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Time dependent reliability analysis and uncertainty quantification of structural system subjected to stochastic forcing function is a challenging endeavour as it necessitates considerable computational time. We investigate the efficacy of…

Energy efficiency remains a critical challenge in deploying physics-informed operator learning models for computational mechanics and scientific computing, particularly in power-constrained settings such as edge and embedded devices, where…

Stochastic Petri Nets (SPNs) are an increasingly popular tool of choice for modeling discrete-event dynamics in areas such as epidemiology and systems biology, yet their parameter estimation remains challenging in general and in particular…

Surrogate neural network-based models have been lately trained and used in a variety of science and engineering applications where the number of evaluations of a target function is limited by execution time. In cell phone camera systems,…

The development of a reliable and robust surrogate model is often constrained by the dimensionality of the problem. For a system with high-dimensional inputs/outputs (I/O), conventional approaches usually use a low-dimensional manifold to…

We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity…

In this work, we introduce a novel neural operator, the Solute Transport Operator Network (STONet), to efficiently model contaminant transport in micro-cracked porous media. STONet's model architecture is specifically designed for this…

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively…

Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…

The existing physical-informed Deep Operator Networks are mostly based on either the well-known mathematical formula of the system or huge amounts of data for different scenarios. However, in some cases, it is difficult to get the exact…

Surrogate models, crucial for approximating complex simulation data across sciences, inherently carry uncertainties that range from simulation noise to model prediction errors. Without rigorous uncertainty quantification, predictions become…

Multiscale problems are widely observed across diverse domains in physics and engineering. Translating these problems into numerical simulations and solving them using numerical schemes, e.g. the finite element method, is costly due to the…

Poroelasticity -- coupled fluid flow and elastic deformation in porous media -- often involves spatially variable permeability, especially in subsurface systems. In such cases, simulations with random permeability fields are widely used for…

Deep neural networks (DNNs) have become integral to a wide range of scientific and practical applications due to their flexibility and strong predictive performance. Despite their accuracy, however, DNNs frequently exhibit poor calibration,…

Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical…

This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…

Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis…

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…

Solving inverse problems is a fundamental component of science, engineering and mathematics. With the advent of deep learning, deep neural networks have significant potential to outperform existing state-of-the-art, model-based methods for…

Modern neural networks have proven to be powerful function approximators, providing state-of-the-art performance in a multitude of applications. They however fall short in their ability to quantify confidence in their predictions - this is…