Inverse Born series based neural operators

What the math gives to ML

The paper exposes a useful architectural pattern: inverse Born expansions represent a nonlinear inverse map as compositions of linear operators and multilinear interaction terms, and those interactions can be implemented explicitly rather than left to a generic neural operator. The extracted construction realizes products exactly with a small square-activation subnetwork, then uses these products to assemble basis-expansion terms involving measured data and oscillatory test functions. This suggests a structured polynomial neural operator whose order and truncation are controlled by the Born expansion, improving parameter efficiency and interpretability for inverse problems. The most practical first test is to replace the pointwise MLP in a Fourier neural operator with explicit bilinear operator blocks and compare accuracy, parameter count, and stability under measurement noise.