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most citedCurvature-Adaptive Perturbation and Subspace Descent for Robust Saddle Point Escape in High-Dimensional Optimization

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math.NA2026

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning

Ronald Katende

We develop a non-asymptotic approximation, sampling, and finite-iteration optimization theory for variational physics-informed approximation of uniformly monotone nonlinear multisc…

math.NA2026

No-Harm Physics-Informed Inverse Learning with Residual-Calibrated Uncertainty

Ronald Katende

Physics-informed learning is increasingly used for partial differential equation (PDE)-governed inverse problems, but its reliability remains difficult to certify. This paper devel…