Related papers: Embedded Nonlocal Operator Regression (ENOR): Quan…

Machine learning inference is increasingly being executed locally on mobile and embedded platforms, due to the clear advantages in latency, privacy and connectivity. In this paper, we present approaches for online resource management in…

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction…

The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…

Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs…

In this work, we introduce a hypergraph representation learning framework called Hypergraph Neural Networks (HNN) that jointly learns hyperedge embeddings along with a set of hyperedge-dependent embeddings for each node in the hypergraph.…

We integrate neural operators with diffusion models to address the spectral limitations of neural operators in surrogate modeling of turbulent flows. While neural operators offer computational efficiency, they exhibit deficiencies in…

We propose a simple, but efficient and accurate machine learning (ML) model for developing high-dimensional potential energy surface. This so-called embedded atom neural network (EANN) approach is inspired by the well-known empirical…

Heterogeneous information networks (HINs) are ubiquitous in real-world applications. In the meantime, network embedding has emerged as a convenient tool to mine and learn from networked data. As a result, it is of interest to develop HIN…

Robust generalization under climate change remains a major challenge for machine learning applications in climate science. Most existing approaches struggle to extrapolate beyond the climate they were trained on, leading to a strong…

This paper integrates deep neural networks (DNNs) into structural economic models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic structure and machine learning are complements in empirical…

Exponential random graph models (ERGMs) are very flexible for modeling network formation but pose difficult estimation challenges due to their intractable normalizing constant. Existing methods, such as MCMC-MLE, rely on sequential…

The study of operator learning involves the utilization of neural networks to approximate operators. Traditionally, the focus has been on single-operator learning (SOL). However, recent advances have rapidly expanded this to include the…

Operator learning seeks to approximate mappings from input functions to output solutions, particularly in the context of partial differential equations (PDEs). While recent advances such as DeepONet and Fourier Neural Operator (FNO) have…

In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear…

We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

The nested error regression model is a useful tool for analyzing clustered (grouped) data, and is especially used in small area estimation. The classical nested error regression model assumes normality of random effects and error terms, and…

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…

A data-driven parametric model order reduction (MOR) method using a deep artificial neural network is proposed. The present network, which is the least-squares hierarchical variational autoencoder (LSH-VAE), is capable of performing…

The increasing penetration of distributed energy resources (DERs) will decrease the rotational inertia of the power system and further degrade the system frequency stability. To address the above issues, this paper leverages the advanced…