Related papers: E-LMC: Extended Linear Model of Coregionalization …

We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…

Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…

In the design optimization of metal forming, it is increasingly significant to use surrogate models to analyse the finite element analysis (FEA) simulations. However, traditional surrogate models using scalar based machine learning methods…

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…

Cyclostationary linear inverse models (CS-LIMs), generalized versions of the classical (stationary) LIM, are advanced data-driven techniques for extracting the first-order time-dependent dynamics and random forcing relevant information from…

We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…

While multimodal large language models (MLLMs) have made groundbreaking progress in embodied intelligence, they still face significant challenges in spatial reasoning for complex long-horizon tasks. To address this gap, we propose…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

These days we live in a world with a permanent electromagnetic field. This raises many questions about our health and the deployment of new equipment. The problem is that these fields remain difficult to visualize easily, which only some…

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…

Using machine learning (ML), high performance computing, and a large body of geospatial information, we develop surrogate models to predict soil liquefaction across regional scales. Two sets of models - one global and one specific to New…

Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations…

Large language models (LLMs) have demonstrated broad utility across molecular domains, spanning drug discovery and materials design. Analyzing LLMs' latent representations is crucial for elucidating their underlying mechanisms, improving…

Cooperative inference in Mobile Edge Computing (MEC), achieved by deploying partitioned Deep Neural Network (DNN) models between resource-constrained user equipments (UEs) and edge servers (ESs), has emerged as a promising paradigm.…

Large language models (LLMs) achieve impressive results over various tasks, and ever-expanding public repositories contain an abundance of pre-trained models. Therefore, identifying the best-performing LLM for a given task is a significant…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…

This paper presents a study on an $\ell_1$-penalized covariance regression method. Conventional approaches in high-dimensional covariance estimation often lack the flexibility to integrate external information. As a remedy, we adopt the…

We introduce a comprehensive data-driven framework aimed at enhancing the modeling of physical systems, employing inference techniques and machine learning enhancements. As a demonstrative application, we pursue the modeling of cathodic…

We consider four main goals when fitting spatial linear models: 1) estimating covariance parameters, 2) estimating fixed effects, 3) kriging (making point predictions), and 4) block-kriging (predicting the average value over a region). Each…

Accurate and high-resolution Earth system model (ESM) simulations are essential to assess the ecological and socio-economic impacts of anthropogenic climate change, but are computationally too expensive to be run at sufficiently high…