Validation

Validation of solver results is recorded in three pages:

• Classical methods - the finite-difference (FD) and least-squares Monte Carlo (BSDE) paths in the Rust solver crate, validated inside cargo test.
• Neural network methods - the deep BSDE, deep HJB (DGM), and neural operator methods in the neural_solver package (JAX), validated by the Python test suite and against committed Rust reference values.
• BSDE precision - the one-time high-precision BSDE verification against exact solutions, targeting \(\leq 0.1\%\) relative error.

Canonical error metric

All numerical-versus-reference comparisons use the canonical error metric in solver::validation. The primary quantity is the normalized relative error

\[ \varepsilon = \frac{|x - x^{\text{ref}}|}{\max(|x^{\text{ref}}|, f)} \]

where f is the small absolute floor (DEFAULT_ABS_FLOOR = 1e-12) that prevents division by zero when the reference is at or near zero. A percentage is \(100\,\varepsilon\). The helpers relative_error, percent_error, assert_within, and assert_close are shared across every solver test and benchmark so that a reported tolerance means the same thing regardless of the magnitude of the quantity under test.