
20 KSP Residual norm 7.449686034356e+03
Linear solve converged due to CONVERGED_ITS iterations 20
1 SNES Function norm 1.085015821006e+04
solve history 2, identical to 1:
0 SNES Function norm 3.424003312857e+04
0 KSP Residual norm 3.424003312857e+04
1 KSP Residual norm 2.871734444536e+04
2 KSP Residual norm 2.490276931041e+04
...
20 KSP Residual norm 7.449686034356e+03
Linear solve converged due to CONVERGED_ITS iterations 20
1 SNES Function norm 1.085015821006e+04
solve history 3, identical KSP at 0 and 1, slight change at 2, growing
difference to the end:
0 SNES Function norm 3.424003312857e+04
0 KSP Residual norm 3.424003312857e+04
1 KSP Residual norm 2.871734444536e+04
2 KSP Residual norm 2.490276930242e+04
...
20 KSP Residual norm 7.449686095424e+03
Linear solve converged due to CONVERGED_ITS iterations 20
1 SNES Function norm 1.085015646971e+04
Ths is using a standard explicit 3-stage Runge-Kutta smoother for 10
iterations, so 30 calls of the same residual evaluation, identical
residuals every time
run 1:
# iteration rho rhou rhov
rhoE abs_res rel_res umin
vmax vmin elapsed_time
#
1.00000e+00 1.086860616292e+00 2.782316758416e+02
4.482867643761e+00 2.993435920340e+02 2.04353e+02
1.00000e+00 -8.23945e-15 -6.15326e-15 -1.35563e-14
6.34834e-01
2.00000e+00 2.310547487017e+00 1.079059352425e+02
3.958323921837e+00 5.058927165686e+02 2.58647e+02
1.26568e+00 -1.02539e-14 -9.35368e-15 -1.69925e-14
6.40063e-01
3.00000e+00 2.361005867444e+00 5.706213331683e+01
6.130016323357e+00 4.688968362579e+02 2.36201e+02
1.15585e+00 -1.19370e-14 -1.15216e-14 -1.59733e-14
6.45166e-01
4.00000e+00 2.167518999963e+00 3.757541401594e+01
6.313917437428e+00 4.054310291628e+02 2.03612e+02
9.96372e-01 -1.81831e-14 -1.28312e-14 -1.46238e-14
6.50494e-01
5.00000e+00 1.941443738676e+00 2.884190334049e+01
6.237106158479e+00 3.539201037156e+02 1.77577e+02
8.68970e-01 3.56633e-14 -8.74089e-15 -1.06666e-14
6.55656e-01
6.00000e+00 1.736947124693e+00 2.429485695670e+01
5.996962200407e+00 3.148280178142e+02 1.57913e+02
7.72745e-01 -8.98634e-14 -2.41152e-14 -1.39713e-14
6.60872e-01
7.00000e+00 1.564153212635e+00 2.149609219810e+01
5.786910705204e+00 2.848717011033e+02 1.42872e+02
6.99144e-01 -2.95352e-13 -2.48158e-14 -2.39351e-14
6.66041e-01
8.00000e+00 1.419280815384e+00 1.950619804089e+01
5.627281158306e+00 2.606623371229e+02 1.30728e+02
6.39715e-01 8.98941e-13 1.09674e-13 3.78905e-14
6.71316e-01
9.00000e+00 1.296115915975e+00 1.794843530745e+01
5.514933264437e+00 2.401524522393e+02 1.20444e+02
5.89394e-01 1.70717e-12 1.38762e-14 1.09825e-13
6.76447e-01
1.00000e+01 1.189639693918e+00 1.665381754953e+01
5.433183087037e+00 2.222572900473e+02 1.11475e+02
5.45501e-01 -4.22462e-12 -7.15206e-13 -2.28736e-13
6.81716e-01
run N:
#
# iteration rho rhou rhov
rhoE abs_res rel_res umin
vmax vmin elapsed_time
#
1.00000e+00 1.086860616292e+00 2.782316758416e+02
4.482867643761e+00 2.993435920340e+02 2.04353e+02
1.00000e+00 -8.23945e-15 -6.15326e-15 -1.35563e-14
6.23316e-01
2.00000e+00 2.310547487017e+00 1.079059352425e+02
3.958323921837e+00 5.058927165686e+02 2.58647e+02
1.26568e+00 -1.02539e-14 -9.35368e-15 -1.69925e-14
6.28510e-01
3.00000e+00 2.361005867444e+00 5.706213331683e+01
6.130016323357e+00 4.688968362579e+02 2.36201e+02
1.15585e+00 -1.19370e-14 -1.15216e-14 -1.59733e-14
6.33558e-01
4.00000e+00 2.167518999963e+00 3.757541401594e+01
6.313917437428e+00 4.054310291628e+02 2.03612e+02
9.96372e-01 -1.81831e-14 -1.28312e-14 -1.46238e-14
6.38773e-01
5.00000e+00 1.941443738676e+00 2.884190334049e+01
6.237106158479e+00 3.539201037156e+02 1.77577e+02
8.68970e-01 3.56633e-14 -8.74089e-15 -1.06666e-14
6.43887e-01
6.00000e+00 1.736947124693e+00 2.429485695670e+01
5.996962200407e+00 3.148280178142e+02 1.57913e+02
7.72745e-01 -8.98634e-14 -2.41152e-14 -1.39713e-14
6.49073e-01
7.00000e+00 1.564153212635e+00 2.149609219810e+01
