Related papers: Physics-Informed CoKriging: A Gaussian-Process-Reg…
This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a…
Gaussian process regression (GPR) is a useful technique to predict composition--property relationships in glasses as the method inherently provides the standard deviation of the predictions. However, the technique remains restricted to…
Coarse graining (CG) is an important task for efficient modeling and simulation of complex multi-scale systems, such as the conformational dynamics of biomolecules. This work presents a projection-based coarse-graining formalism for general…
Physics-informed neural networks have shown promise in solving partial differential equations (PDEs) by integrating physical constraints into neural network training, but their performance is sensitive to the sampling of points. Based on…
Uncertainty quantification (UQ) over graphs arises in a number of safety-critical applications in network science. The Gaussian process (GP), as a classical Bayesian framework for UQ, has been developed to handle graph-structured data by…
Gaussian processes offer an attractive framework for predictive modeling from longitudinal data, i.e., irregularly sampled, sparse observations from a set of individuals over time. However, such methods have two key shortcomings: (i) They…
Accurately estimating friction coefficients between arbitrary material pairs is critical for robotics, digital fabrication, and physics-based simulation, but exhaustive pairwise testing scales quadratically with the number of materials. We…
In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and…
Coarse-graining is a molecular modeling technique in which an atomistic system is represented in a simplified fashion that retains the most significant system features that contribute to a target output, while removing the degrees of…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
Traffic state estimation (TSE) becomes challenging when probe-vehicle penetration is low and observations are spatially sparse. Pure data-driven methods lack physical explanations and have poor generalization when observed data is sparse.…
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…
We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…
Many physical systems are described by partial differential equations (PDEs), and solving these equations and estimating their coefficients or boundary conditions (BCs) from observational data play a crucial role in understanding the…
This paper is motivated by a computer experiment conducted for optimizing residual stresses in the machining of metals. Although kriging is widely used in the analysis of computer experiments, it cannot be easily applied to model the…
When applying machine learning methods to learn viscoelastic constitutive relations, the polymer history dependence in viscoelastic fluids and the generalization ability of machine learning models are challenging. In this paper, guided by…
Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both…
A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states along the Hugoniot curve using data from a small number of shockwave simulations. The proposed Gaussian process employs a…
We propose a new scalable framework for spatio-temporal data fusion with multi-fidelity Gaussian processes (MFGPs) that enables fully likelihood-based inference for both stationary and non-stationary fidelity integration. The framework is…
We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…