Related papers: Probabilistic Deep Learning for Real-Time Large De…

We investigate a deep learning approach to efficiently perform Bayesian inference in partial differential equation (PDE) and integral equation models over potentially high-dimensional parameter spaces. The contributions of this paper are…

Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…

Structured prediction involves learning to predict complex structures rather than simple scalar values. The main challenge arises from the non-Euclidean nature of the output space, which generally requires relaxing the problem formulation.…

A common trend in simulation-driven engineering applications is the ever-increasing size and complexity of the problem, where classical numerical methods typically suffer from significant computational time and huge memory cost. Methods…

Surrogate models for the rapid inference of nonlinear boundary value problems in mechanics are helpful in a broad range of engineering applications. However, effective surrogate modeling of applications involving the contact of deformable…

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…

We are interested in the development of surrogate models for uncertainty quantification and propagation in problems governed by stochastic PDEs using a deep convolutional encoder-decoder network in a similar fashion to approaches considered…

We introduce a unified probabilistic framework for solving sequential decision making problems ranging from Bayesian optimisation to contextual bandits and reinforcement learning. This is accomplished by a probabilistic model-based approach…

Parameter estimation in structural dynamics generally involves inferring the values of physical, geometric, or even customized parameters based on first principles or expert knowledge, which is challenging for complex structural systems. In…

Optimization and uncertainty quantification have been playing an increasingly important role in computational hemodynamics. However, existing methods based on principled modeling and classic numerical techniques have faced significant…

Microfluidics have shown great promise in multiple applications, especially in biomedical diagnostics and separations. While the flow properties of these microfluidic devices can be solved by numerical methods such as computational fluid…

In many cutting-edge applications, high-fidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, deep learning techniques have increasingly been utilized to…

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of…

Deep Gaussian processes (DGPs) are increasingly popular as predictive models in machine learning (ML) for their non-stationary flexibility and ability to cope with abrupt regime changes in training data. Here we explore DGPs as surrogates…

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an…

Direct numerical simulation of hierarchical materials via homogenization-based concurrent multiscale models poses critical challenges for 3D large scale engineering applications, as the computation of highly nonlinear and path-dependent…

Not being able to understand and predict the behavior of deep learning systems makes it hard to decide what architecture and algorithm to use for a given problem. In science and engineering, modeling is a methodology used to understand…

A deep-learning-based surrogate model is developed and applied for predicting dynamic subsurface flow in channelized geological models. The surrogate model is based on deep convolutional and recurrent neural network architectures,…

This paper proposes a technique for training a neural network by minimizing a surrogate loss that approximates the target evaluation metric, which may be non-differentiable. The surrogate is learned via a deep embedding where the Euclidean…

We present a combined numerical and data-driven workflow for efficient prediction of nonlinear, instationary convection-diffusion-reaction dynamics on a two-dimensional phenotypic domain, motivated by macroscopic modeling of cancer cell…