Electrostatics Benchmarks#

This page presents benchmark results for electrostatic interaction methods including Ewald summation and Particle Mesh Ewald (PME) across different GPU hardware. Results show the scaling behavior with increasing system size for periodic systems, including both single-system and batched computations.

Warning

These results are intended to be indicative only: your actual performance may vary depending on the atomic system topology, software and hardware configuration and we encourage users to benchmark on their own systems of interest.

How to Read These Charts#

Time Scaling : Median execution time (ms) vs. system size. Lower is better. Timings include both real-space and reciprocal-space contributions when running “full” mode.

Throughput : Atoms processed per millisecond. Higher is better. This indicates the scaling point where the GPU saturates.

Memory : Peak GPU memory usage (MB) vs. system size. This is particularly useful for estimating/gauging memory requirements for your system.

Ewald Summation#

The Ewald summation method splits the Coulomb interaction into real-space and reciprocal-space components. This is the traditional \(O(N^{3/2})\) to \(O(N^2)\) method depending on parameter choices.

Scaling of single and batched Ewald computation with the nvalchemiops backend. Shows how performance scales with different batch sizes.

Time Scaling#

Throughput#

Memory Usage#

Particle Mesh Ewald (PME)#

PME achieves \(O(N \log N)\) scaling by using FFTs for the reciprocal-space contribution. This is the recommended method for large systems.

Scaling of single and batched PME computation with the nvalchemiops backend. Shows how performance scales with different batch sizes.

Time Scaling#

Throughput#

Memory Usage#

Hardware Information#

GPU: NVIDIA H100 80GB HBM3

Benchmark Configuration#

Parameter	Value
System Type	FCC crystal lattice with periodic boundaries
Neighbor List	Cell list algorithm (\(O(N)\) scaling)
Warmup Iterations	3
Timing Iterations	10
Precision	`float32`

Ewald/PME Parameters#

Parameters are automatically estimated using accuracy-based parameter estimation targeting \(10^{-6}\) relative accuracy:

Parameter	Description
`alpha`	Ewald splitting parameter (auto-estimated)
`k_cutoff`	Reciprocal-space cutoff for Ewald (auto-estimated)
`real_space_cutoff`	Real-space cutoff distance (auto-estimated)
`mesh_dimensions`	PME mesh grid size (auto-estimated)
`spline_order`	B-spline interpolation order (4)

Interpreting Results#

total_atoms : Total number of atoms in the supercell (or across all batched systems).

batch_size : Number of systems processed simultaneously (1 for single-system mode).

method : The electrostatics method used (ewald or pme).

backend : The computational backend (nvalchemiops or torchpme).

component : Which part of the calculation was benchmarked (real, reciprocal, or full).

compute_forces : Whether forces were computed in addition to energies.

median_time_ms : Median execution time in milliseconds (lower is better).

peak_memory_mb : Peak GPU memory usage in megabytes.

Note

Timings include the full electrostatics calculation (real-space + reciprocal-space for “full” mode). Neighbor list construction is excluded from timings.

Running Your Own Benchmarks#

To generate benchmark results for your hardware:

cd benchmarks/interactions/electrostatics
python benchmark_electrostatics.py \
    --config benchmark_config.yaml \
    --backend nvalchemiops \
    --method both \
    --output-dir ../../../docs/benchmarks/benchmark_results

Options#

--backend nvalchemiops : Use the nvalchemiops backend (default).

--method {ewald,pme,both} : Select electrostatics method (default: both).

--gpu-sku <name> : Override GPU SKU name for output files (default: auto-detect).

--config <path> : Path to YAML configuration file.

Results will be saved as CSV files and plots will be automatically generated during the next documentation build.