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Lagrangian data assimilation exploits the trajectories of moving tracers as observations to recover the underlying flow field. One major challenge in Lagrangian data assimilation is the intrinsic nonlinearity that impedes using exact…

Graph condensation reduces the size of large graphs while preserving performance, addressing the scalability challenges of Graph Neural Networks caused by computational inefficiencies on large datasets. Existing methods often rely on…

This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…

A pre-trained generator has been frequently adopted in compressed sensing (CS) due to its ability to effectively estimate signals with the prior of NNs. In order to further refine the NN-based prior, we propose a framework that allows the…

We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes…

Surrogate models are often used to replace costly-to-evaluate complex coastal codes to achieve substantial computational savings. In many of those models, the hydrometeorological forcing conditions (inputs) or flood events (outputs) are…

For general non-Gaussian distributions, the covariance and precision matrices do not encode the independence structure of the variables, as they do for the multivariate Gaussian. This paper builds on previous work to show that for a class…

Graph network-based simulators (GNS) have demonstrated strong potential for learning particle-based physics (such as fluids, deformable solids, and granular flows) while generalizing to unseen geometries due to their inherent inductive…

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…

This paper addresses the problem of scalable optimization for L1-regularized conditional Gaussian graphical models. Conditional Gaussian graphical models generalize the well-known Gaussian graphical models to conditional distributions to…

We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The…

The mechanical properties of periodic microstructures are pivotal in various engineering applications. Homogenization theory is a powerful tool for predicting these properties by averaging the behavior of complex microstructures over a…

We propose GNN-Surrogate, a graph neural network-based surrogate model to explore the parameter space of ocean climate simulations. Parameter space exploration is important for domain scientists to understand the influence of input…

Numerical simulation is powerful to study nonlinear solid mechanics problems. However, mesh-based or particle-based numerical methods suffer from the common shortcoming of being time-consuming, particularly for complex problems with…

The use of the Preconditioned Conjugate Gradient (PCG) method for computing the Generalized Least Squares (GLS) estimator of the General Linear Model (GLM) is considered. The GLS estimator is expressed in terms of the solution of an…

We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…

In a modern observational study based on healthcare databases, the number of observations and of predictors typically range in the order of $10^5$ ~ $10^6$ and of $10^4$ ~ $10^5$. Despite the large sample size, data rarely provide…

Engineering disciplines often rely on extensive simulations to ensure that structures are designed to withstand harsh conditions while avoiding over-engineering for unlikely scenarios. Assessments such as Serviceability Limit State (SLS)…

Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these…