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To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…
In a performance based earthquake engineering (PBEE) framework, nonlinear time-history response analysis (NLTHA) for numerous ground motions are required to assess the seismic risk of buildings or civil engineering structures. However, such…
For civil structures, structural damage due to severe loading events such as earthquakes, or due to long-term environmental degradation, usually occurs in localized areas of a structure. A new sparse Bayesian probabilistic framework for…
Understanding the properties of transient gravitational waves and their sources is of broad interest in physics and astronomy. Bayesian inference is the standard framework for astro-physical measurement in transient gravitational-wave…
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…
Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…
Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning literature, existing correction methods typically operate in…
This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
This paper presents a new adaptive multiscale homogenization scheme for the simulation of damage and fracture in concrete structures. A two-scale homogenization method, coupling meso-scale discrete particle models to macro- scale finite…
In full-scale forced vibration tests, the demand often arises to capture high-spatial-resolution mode shapes with limited number of sensors and shakers. Multi-setup experimental modal analysis (EMA) addresses this challenge by roving…
We address the problem of the response to a seismic wave of an urban site consisting of $N$ non-identical, non-equispaced blocks overlying a soft layer underlain by a hard substratum. The results of a theoretical analysis, appealing to a…
We introduce an enriched immersed finite element method for addressing interface problems characterized by general non-homogeneous jump conditions. Unlike many existing unfitted mesh methods, our approach incorporates a homogenization…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
Exemplar replay has become an effective strategy for mitigating catastrophic forgetting in federated continual learning (FCL) by retaining representative samples from past tasks. Existing studies focus on designing sample-importance…
Geostatistical seismic inversion is commonly used to infer the spatial distribution of the subsurface petro-elastic properties by perturbing the model parameter space through iterative stochastic sequential simulations/co-simulations. The…
FeFETs hold strong potential for advancing memory and logic technologies, but their inherent randomness arising from both operational cycling and fabrication variability poses significant challenges for accurate and reliable modeling.…
We present a fully Bayesian sequential strategy for predicting the mean response surface of heteroscedastic stochastic simulation functions. Leveraging dual Gaussian processes as the surrogate model and a criterion based on empirical…
We combine Bayesian networks (BNs) and structural reliability methods (SRMs) to create a new computational framework, termed enhanced Bayesian network (eBN), for reliability and risk analysis of engineering structures and infrastructure.…
Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational…