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

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…

Recently, neural surrogate models have emerged as a compelling alternative to traditional simulation workflows. This is accomplished by modeling the underlying function of scientific simulations, removing the need to run expensive…

Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their…

Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in unprecedented advancements in various domains such as…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Thanks to their versatility, ease of deployment and high-performance, surrogate models have become staple tools in the arsenal of uncertainty quantification (UQ). From local interpolants to global spectral decompositions, surrogates are…

The ubiquity of fluids in the physical world explains the need to accurately simulate their dynamics for many scientific and engineering applications. Traditionally, well established but resource intensive CFD solvers provide such…

Inferring topological and geometrical information from data can offer an alternative perspective on machine learning problems. Methods from topological data analysis, e.g., persistent homology, enable us to obtain such information,…

The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail 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 neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing…

Neural networks (NNs) have proven to be a viable alternative to traditional direct numerical algorithms, with the potential to accelerate computational time by several orders of magnitude. In the present paper we study the use of…

We introduce Universal Solution Manifold Network (USM-Net), a novel surrogate model, based on Artificial Neural Networks (ANNs), which applies to differential problems whose solution depends on physical and geometrical parameters. Our…

Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…

Complex systems can be effectively modeled via graphs that encode networked interactions, where relations between entities or nodes are often quantified by signed edge weights, e.g., promotion/inhibition in gene regulatory networks, or…

Driven by the need to accelerate numerical simulations, the use of machine learning techniques is rapidly growing in the field of computational solid mechanics. Their application is especially advantageous in concurrent multiscale finite…

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…

Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for training. The construction of such emulators is by definition a…

Deep neural networks often fail when deployed in real-world contexts due to distribution shift, a critical barrier to building safe and reliable systems. An emerging approach to address this problem relies on \emph{disagreement discrepancy}…

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…