5.786910705204e+00 2.848717011033e+02 1.42872e+02
6.99144e-01 -2.95352e-13 -2.48158e-14 -2.39351e-14
6.54167e-01
8.00000e+00 1.419280815384e+00 1.950619804089e+01
5.627281158306e+00 2.606623371229e+02 1.30728e+02
6.39715e-01 8.98941e-13 1.09674e-13 3.78905e-14
6.59394e-01
9.00000e+00 1.296115915975e+00 1.794843530745e+01
5.514933264437e+00 2.401524522393e+02 1.20444e+02
5.89394e-01 1.70717e-12 1.38762e-14 1.09825e-13
6.64516e-01
1.00000e+01 1.189639693918e+00 1.665381754953e+01
5.433183087037e+00 2.222572900473e+02 1.11475e+02
5.45501e-01 -4.22462e-12 -7.15206e-13 -2.28736e-13
6.69677e-01
On Thu, May 4, 2023 at 8:41 AM Mark Adams <mfadams at lbl.gov> wrote:
> ASM is just the sub PC with one proc but gets weaker with more procs
> unless you use jacobi. (maybe I am missing something).
>
> On Thu, May 4, 2023 at 8:31 AM Mark Lohry <mlohry at gmail.com> wrote:
>
>> Please send the output of -snes_view.
>>>
>> pasted below. anything stand out?
>>
>>
>> SNES Object: 1 MPI process
>> type: newtonls
>> maximum iterations=1, maximum function evaluations=-1
>> tolerances: relative=0.1, absolute=1e-15, solution=1e-15
>> total number of linear solver iterations=20
>> total number of function evaluations=22
>> norm schedule ALWAYS
>> Jacobian is never rebuilt
>> Jacobian is applied matrix-free with differencing
>> Preconditioning Jacobian is built using finite differences with coloring
>> SNESLineSearch Object: 1 MPI process
>> type: basic
>> maxstep=1.000000e+08, minlambda=1.000000e-12
>> tolerances: relative=1.000000e-08, absolute=1.000000e-15,
>> lambda=1.000000e-08
>> maximum iterations=40
>> KSP Object: 1 MPI process
>> type: gmres
>> restart=30, using Classical (unmodified) Gram-Schmidt
>> Orthogonalization with no iterative refinement
>> happy breakdown tolerance 1e-30
>> maximum iterations=20, initial guess is zero
>> tolerances: relative=0.1, absolute=1e-15, divergence=10.
>> left preconditioning
>> using PRECONDITIONED norm type for convergence test
>> PC Object: 1 MPI process
>> type: asm
>> total subdomain blocks = 1, amount of overlap = 0
>> restriction/interpolation type - RESTRICT
>> Local solver information for first block is in the following KSP
>> and PC objects on rank 0:
>> Use -ksp_view ::ascii_info_detail to display information for all
>> blocks
>> KSP Object: (sub_) 1 MPI process
>> type: preonly
>> maximum iterations=10000, initial guess is zero
>> tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
>> left preconditioning
>> using NONE norm type for convergence test
>> PC Object: (sub_) 1 MPI process
>> type: ilu
>> out-of-place factorization
>> 0 levels of fill
>> tolerance for zero pivot 2.22045e-14
>> matrix ordering: natural
>> factor fill ratio given 1., needed 1.
>> Factored matrix follows:
>> Mat Object: (sub_) 1 MPI process
>> type: seqbaij
>> rows=16384, cols=16384, bs=16
>> package used to perform factorization: petsc
>> total: nonzeros=1277952, allocated nonzeros=1277952
>> block size is 16
>> linear system matrix = precond matrix:
>> Mat Object: (sub_) 1 MPI process
>> type: seqbaij
>> rows=16384, cols=16384, bs=16
>> total: nonzeros=1277952, allocated nonzeros=1277952
>> total number of mallocs used during MatSetValues calls=0
>> block size is 16
>> linear system matrix followed by preconditioner matrix:
>> Mat Object: 1 MPI process
>> type: mffd
>> rows=16384, cols=16384
>> Matrix-free approximation:
>> err=1.49012e-08 (relative error in function evaluation)
>> Using wp compute h routine
>> Does not compute normU
>> Mat Object: 1 MPI process
>> type: seqbaij
>> rows=16384, cols=16384, bs=16
>> total: nonzeros=1277952, allocated nonzeros=1277952
>> total number of mallocs used during MatSetValues calls=0
>> block size is 16
>>
>> On Thu, May 4, 2023 at 8:30 AM Mark Adams <mfadams at lbl.gov> wrote:
>>
>>> If you are using MG what is the coarse grid solver?
>>> -snes_view might give you that.
