Neural Operators
Cross-source consensus on Neural Operators from 1 sources and 4 claims.
1 sources · 4 claims
How it works
Benefits
Comparisons
Highlighted claims
- Neural operators such as FNO and DeepONet learn mappings between infinite-dimensional function spaces, achieving resolution invariance and orders-of-magnitude speedups over classical solvers. — Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization
- Training standard neural operators with L2 loss on stochastic PDE data forces convergence to the conditional mean, discarding the full terminal law including spatial variance and tail structure. — Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization
- FNO achieves competitive mean accuracy on stochastic Burgers but has no variance head and cannot provide stochastic residual information. — Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization
- FNO outperforms MNO on Gray-Scott because it can allocate its full capacity to mean prediction without a competing variance head. — Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization