The paper introduces asymptotically-informed neural‑network architectures for computing Black‑Scholes implied volatility. By learning a trainable partition of the price‑log‑moneyness domain and combining specialised local approximations, the models outperform standard feed‑forward networks across a wide range of parameters. The neural‑network outputs also serve as highly accurate initial guesses for a third‑order Householder scheme, enabling near machine‑precision results after only two refinement iterations.
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