Related papers: Robust Adaptive Meshing, Mesh Density Functions, a…

Adaptive moving spatial meshes are useful for solving physical models given by time-dependent partial differentialequations. However, special consideration must be given when combining adaptive meshing procedures with ensemble-based data…

Numerical solvers using adaptive meshes can focus computational power on important regions of a model domain capturing important or unresolved physics. The adaptation can be informed by the model state, external information, or made to…

Accurate time series forecasting is critical for a wide range of problems with temporal data. Ensemble modeling is a well-established technique for leveraging multiple predictive models to increase accuracy and robustness, as the…

IIn recent years, there has been a growing interest in applying data assimilation (DA) methods, originally designed for state estimation, to the model selection problem. In this setting, Carrassi et al. (2017) introduced the contextual…

Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…

Data assimilation algorithms integrate prior information from numerical model simulations with observed data. Ensemble-based filters, regarded as state-of-the-art, are widely employed for large-scale estimation tasks in disciplines such as…

Modern data analytics take advantage of ensemble learning and transfer learning approaches to tackle some of the most relevant issues in data analysis, such as lack of labeled data to use to train the analysis models, sparsity of the…

We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domains in $d\geq 1$ dimensions. Our main approach consists of…

Prediction of chaotic systems relies on a floating fusion of sensor data (observations) with a numerical model to decide on a good system trajectory and to compensate nonlinear feedback effects. Ensemble-based data assimilation (DA) is a…

Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…

Physical dynamical systems can be viewed as natural information processors: their systems preserve, transform, and disperse input information. This perspective motivates learning not only from data generated by such systems, but also how to…

Data Assimilation is a cornerstone of atmospheric system modeling, tasked with reconstructing system states by integrating sparse, noisy observations with prior estimation. While traditional approaches like variational and ensemble Kalman…

This study presents constructions of the space-time Conservation Element and Solution Element (CESE) methods to accommodate adaptive unstructured quadrilateral meshes. Subsequently, a novel algorithm is devised to effectively manage the…

Data assimilation (DA) combines partial observations with dynamical models to improve state estimation. Filter-based DA uses only past and present data and is the prerequisite for real-time forecasts. Smoother-based DA exploits both past…

In this paper, we present an Adaptive Ensemble Learning framework that aims to boost the performance of deep neural networks by intelligently fusing features through ensemble learning techniques. The proposed framework integrates ensemble…

In semi-supervised semantic segmentation (SSSS), data augmentation plays a crucial role in the weak-to-strong consistency regularization framework, as it enhances diversity and improves model generalization. Recent strong augmentation…

Transformer models based on the Mixture of Experts (MoE) architecture have made significant progress in long-sequence modeling, but existing models still have shortcomings in computational efficiency and the ability to capture long-range…

While deep neural networks can attain good accuracy on in-distribution test points, many applications require robustness even in the face of unexpected perturbations in the input, changes in the domain, or other sources of distribution…

We present a detailed comparison between two adaptive numerical approaches to solve partial differential equations (PDEs), adaptive multiresolution (MR) and adaptive mesh refinement (AMR). Both discretizations are based on finite volumes in…

Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…