[dyzheng]

Summary

Fix GPU single-precision DAV restart failures, unstable basis orthogonalization, insufficient reduced-eigensolve accuracy, and rounding errors in density and stress accumulation. Also correct omitted meta-GGA XC contributions in the shared CPU/GPU path.

This PR contains 8 commits across 6 source files, with 101 insertions and 6 deletions. Wavefunctions and FFTs remain single precision; selected accumulations and the existing reduced eigensolve use double precision. No failure-triggered rerun is added, and scientific INPUT settings and convergence criteria are unchanged.

Overall results

Of the original 500 structures, 472 have converged CPU-double references. The 75 structures with anomalous GPU DAV results were retested; previously passing structures retain their original results.

Metric	Before	Cumulative after repair
GPU execution completed with SCF convergence	456/472 (96.61%)	472/472 (100%)
All four accuracy criteria met against the original CPU references	397/472 (84.11%)	465/472 (98.52%)
GPU errors / unconverged runs	3 / 13	0 / 0

68 of the 75 anomalous structures now meet all four accuracy criteria against the original CPU references. Four additional structures meet the criteria against corrected candidate CPU references after addressing the shared XC omission, bringing the cumulative count to 469/472 (99.36%). These four are reference corrections, not evidence of improved GPU accuracy alone.

The screening criteria used in this campaign are energy error ≤1 meV/atom, maximum per-atom force-vector error ≤0.05 eV/Å, maximum stress-component error ≤0.5 kbar, and absolute pressure error ≤0.5 kbar. These are campaign screening criteria, not universal physical-accuracy guarantees.

Changes and measured effects

The following are per-change validation results. Each timing change uses its stated comparator; the percentages are not additive and the intermediate results should not be interpreted as measurements of the final combined version.

Change	Problem addressed and measured effect	Performance impact
1. Double-precision NLCC stress accumulation	POSCAR0224272: maximum stress error 0.420 → 0.017 kbar; pressure error 0.403 → 0.001 kbar.	Runtime approximately unchanged; 23.1× CPU-double speedup.
2. Clear stale DAV restart coefficients	POSCAR0448336: a first-SCF-step failure becomes convergence in 24 steps.	Complete runtime 486.5 s; 19.2× CPU-double speedup. No timing improvement is claimed against the failed run.
3. Double-precision kinetic-stress accumulation	POSCAR0159503: maximum stress error 1.312 → 0.140 kbar.	Runtime approximately unchanged; 8.4× CPU-double speedup.
4. Block long single-precision conjugate inner products	POSCAR1762323: energy error 3.014 → 0.0376 meV/atom.	Runtime +9.7%; still 23.3× faster than CPU double.
5. Double-precision density accumulation across k-points	POSCAR0317955: maximum stress error 0.564 → 0.108 kbar; pressure error 0.529 → 0.099 kbar. Single-precision FFTs are retained.	Runtime approximately unchanged; 12.1× CPU-double speedup.
6. Single-pass block QR for DAV bases	POSCAR0058587: an SCF-step-20 failure becomes a converged calculation, avoiding cancellation in the previous orthogonalization path.	Runtime −9.6% versus the previously converged reorthogonalization implementation. POSCAR0030651: −28.2% versus the version containing fixes 1–5, with increases in some numerical errors.
7. Double-precision DAV reduced eigensolve	POSCAR0056851: unconverged after 100 steps → converged in 68 steps. POSCAR0186922: 73 → 33 steps. The same reduced problem is solved once, then its eigenpairs are cast back to single precision.	Versus the previously converged single-precision Jacobi implementation: POSCAR0186922 runtime −47.6%; POSCAR1729347 runtime +6.2%.
8. Retain meta-GGA XC contributions at zero gradient	POSCAR0130197 and POSCAR0395353: restore approximately −0.267 eV and −0.371 eV of omitted CPU XC contributions, respectively.	GPU runtimes approximately unchanged in both cases. This correction affects the shared CPU/GPU path.

Overall performance

CPU references use 11 MPI ranks × 1 OMP thread. GPU runs use one NVIDIA L20, 1 MPI rank × 1 OMP thread. CPU references generally use dav_subspace, while GPU runs use dav; the ratios describe these execution configurations, not a pure hardware or cost comparison.

• Across the 75 GPU retests, mean GPU runtime is 423.9 s, versus 6724.9 s for the corresponding original CPU references: an aggregate CPU/GPU runtime ratio of approximately 15.9×. This set still includes structures outside the accuracy criteria.
• For the same 59 structures whose old and new GPU runs both converged, mean GPU runtime decreases from 415.5 to 400.2 s, approximately 3.7% less time.
• The 16 previously failed or unconverged runs are excluded from before/after performance comparisons.

Build, validation scope, and remaining issues

The final commit was clean-built on L20; the archived executable and recorded source files match the submitted source. The principal validated configuration is CUDA, GPU single-precision DAV, non-USPP, and one MPI rank. Block QR is restricted to that configuration. The restart reset, stress accumulator types, and XC correction also touch shared code; comprehensive regression coverage of other execution paths is not established by these records.

Residual accuracy issues remain for three structures: stress in POSCAR0955272 and POSCAR0131516, and forces in POSCAR1574549.

The original 397 passing structures were not rerun with the final executable, so the overall figures are cumulative validation results rather than a full final-version rerun. The four corrected CPU references remain candidate references without independent external numerical certification. The results demonstrate the combined effect of the fixes, not a full per-commit ablation study.