ANOVA approximation for high-dimensional control systems

High‑dimensional control systems—like those that model how pollutants spread in the atmosphere or how photochemical smog forms—are usually described by complex advection‑diffusion equations. Solving and controlling these equations in real time is almost impossible because the number of dimensions makes the computations explode. This project looks at a data‑driven way to approximate control‑affine systems using an ANalysis Of VAriance (ANOVA) decomposition. Typical ANOVA methods ignore the fact that the system is control‑affine. To fix that, the paper proposes a coupled least‑squares technique. It builds an ansatz that is linear in the control variables by first preprocessing the ANOVA index sets. A main theoretical result is a probabilistic (L_2)‑error bound derived

with a Marcinkiewicz–Zygmund inequality. This bound lets us control the error in the drift term and the input vector field separately. The approach is tested on discretized nonlinear advection‑diffusion equations that directly model environmental transport. The framework gives M.Tech students a clear path to create reduced‑order models for air‑quality control, making sensitivity analysis and simulations with varying parameters much more efficient.

Message: Hi FE, I need help with “ANOVA approximation for high-dimensional control systems” in “Environmental Engineering”