相关论文: Use of Deep Neural Networks for Uncertain Stress F…

A Deep Learning approach is devised to estimate the elastic energy density $\rho$ at the free surface of an undulated stressed film. About 190000 arbitrary surface profiles h(x) are randomly generated by Perlin noise and paired with the…

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainties by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have…

Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some…

Uncertainty quantification (UQ) in deep learning regression is of wide interest, as it supports critical applications including sequential decision making and risk-sensitive tasks. In heteroskedastic regression, where the uncertainty of the…

Recurrent neural networks (RNNs) are instrumental in modelling sequential and time-series data. Yet, when using RNNs to inform decision-making, predictions by themselves are not sufficient; we also need estimates of predictive uncertainty.…

The effectiveness of univariate forecasting models is often hampered by conditions that cause them stress. A model is considered to be under stress if it shows a negative behaviour, such as higher-than-usual errors or increased uncertainty.…

Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…

The success of deep learning in many real-world tasks has triggered an intense effort to understand the power and limitations of deep learning in the training and generalization of complex tasks, so far with limited progress. In this work,…

In large-eddy simulations, subgrid-scale (SGS) processes are parameterized as a function of filtered grid-scale variables. First-order, algebraic SGS models are based on the eddy-viscosity assumption, which does not always hold for…

The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…

We propose a machine learning approach to address a key challenge in materials science: predicting how fractures propagate in brittle materials under stress, and how these materials ultimately fail. Our methods use deep learning and train…

Deep Bayesian neural network has aroused a great attention in recent years since it combines the benefits of deep neural network and probability theory. Because of this, the network can make predictions and quantify the uncertainty of the…

Dynamic models of mechatronic systems are abundantly used in the context of motion control and design of complex servo applications. In practice, these systems are often plagued by unknown interactions, which make the physics-based…

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

Modeling uncertainty in deep neural networks, despite recent important advances, is still an open problem. Bayesian neural networks are a powerful solution, where the prior over network weights is a design choice, often a normal…

The significance of learning constraints from data is underscored by its potential applications in real-world problem-solving. While constraints are popular for modeling and solving, the approaches to learning constraints from data remain…

Engineering design and scientific analysis rely upon computer simulations of turbulent fluid flows using turbulence models. These turbulence models are empirical and approximate, leading to large uncertainties in their predictions that…

In this paper, we propose a Network-Weighted Functional Regression (NWFR) model, an extension of Spatially Weighted Functional Regression (SWFR) to functional data defined on network-structured settings. To asses predictive uncertainity, we…

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…

The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale…