Related papers: Deep UQ: Learning deep neural network surrogate mo…

For computational efficiency, surrogate models have been used to emulate mathematical simulators for physical or biological processes. High-speed simulation is crucial for conducting uncertainty quantification (UQ) when the simulation is…

The high dimensionality of kinetic equations with stochastic parameters poses major computational challenges for uncertainty quantification (UQ). Traditional Monte Carlo (MC) sampling methods, while widely used, suffer from slow convergence…

To reduce training costs, several Deep neural networks (DNNs) that can learn from a small set of HF data and a sufficient number of low-fidelity (LF) data have been proposed. In these established neural networks, a parallel structure is…

A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications…

Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural…

We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet)…

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 introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…

Predicting the behavior of complex systems in engineering often involves significant uncertainty about operating conditions, such as external loads, environmental effects, and manufacturing variability. As a result, uncertainty…

Neural operators (NOs) provide fast, resolution-invariant surrogates for mapping input fields to PDE solution fields, but their predictions can exhibit significant epistemic uncertainty due to finite data, imperfect optimization, and…

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the…

Predictive estimation, which comprises model calibration, model prediction, and validation, is a common objective when performing inverse uncertainty quantification (UQ) in diverse scientific applications. These techniques typically require…

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e.g., forcing terms, boundary conditions,…

This study investigates whether Physically Recurrent Neural Networks (PRNNs), a recent surrogate model for heterogeneous materials, trained on a micromodel with fixed material parameters, can maintain accuracy for varying material…

Deep neural networks (DNNs) have achieved tremendous success in computer vision, natural language processing, and scientific and engineering domains. However, DNNs can make unexpected, incorrect, yet overconfident predictions, leading to…

Uncertainty Quantification (UQ) is a booming discipline for complex computational models based on the analysis of robustness, reliability and credibility. UQ analysis for nonlinear crash models with high dimensional outputs presents…

Recent performance breakthroughs in Artificial intelligence (AI) and Machine learning (ML), especially advances in Deep learning (DL), the availability of powerful, easy-to-use ML libraries (e.g., scikit-learn, TensorFlow, PyTorch.), and…

Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model…

Deep learning-based surrogate models have demonstrated remarkable advantages over classical solvers in terms of speed, often achieving speedups of 10 to 1000 times over traditional partial differential equation (PDE) solvers. However, a…

High-performance scientific simulations, important for comprehension of complex systems, encounter computational challenges especially when exploring extensive parameter spaces. There has been an increasing interest in developing deep…