Performance¶

A nefi solve is a few thousand small optimization steps. On problems of 10³–10⁵ cells a step is limited by per-operator overhead rather than arithmetic, so nefi optimizes ops per step, sweeps per solve and problems per launch. The dashboards below come from the gallery run (CPU, torch 2.11); the measurements, switches and CUDA estimates are in Performance.

What is measured and what is estimated

Every number on this page was measured on a CPU. Expected CUDA speed-ups in the performance guide are estimates from launch counts and still have to be validated on a GPU.

Step time of every system¶

Step time per system on a log scale, from 0.54 ms (toy1d) to about 70 ms (dot3d), and the split of each step into forward, backward and optimizer — Milliseconds per optimization step at each system's smoke size, and the share of forward, backward and optimizer. FFT-based problems take about a millisecond; PDE solves (heat, elliptic, wave, reaction–diffusion) dominate their own steps.

Wall-clock breakdown of every gallery system: data generation, stage 1, stage 2, solver overhead, evaluation and figures — Where the seconds of each gallery entry go: generating the data with the independent simulator, the two curriculum stages, evaluation and the figures.

Switches¶

Speed-up against eager execution for compile=field, compile=step, the Chebyshev heat solver and bf16 autocast on four systems — Opt-in switches against eager execution on the CPU: whole-step compilation helps the small MLP problems (×1.22–1.23), Chebyshev sweeps speed up the heat solver (×1.21–1.26), and bf16 autocast is slower on a CPU (no fast bf16 GEMM) — it is meant for CUDA tensor cores.

heat solver (NeFTY), CPU	before	after
kernels per Jacobi sweep	12 (`torch.roll`)	7 (flat padded layout)
thermal smoke step	21.2 ms	9.4 ms (7.7 ms with Chebyshev, same accuracy)
sweeps at the paper step for equal accuracy	50 Jacobi	20 Chebyshev

batched solving (`nefi.batch_invert`), per-problem step on CPU	sequential	batch 64
toy1d	0.41 ms	0.048 ms (8.4×)
nv_relaxometry	0.90 ms	0.37 ms (2.5×)
deconvolution	1.31 ms	0.66 ms (2.0×)

Scaling and memory¶

Step time and autograd memory against the number of grid points for toy1d, deconvolution and thermal tomography, with an O(N) guide — Step time grows far slower than the grid at these sizes (overhead-bound); saved autograd memory grows linearly.

Autograd saved-tensor memory of the heat solver by gradient mode: adjoint, checkpoint and autograd at two grid sizes — Memory of the heat solver by gradient mode (smoke grids): the discrete adjoint stores only the trajectory — 2.45 MB against 8.71 MB for unrolled autograd at 16×16×6. At the paper grid (64×64×16, 100 frames) it is 26.5 MB against 15.7 GB (thermal tomography).

Benchmark in one command¶

Benchmark summary: PSNR mean and 95 % confidence interval of the neural field and the grid on toy1d — `nefi bench toy1d --methods neural,grid` at the gallery budget (2 samples × 2 seeds): on this smooth 1-D linear problem the free grid wins (32.9 ± 4.2 dB against 22.0 ± 5.5 dB). Benchmarks report such results as they are — see Limitations and caveats.

python tools/profile_instance.py thermal_tomography --config configs/thermal_tomography_smoke.yaml
nefi bench configs/deconvolution_full.yaml --n 32 --seeds 0,1,2 --batched --shard 0/8 --out runs/dc
nefi bench-merge runs/dc                      # identical to the unsharded table (tested)