Related papers: ARC-STAR: Auditable Post-Hoc Correction for PDE Fo…

This paper presents AFD-STA Net, a neural framework integrating adaptive filtering and spatiotemporal dynamics learning for predicting high-dimensional chaotic systems governed by partial differential equations. The architecture combines:…

When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…

In this paper, we demonstrate that the explicit ADER approach as it is used inter alia in [1] can be seen as a special interpretation of the deferred correction (DeC) method as introduced in [2]. By using this fact, we are able to embed…

We propose a stochastic nonconvex optimization algorithm that achieves almost sure $\tilde{\mathcal{O}}(\epsilon^{-1.5})$ iteration complexity for problems with smooth objective functions and gradients only observable with noise. The…

Supporting decision-making has long been a central vision in the field of spatio-temporal intelligence. While prior work has improved the timeliness and accuracy of spatio-temporal forecasting, converting these forecasts into actionable…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

LLM-based root cause analysis (RCA) agents have recently emerged as a promising paradigm for incident diagnosis in microservice AIOps. However, their reliability remains fragile: an error in early evidence collection, hypothesis…

Robustness across heterogeneous optimization regimes remains a central challenge in bound-constrained continuous optimization. In practice, users often prefer optimizers that remain reliable across different dimensionalities, landscape…

We derive a computable a posteriori error estimator for the $\alpha$-harmonic extension problem, which localizes the fractional powers of elliptic operators supplemented with Dirichlet boundary conditions. Our a posteriori error estimator…

In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator…

We propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the…

We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…

Self-Taught Reasoners (STaR), synonymously known as Rejection sampling Fine-Tuning (RFT), is an integral part of the training pipeline of self-improving reasoning Language Models (LMs). The self-improving mechanism often employs random…

In this paper, by employing the asymptotic expansion method, we prove the existence and uniqueness of a smoothing solution for a time-dependent nonlinear singularly perturbed partial differential equation (PDE) with a small-scale parameter.…

We consider nonlinear inverse problems arising in the context of parameter identification for parabolic partial differential equations (PDEs). For stable reconstructions, regularization methods such as the iteratively regularized…

This paper addresses boundary prescribed-time stabilization of a one-dimensional heat equation with spatially and temporally varying coefficients. In contrast to asymptotic or exponential stabilization, prescribed-time stabilization ensures…

Models that are indistinguishable on in-distribution data can behave very differently under distribution shift. We introduce Perturb-and-Correct (P&C), a post-hoc method for constructing epistemically diverse predictors from a single…

Synthetic aperture radar (SAR) images are often blurred by phase perturbations induced by uncompensated sensor motion and /or unknown propagation effects caused by turbulent media. To get refocused images, autofocus proves to be useful…

Minimizing PDE-residual losses is a common strategy to promote physical consistency in neural operators. However, standard formulations often lack variational correctness, meaning that small residuals do not guarantee small solution errors…

In this work, we propose a residual-based a posteriori error estimator for algebraic flux-corrected (AFC) schemes for stationary convection-diffusion equations. A global upper bound is derived for the error in the energy norm for a general…