Tikhonov
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Related Articles from SNS
A Unifying View of Anchoring via Operator-Side Tikhonov Regularization
Announce Type: cross Abstract: Anchored fixed point and monotone equation methods, including Halpern iteration, extra anchored gradient, and their relatives, add a vanishing pull toward a reference point to obtain last-iterate guarantees. Existing anchored variants often achieve sharp last-iterate guarantees, but from the update-level perspective the placement of the anchor can be algorithm-specific and conceptually opaque. We show that anchoring admits a single operator-side construction:...
The Coercivity Gap in Neural PDE Solvers: Parameter Escape and Functional Convergence
arXiv:2606.04018v1 Announce Type: new Abstract: We study neural approximation of elliptic PDE solutions from a variational perspective. The central point is the distinction between the geometry of neural parameters and the convergence of the corresponding physical states. Even when the original elliptic energy is coercive and strictly convex in the natural energy space, its restriction to a nonlinear neural ansatz may fail to be coercive in parameter space.
Adjoint-based Perfusion Estimation from Dynamic Contrast-Enhanced Ultrasound: Advection-Diffusion and Two-Compartment Models
Announce Type: new Abstract: Tumor perfusion and vascular properties are important determinants of a cancer's response to therapy. In this paper, we discuss the estimation of spatially varying blood flow velocities and perfusion parameters from time-resolved contrast agent concentration data. We compare a standard parabolic advection-diffusion model against a two-compartment model governed by a coupled system of hyperbolic advection-reaction equations, which is physiologically more sound.