Neural Network Methods
This page records how the neural methods are validated. The neural_solver
package (JAX) implements mesh-free deep BSDE, deep HJB (DGM), and neural
operator methods. Unlike the classical solver, its validation is not part of
cargo test: it is exercised by the Python test suite in neural_solver/tests/
and its measured results are documented in the
neural empirical results. This page is
the single-place summary; the per-architecture numbers are stated once in the
empirical pages and are not duplicated here beyond the headline figures.
The neural methods are validated in two ways:
- Against exact references - the same closed forms the classical solver uses (Black-Scholes, Merton, LQ, jump-LQ), and for the jump path a Riccati closed form that exercises the learned jump integrand directly.
- Against the classical solver's committed values - reference agreement
with no training: the JAX closed forms reproduce the Rust
solvervalues to float32 precision.
| Problem | Neural method | Reference | Obtained error | Source |
|---|---|---|---|---|
| Black-Scholes call | deep BSDE | closed form | 0.19%-2.29% (per seed) | results |
| Black-Scholes call | DGM | closed form | 1.10% | results |
| Merton portfolio | deep BSDE | closed form | within 10% (test tolerance) | results |
| jump-LQ | deep BSDE | Riccati closed form | 0.70% | results |
| jump-LQ | DGM | Riccati closed form | 1.33% | results |
| Merton jump | deep BSDE | closed form | 0.022% | results |
| Reference agreement | JAX closed forms | Rust solver values | 1e-6 (float32) | results |
Cross-architecture cost and error (deep BSDE vs DGM vs operator, including the no-exact-solution targets) are in comparison; which architecture fits which exact-solution problem is in coverage. The reference schema the agreement check consumes is documented in usage.