>>>
>>> On Thu, May 4, 2023 at 8:25 AM Matthew Knepley <knepley at gmail.com>
>>> wrote:
>>>
>>>> On Thu, May 4, 2023 at 8:21 AM Mark Lohry <mlohry at gmail.com> wrote:
>>>>
>>>>> Do they start very similarly and then slowly drift further apart?
>>>>>
>>>>>
>>>>> Yes, this. I take it this sounds familiar?
>>>>>
>>>>> See these two examples with 20 fixed iterations pasted at the end. The
>>>>> difference for one solve is slight (final SNES norm is identical to 5
>>>>> digits), but in the context I'm using it in (repeated applications to solve
>>>>> a steady state multigrid problem, though here just one level) the
>>>>> differences add up such that I might reach global convergence in 35
>>>>> iterations or 38. It's not the end of the world, but I was expecting that
>>>>> with -np 1 these would be identical and I'm not sure where the root cause
>>>>> would be.
>>>>>
>>>>
>>>> The initial KSP residual is different, so its the PC. Please send the
>>>> output of -snes_view. If your ASM is using direct factorization, then it
>>>> could be randomness in whatever LU you are using.
>>>>
>>>> Thanks,
>>>>
>>>> Matt
>>>>
>>>>
>>>>> 0 SNES Function norm 2.801842107848e+04
>>>>> 0 KSP Residual norm 4.045639499595e+01
>>>>> 1 KSP Residual norm 1.917999809040e+01
>>>>> 2 KSP Residual norm 1.616048521958e+01
>>>>> [...]
>>>>> 19 KSP Residual norm 8.788043518111e-01
>>>>> 20 KSP Residual norm 6.570851270214e-01
>>>>> Linear solve converged due to CONVERGED_ITS iterations 20
>>>>> 1 SNES Function norm 1.801309983345e+03
>>>>> Nonlinear solve converged due to CONVERGED_ITS iterations 1
>>>>>
>>>>>
>>>>> Same system, identical initial 0 SNES norm, 0 KSP is slightly different
>>>>>
>>>>> 0 SNES Function norm 2.801842107848e+04
>>>>> 0 KSP Residual norm 4.045639473002e+01
>>>>> 1 KSP Residual norm 1.917999883034e+01
>>>>> 2 KSP Residual norm 1.616048572016e+01
>>>>> [...]
>>>>> 19 KSP Residual norm 8.788046348957e-01
>>>>> 20 KSP Residual norm 6.570859588610e-01
>>>>> Linear solve converged due to CONVERGED_ITS iterations 20
>>>>> 1 SNES Function norm 1.801311320322e+03
>>>>> Nonlinear solve converged due to CONVERGED_ITS iterations 1
>>>>>
>>>>> On Wed, May 3, 2023 at 11:05 PM Barry Smith <bsmith at petsc.dev> wrote:
>>>>>
>>>>>>
>>>>>> Do they start very similarly and then slowly drift further apart?
>>>>>> That is the first couple of KSP iterations they are almost identical but
>>>>>> then for each iteration get a bit further. Similar for the SNES iterations,
>>>>>> starting close and then for more iterations and more solves they start
>>>>>> moving apart. Or do they suddenly jump to be very different? You can run
>>>>>> with -snes_monitor -ksp_monitor
>>>>>>
>>>>>> On May 3, 2023, at 9:07 PM, Mark Lohry <mlohry at gmail.com> wrote:
>>>>>>
>>>>>> This is on a single MPI rank. I haven't checked the coloring, was
>>>>>> just guessing there. But the solutions/residuals are slightly different
>>>>>> from run to run.
>>>>>>
>>>>>> Fair to say that for serial JFNK/asm ilu0/gmres we should expect
>>>>>> bitwise identical results?
>>>>>>
>>>>>>
>>>>>> On Wed, May 3, 2023, 8:50 PM Barry Smith <bsmith at petsc.dev> wrote:
>>>>>>
>>>>>>>
>>>>>>> No, the coloring should be identical every time. Do you see
>>>>>>> differences with 1 MPI rank? (Or much smaller ones?).
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> > On May 3, 2023, at 8:42 PM, Mark Lohry <mlohry at gmail.com> wrote:
>>>>>>> >
>>>>>>> > I'm running multiple iterations of newtonls with an MFFD/JFNK
>>>>>>> nonlinear solver where I give it the sparsity. PC asm, KSP gmres, with
>>>>>>> SNESSetLagJacobian -2 (compute once and then frozen jacobian).
>>>>>>> >
>>>>>>> > I'm seeing slight (<1%) but nonzero differences in residuals from
>>>>>>> run to run. I'm wondering where randomness might enter here -- does the
>>>>>>> jacobian coloring use a random seed?
>>>>>>>
>>>>>>>
>>>>>>
>>>>
>>>> --
>>>> What most experimenters take for granted before they begin their
>>>> experiments is infinitely more interesting than any results to which their
>>>> experiments lead.
>>>> -- Norbert Wiener
>>>>
>>>> https://www.cse.buffalo.edu/~knepley/
>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>
>>>
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