| { |
| "model_type": "physics-informed-neural-network", |
| "version": "1.0.0", |
| "author": "Ramprasad Atluri (@At1uri)", |
| "framework": "scipy / numpy / pytorch-compatible", |
| "architecture": { |
| "network_type": "Deep Collocation Multi-Layer Perceptron (MLP)", |
| "input_dimension": 2, |
| "input_features": ["spot_price_S", "time_to_maturity_tau"], |
| "hidden_layers": [64, 64, 64], |
| "output_dimension": 1, |
| "output_feature": "solution_u", |
| "activation_function": "tanh" |
| }, |
| "loss_formulation": { |
| "interior_pde_loss": "Mean Squared Residual of Parabolic Black-Scholes Operator", |
| "terminal_condition_loss": "Mean Squared Error against max(S - K, 0) at tau = 0", |
| "boundary_condition_loss": "Asymptotic Dirichlet Boundary Loss as S -> 0 and S -> S_max", |
| "loss_weights": { |
| "lambda_pde": 1.0, |
| "lambda_initial": 15.0, |
| "lambda_boundary": 10.0 |
| } |
| }, |
| "diagnostics": { |
| "training_collocation_points": 5000, |
| "final_pde_residual_l2_norm": 0.000421, |
| "relative_sobolev_h1_error": 0.00185 |
| } |
| } |
|
|
