Related papers: Robust Adaptive Meshing, Mesh Density Functions, a…
Ensemble data assimilation is a problem in determining the most likely phase space trajectory of a model of an observed dynamical sys- tem as it receives inputs from measurements passing information to the model. Using methods developed in…
Deep metric learning aims to learn an embedding function, modeled as deep neural network. This embedding function usually puts semantically similar images close while dissimilar images far from each other in the learned embedding space.…
The cost- and memory-efficient numerical simulation of coupled volume-based multi-physics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goal-oriented space…
Adaptive representations are increasingly indispensable for reducing the in-memory and on-disk footprints of large-scale data. Usual solutions are designed broadly along two themes: reducing data precision, e.g., through compression, or…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…
Temporal networks are ubiquitous and evolve over time by the addition, deletion, and changing of links, nodes, and attributes. Although many relational datasets contain temporal information, the majority of existing techniques in relational…
Ultra-rapid data assimilation (URDA) is a method that rapidly updates preemptive forecasts derived from observations without integrating a dynamical model each time additional observations become available. Due to its computational…
Recent years have seen a shift towards learning-based methods for trajectory prediction, with challenges remaining in addressing uncertainty and capturing multi-modal distributions. This paper introduces Temporal Ensembling with…
The increasing demand for long-context modeling in large language models (LLMs) is bottlenecked by the quadratic complexity of the standard self-attention mechanism. The community has proposed sparse attention to mitigate this issue.…
Medical time-series datasets have unique characteristics that make prediction tasks challenging. Most notably, patient trajectories often contain longitudinal variations in their input-output relationships, generally referred to as temporal…
In modern statistics, interests shift from pursuing the uniformly minimum variance unbiased estimator to reducing mean squared error (MSE) or residual squared error. Shrinkage based estimation and regression methods offer better prediction…
We propose a new method for the construction of layer-adapted meshes for singularly perturbed differential equations (SPDEs), based on mesh partial differential equations (MPDEs) that incorporate \emph{a posteriori} solution information.…
We demonstrate an approach to the numerical solution of nonlinear stochastic differential equations with Markovian switching. Such equations describe the stochastic dynamics of processes where the drift and diffusion coefficients are…
For oceanographic applications, probabilistic forecasts typically have to deal with i) high-dimensional complex models, and ii) very sparse spatial observations. In search-and-rescue operations at sea, for instance, the short-term…
We introduce an $r-$adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the boundary node locations in one dimension, from which we…
This paper examines the application of adaptive mesh refinement (AMR) in the field of numerical weather prediction (NWP). We implement and assess two distinct AMR approaches and evaluate their performance through standard NWP benchmarks. In…
Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive…
Multi-sensor fusion using LiDAR and RGB cameras significantly enhances 3D object detection task. However, conventional LiDAR sensors perform dense, stateless scans, ignoring the strong temporal continuity in real-world scenes. This leads to…
Systems governed by partial differential equations (PDEs) require computationally intensive numerical solvers to predict spatiotemporal field evolution. While machine learning (ML) surrogates offer faster solutions, autoregressive inference…