Stable and Efficient One-Way Modelling of Convective Disturbances in Laminar Boundary Layers: OWNS-Summation

What the math gives to ML

The paper isolates a broadly useful numerical principle: evaluate a high-order rational spectral filter as an additive partial-fraction sum rather than as a recursive product. Although the target application is one-way fluid marching, the same distinction applies to neural spectral layers, graph filters, implicit networks, and differentiable projectors, where products of poorly conditioned factors can amplify roundoff and gradient errors. Each resolvent term uses the same input and can be computed independently, making the method both numerically safer and naturally parallel. The most direct ML experiment is a rational graph spectral layer whose filter is evaluated by parallel shifted linear solves and compared against recursive factor evaluation at equal approximation order.