Diffusion-based generative emulators enable training-free optimal particle filtering that scales Bayesian state estimation to high-dimensional nonlinear chaotic systems including atmospheric dynamics.
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Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems
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A plug-and-play differentiable model bridging ray and wave optics for hybrid systems that enables end-to-end optimization of planar and conformal diffractive elements.
Forward-mode automatic differentiation replaces finite-difference approximations for Jacobian-vector products in JFNK solvers, delivering 2-3 orders of magnitude speedup and lifting minimum solver completion from 42% to 95% across Burgers, radiation diffusion, reaction-diffusion, and nonlinear time-
NSPOD is a multigrid-like preconditioner using DeepONet-learned POD subspaces that dramatically cuts Krylov solver iterations for solid mechanics PDEs on unstructured CAD geometries, outperforming algebraic multigrid.
A JAX-based differentiable BEM solver matches traditional BEM accuracy on benchmarks and supports gradient-driven acoustic geometry optimization.
Two generalizations of reduced rank extrapolation are derived for low-rank matrix sequences and iteration-dependent mapping functions, with numerical tests on Lyapunov and Riccati equations.
MUDRA extends FLDA to multivariate time series with missing data via an ECM algorithm and shows improved classification over prior methods on the Articulary Word Recognition dataset.
A new preparedness metric for ambulance fleet operations under uncertainty enables optimized selection and reassignment decisions and outperforms nine existing methods on real emergency medical service data.
Low-rank structure in HBVM stage equations is exploited via Krylov projection for linear cases and Newton-Krylov with adaptive time-stepping for nonlinear cases, shown efficient on semi-discretized wave equations.
Integrating RACE into Trilinos applies algebraic temporal blocking to MPK in s-step GMRES, polynomial preconditioners, and AMG, yielding up to 3x speedups on multi-core CPUs for MPK-dominated algorithms.
This is an introductory review of the linear algebraic subproblems and contemporary solvers in variational data assimilation for geophysical applications.
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A General Differentiable Ray-Wave Framework for Hybrid Refractive-Diffractive System Modeling and Optimization
A plug-and-play differentiable model bridging ray and wave optics for hybrid systems that enables end-to-end optimization of planar and conformal diffractive elements.