A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
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Diffusion-based generative emulators enable training-free optimal particle filtering that scales Bayesian state estimation to high-dimensional nonlinear chaotic systems including atmospheric dynamics.
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-
A unified methodology achieves floating-point consistent results across DDSCAT, ADDA, and IFDDA solvers and enables fair CPU/GPU benchmarking with provided equivalence tables and software.
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A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
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Training-Free Bayesian Filtering with Generative Emulators
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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Robust Matrix-Free Newton-Krylov Solvers via Automatic Differentiation
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-
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Floating-point consistent cross-verification methodology for reproducible and interoperable DDA solvers with fair benchmarking
A unified methodology achieves floating-point consistent results across DDSCAT, ADDA, and IFDDA solvers and enables fair CPU/GPU benchmarking with provided equivalence tables and software.