Related papers: E-LMC: Extended Linear Model of Coregionalization …
The prevalence of spatially referenced multivariate data has impelled researchers to develop a procedure for the joint modeling of multiple spatial processes. This ordinarily involves modeling marginal and cross-process dependence for any…
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…
Deep structured models are widely used for tasks like semantic segmentation, where explicit correlations between variables provide important prior information which generally helps to reduce the data needs of deep nets. However, current…
Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…
In geosciences, the use of classical Euclidean methods is unsuitable for treating and analyzing some types of data, as this may not belong to a vector space. This is the case for correlation matrices, belonging to a subfamily of symmetric…
Model predictive control (MPC) has become the de facto standard action space for local planning and learning-based control in many continuous robotic control tasks, including autonomous driving. MPC solves a long-horizon cost optimization…
Extreme learning machines (ELMs), which preset hidden layer parameters and solve for last layer coefficients via a least squares method, can typically solve partial differential equations faster and more accurately than Physics Informed…
Predictive models that accurately emulate complex scientific processes can achieve exponential speed-ups over numerical simulators or experiments, and at the same time provide surrogates for improving the subsequent analysis. Consequently,…
The performance of land surface models (LSMs) significantly affects the understanding of atmospheric and related processes. Many of the LSMs' soil and vegetation parameters were unknown so that it is crucially important to efficiently…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
Large Language Model (LLM) agents deployed in complex real-world scenarios increasingly operate as spatially distributed entities. However, this physical dispersion constrains agents to limited local perception and finite temporal horizons.…
Semi-structured regression models enable the joint modeling of interpretable structured and complex unstructured feature effects. The structured model part is inspired by statistical models and can be used to infer the input-output…
The recent rapid development of Large Vision-Language Models (LVLMs) has indicated their potential for embodied tasks.However, the critical skill of spatial understanding in embodied environments has not been thoroughly evaluated, leaving…
Time series forecasting remains a challenging task, particularly in the context of complex multiscale temporal patterns. This study presents LLM-Mixer, a framework that improves forecasting accuracy through the combination of multiscale…
A fundamental limitation of various Equivalent Linearization Methods (ELMs) in nonlinear random vibration analysis is that they are approximate by their nature. A quantity of interest estimated from an ELM has no guarantee to be the same as…
High-dimensional longitudinal data is increasingly used in a wide range of scientific studies. To properly account for dependence between longitudinal observations, statistical methods for high-dimensional linear mixed models (LMMs) have…
Extended Dynamic Mode Decomposition (eDMD) is a powerful tool to generate data-driven surrogate models for the prediction and control of nonlinear dynamical systems in the Koopman framework. In eDMD a compression of the lifted system…
Parametric surrogate models of electric machines are widely used for efficient design optimization and operational monitoring. Addressing geometry variations, spline-based computer-aided design representations play a pivotal role. In this…
Metamodeling of complex numerical systems has recently attracted the interest of the mathematical programming community. Despite the progress in high performance computing, simulations remain costly, as a matter of fact, the assessment of…
Large Language Models (LLMs) have shown remarkable ability in solving complex tasks, making them a promising tool for enhancing tabular learning. However, existing LLM-based methods suffer from high resource requirements, suboptimal…