Related papers: Deep neural network surrogates for non-smooth quan…

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…

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…

Shallow water equations are the foundation of most models for flooding and river hydraulics analysis. These physics-based models are usually expensive and slow to run, thus not suitable for real-time prediction or parameter inversion. An…

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…

Deep neural networks (DNN) are versatile parametric models utilised successfully in a diverse number of tasks and domains. However, they have limitations---particularly from their lack of robustness and over-sensitivity to out of…

Coarse-scale surrogate models in the context of numerical homogenization of linear elliptic problems with arbitrary rough diffusion coefficients rely on the efficient solution of fine-scale sub-problems on local subdomains whose solutions…

In recent work it has been established that deep neural networks are capable of approximating solutions to a large class of parabolic partial differential equations without incurring the curse of dimension. However, all this work has been…

Many imaging problems require computing spatial transformations induced by spatially varying intensity, feature, or density fields. Canonical examples include distortion correction, deformable image registration, atlas-based segmentation,…

Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…

In complex large-scale systems such as climate, important effects are caused by a combination of confounding processes that are not fully observable. The identification of sources from observations of system state is vital for attribution…

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…

Numerical models based on physics represent the state-of-the-art in earth system modeling and comprise our best tools for generating insights and predictions. Despite rapid growth in computational power, the perceived need for higher model…

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…

This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network based on the DeepONet framework. We consider a 2D square domain with an inclusion of arbitrary boundary…

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)…

Numerical simulations on fluid dynamics problems primarily rely on spatially or/and temporally discretization of the governing equation into the finite-dimensional algebraic system solved by computers. Due to complicated nature of the…

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…

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be…

This paper proposes a machine-learning-based solution approach for solving multi-horizon stochastic programs. The approach embeds a deep learning neural network into a multi-horizon stochastic program to approximate the recourse operational…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…