Random Feature Method for Solving Partial Differential Equations
This work solves PDEs with a random feature model, a randomized shallow neural network that approximates a kernel machine, by minimizing the PDE residual at collocation points and training only the output weights, avoiding the cubic cost of kernel-matrix methods. Students learn how random features reduce the computational complexity of kernel-based PDE solvers and how a two-step convergence analysis bounds the total error by combining kernel-method estimates with the random-feature approximation error.
2501.00288
Introduces a random feature framework for numerically solving partial differential equations. A random feature model maps inputs through randomly generated hidden-layer weights (a randomized shallow …