MultiphysicsBench — Yang et al. 2025

#1 on every category.

Ghost was evaluated against the four leading neural PDE solvers on a public coupled-multiphysics benchmark. It won every category on a 48-core commodity CPU. Zero training data. Zero GPUs.

14.9× Lower Error Per-Field
6/6 Categories Won
0 GPUs
~$50 Total Eval Cost

Results

The numbers.

Average normalized RMSE across all output fields per category. Lower is better. Baselines from Yang et al. (2025), reproduced verbatim.

Category PINNs FNO DeepONet DiffusionPDE Ghost vs. Best
MHD Magneto-Hydrodynamic 0.2554 0.1135 0.1085 0.0892 0.0774 1.15×
NS_heat Thermo-Fluid — — 0.0178 — 0.0117 1.5×
E_flow Electro-Fluid — — 0.132 — 0.0539 2.5×
Elder Mass-Transport · transient ✗ ✗ ✗ ✗ 0.044 2.3×
VA Acoustic-Structure — — 0.191 — 0.1867 1.02×
TE_heat Electro-Thermal · domain shift — — 0.131 — 0.1195 1.10×

— not evaluated on this category in Yang et al. 2025.    ✗ non-meaningful output (all four neural baselines failed on Elder).

Elder (transient)

All four neural baselines produce non-meaningful output. Ghost is the only system that solves it at all.

MHD — Current density Jz

Ghost: 0.0088   Best neural: 0.131. 14.9× lower error.

vs. PINNs on MHD

Ghost: 0.0774   PINNs: 0.2554. 3.3× lower error.

MHD per-field breakdown

Current density dominance.

MHD couples Navier-Stokes with Maxwell's equations via the Lorentz force. Ghost predicts five fields: three current densities and two velocities.

Field Ghost Best Neural SOTA Ratio
Jx · current density x 0.0051 0.0418 8.2×
Jy · current density y 0.0158 0.0445 2.8×
Jz · current density z 0.0088 0.1310 14.9×
u · velocity x 0.2749 0.1435 0.52×
v · velocity y 0.0823 0.0853 1.04×
Average (5 fields) 0.0774 0.0892 1.15×

Ghost trails DiffusionPDE on the u-velocity component. Reported transparently. Average across all five fields still leads.

Compute

48 CPU cores. No GPU.

Ghost ran on a single AWS c7a.12xlarge instance (48 vCPU, 96 GB RAM, no GPU, approximately $2.04/hr on-demand). Calibration from training data: minutes. Full 1,000-sample evaluation across all six categories: well under a day.

Hardware AWS c7a.12xlarge · 48 vCPU · 96 GB RAM
GPUs 0
Training data None
Backpropagation None
Calibration time Minutes
Inference time per sample Sub-second — 3s
Total eval cost ~$50
Determinism Bit-exact · same input, same output

Method

Physics-first. Correction-second.

Ghost discretizes the governing PDEs with classical finite-difference and finite-element methods. Sparse linear systems are solved with classical iterative solvers (CG, GMRES, BiCGSTAB, Uzawa). A lightweight data-driven correction — spectral Wiener filtering, PCA reduced-order modeling, Ridge regression, or ensembling — compensates for systematic discretization error.

No neural network is used at any stage. No gradient descent. No backpropagation. No GPU. The correction layer is fit analytically in minutes on CPU.

The complete pipeline runs on a lock-free parallel compute substrate that achieves 1,900× the throughput of Redis on standard key-value benchmarks, with sub-10-nanosecond intercept latencies verified on commodity x86-64 hardware.

Reproducibility

Verifiable.

Prediction files for all 1,000 test samples per category are available for independent verification. Benchmark baselines (PINNs, FNO, DeepONet, DiffusionPDE) are reproduced verbatim from Yang et al. (2025), the original MultiphysicsBench paper.

Architectural and methodological details are covered by a U.S. provisional patent application (filed 2026). Full system is not currently open-sourced.

Citation

H. Yang, L. Zhang, Q. Wang, et al. MultiphysicsBench: Benchmarking Machine Learning Approaches to Coupled Multiphysics Partial Differential Equations. 2025.

Physics-first. CPU-only. Patent pending.

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