Mixed precision explicit numerical methods for ordinary differential equations

What the math gives to ML

The paper's transferable asset is not mixed precision in general, which is already common in deep learning, but the selective placement of precision inside explicit ODE integrators. An explicit multistage method can evaluate expensive nonlinear right-hand-side stages in low precision while retaining the state update and weighted accumulation in higher precision, potentially reducing the cost of neural ODE, continuous-depth, and probability-flow sampling computations. The most direct experiment is a precision-partitioned Runge–Kutta solver that compares accuracy, wall-clock cost, and failure rates against all-high-precision and all-low-precision baselines.