Discretization Error
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions
arXiv:2502.03847v2 Announce Type: replace Abstract: A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order one to five in time. The error estimates are obtained by a consistency and stability analysis, based on an energy...
Intra-Modal Neighbors Never Lie: Rectifying Inter-Modal Noisy Correspondence via Graph-Based Intra-Modal Reasoning
Announce Type: new Abstract: Large-scale web-harvested datasets have fueled the progress of cross-modal retrieval but inevitably suffer from noisy correspondence, which severely degrades model generalization. Existing methods primarily address this by filtering out noise or seeking a substitute label, yet they predominantly remain bound by a "Discrete Selection" paradigm. We argue that relying on a single discrete proxy induces Single-Point Fragility and Discretization Error.
A Koopman Set-Membership Approach for Nonlinear Data-Driven Control with Stability Guarantees
arXiv:2606.01378v1 Announce Type: new Abstract: This paper proposes a data-driven controller design method for unknown nonlinear systems based on a Koopman bilinear realization. Using Koopman operator theory, the nonlinear system can be represented as a bilinear discrete-time system with a residual error term. The residual error is proportionally bounded by the norm of the lifted state and input, while the system matrices of the bilinear model are unknown.
FlowTime: Towards Continuous Generative Watch Time Prediction via Flow-based Personalized Priors
Announce Type: new Abstract: Watch time has emerged as a pivotal metric for optimizing deep user engagement in short-video recommender systems. However, current methods of watch time prediction (WTP) suffer from inherent paradigm-specific limitations. Direct Regression faces mean-collapse due to unimodal Gaussian assumptions, while Ordinal Regression is hampered by quantization errors from rigid discretization.
Improved Guarantees for Langevin Monte Carlo with Average Smoothness
arXiv:2605.31413v1 Announce Type: cross Abstract: We establish improved nonasymptotic bounds for Langevin Monte Carlo in the strongly log-concave setting, when the error is measured by the Wasserstein distance. The main result shows that the discretization error is governed by an average coordinate-wise smoothness constant, rather than by the usual global smoothness constant. The proof is short and probabilistic, and relies on a refined use of the synchronous coupling.
Flow-Based Density Ratio Estimation for Intractable Distributions with Applications in Genomics
arXiv:2602.24201v2 Announce Type: replace Abstract: Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions. While exact-likelihood models such as normalizing flows offer a promising approach to density ratio estimation, naive evaluations are computationally expensive and prone to discretization errors because they...
Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers
Announce Type: replace Abstract: Deep generative models based on neural differential equations have become state-of-the-art for many generation tasks. These models rely on ODE/SDE solvers that integrate from a prior distribution to the data distribution; in many applications it is also highly desirable to integrate in the inverse direction. Standard solvers, however, accumulate discretization errors that prohibit exact inversion, an inaccuracy that is unacceptable in precision-critical...
Distributed optimal control problems governed by poroelasticity equations
arXiv:2605.30839v1 Announce Type: cross Abstract: In this paper, we propose and analyze a novel two-field symmetric formulation with solid displacement and fluid pressure as main unknowns for the Biot's consolidation model in poroelasticity. Firstly, we prove the well-posedness of the new formulation and then show the existence and uniqueness of optimal control where the fluid sources in the model act as a control variable. We prove a priori error estimates for the fully discrete scheme with...
Bregman divergences and error control via convex duality
arXiv:2606.05088v1 Announce Type: new Abstract: Convex duality relations are a useful tool for deriving error estimates for challenging nonlinear and non-smooth variational problems. Applied at the continuous level they can deliver nonlinear analogues of the Prager-Synge a posteriori error identity, while at the discrete level they allow the derivation of minimal regularity a priori estimates. By leveraging elementary properties of Bregman divergences, we obtain three results on the error...
Numerical analysis of the second-order time-dependent saddle point Maxwell system via a parameter-free discontinuous Galerkin method: The first optimal ${\bf L}^{2}$-norm error estimates
Announce Type: new Abstract: We present a novel parameter-free discontinuous Galerkin (dG) finite element method (FEM) for the time-dependent Maxwell system formulated as a saddle point problem. We establish the stability of the proposed semi-discrete problem and derive optimal error estimates in energy and \( {\bf L}^{2} \) norms for the electric field variable, as well as in \( L^{2} \) norm for the potential function. To the best of our knowledge, this work provides the first optimal \(...