Related papers: Deep Adaptive Arbitrary Polynomial Chaos Expansion…

We apply the Tensor Train (TT) decomposition to construct the tensor product Polynomial Chaos Expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with the stochastic Galerkin discretization, and to compute some…

This article presents two novel adaptive-sparse polynomial dimensional decomposition (PDD) methods for solving high-dimensional uncertainty quantification problems in computational science and engineering. The methods entail global…

Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

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…

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…

In numerous applications, surrogate models are used as a replacement for accurate parameter-to-observable mappings when solving large-scale inverse problems governed by partial differential equations (PDEs). The surrogate model may be a…

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)…

Modeling distributions of covariates, or density estimation, is a core challenge in unsupervised learning. However, the majority of work only considers the joint distribution, which has limited utility in practical situations. A more…

Neural PDE surrogates are often deployed in data-limited or partially observed regimes where downstream decisions depend on calibrated uncertainty in addition to low prediction error. Existing approaches obtain uncertainty through ensemble…

Gradient-enhanced Uncertainty Quantification (UQ) has received recent attention, in which the derivatives of a Quantity of Interest (QoI) with respect to the uncertain parameters are utilized to improve the surrogate approximation.…

Parametric surrogate models for partial differential equations (PDEs) are a necessary component for many applications in the computational sciences, and convolutional neural networks (CNNs) have proved as an excellent tool to generate these…

This work suggests an interpolation-based stochastic collocation method for the non-intrusive and adaptive construction of sparse polynomial chaos expansions (PCEs). Unlike pseudo-spectral projection and regression-based stochastic…

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…

Neural networks can be used as surrogates for PDE models. They can be made physics-aware by penalizing underlying equations or the conservation of physical properties in the loss function during training. Current approaches allow to…

Control of nonlinear distributed parameter systems (DPS) under uncertainty is a meaningful task for many industrial processes. However, both intrinsic uncertainty and high dimensionality of DPS require intensive computations, while…

Machine learning classification techniques have been used widely to recognize the feasible design domain and discover hidden patterns in engineering design. An accurate classification model needs a large dataset; however, generating a large…

Surrogate models are used to alleviate the computational burden in engineering tasks, which require the repeated evaluation of computationally demanding models of physical systems, such as the efficient propagation of uncertainties. For…

Domain Adaptation (DA) has received widespread attention from deep learning researchers in recent years because of its potential to improve test accuracy with out-of-distribution labeled data. Most state-of-the-art DA algorithms require an…

Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate may require many high-fidelity evaluations, adaptive…