Beyond Pricing Accuracy: A Multicriteria Diagnostic Benchmark of Neural Approaches to Financial PDE Approximation

Abstract

Neural approximations of financial PDEs are often ranked by aggregate pricing error, although price accuracy alone does not establish differential, physical, or financial consistency. We present a multicriteria diagnostic benchmark of seven representative configurations in a common Black–Scholes setting. The primary comparison uses a frozen 20,000-point test set and five optimization seeds; targeted three-seed controls examine domain truncation, collocation density, DGM update allocation and loss scaling, checkpoint selection, Hybrid order and activation, and Monte Carlo path allocation. Evaluation covers price and Greek errors, PDE residuals and tails, financial-violation frequencies and magnitudes, regime performance, runtime, and seed variability. The MLP achieves the lowest primary price MAE, 0.0675 ± 0.0057, whereas the Standard PINN at Smax = 400 achieves the lowest primary PDE MAE, 0.2648 ± 0.0432. The data-first Hybrid is competitive on both and obtains the lowest Greek errors and NEG, LBV, and monotonicity-violation frequencies. Moving Smax from 200 to 400 reduces PINN price MAE from 2.596 to 0.212, whereas extension to 800 raises it to 0.402; restoring collocation density does not recover Smax = 400 performance. Increasing DGM allocation from one to 20 updates per epoch reduces its PDE MAE from 0.4539 to 0.1498, below the matched-seed PINN value of 0.2662, but raises training time from 230.6 to 3022.4 seconds. Hybrid and checkpoint controls reveal criterion-specific trade-offs, while path-count diagnostics quantify stochastic-target noise. No configuration is uniformly dominant. Reliable neural-PDE benchmarking requires joint reporting of accuracy, physical and financial consistency, protocol choices, and cost.