Optimizer-Dependent Trade-Offs in Variational Multiple-Doppler Wind Retrieval: A Comparison of Adam, L-BFGS, and Newton-CG

The Wind Synthesis System using Doppler Measurements (WISSDOM) retrieves three-dimensional winds by minimizing a variational objective that combines Doppler-radar observations and physical constraints. Using a common Python implementation with PyTorch (2.9.1+cu130) automatic differentiation on an NVIDIA GPU, this study compared Adam, limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS), and trust-region Newton conjugate-gradient (Newton-CG) for the same Typhoon Bavi case, initial wind field, and objective. At solver-specific stopping points, all three methods substantially reduced the objective and produced broadly similar principal horizontal- and vertical-wind structures. L-BFGS and Newton-CG produced the closest final wind fields, whereas Adam showed somewhat larger local differences. Their final objective values and gradient norms nevertheless differed: Newton-CG reached the smallest objective and relative full-gradient norm, while L-BFGS reached similar final values at much lower computational cost. Separate timing runs compared execution with compilation disabled for all solvers and with compilation enabled for Adam and L-BFGS only. Comparisons at common objective targets and common elapsed-time budgets provided complementary measures of computational cost and objective reduction. Within the tested solver-specific configurations, these results identify different balances between computational cost and convergence: Adam provided the lowest-cost route to broadly similar principal wind structures, L-BFGS balanced computational cost and numerical convergence, and Newton-CG reached the smallest monitored gradient norm at the highest computational cost.