32 citations · 75 across the 11 of their papers we have counts for
11 papers
Surrogate-assisted global sensitivity analysis of a hybrid-dimensional Stokes--Brinkman--Darcy model
Linheng Ruan, Ilja Kröker, Sergey Oladyshkin +1
Development of new multiscale mathematical models often entails considerable complexity and multiple undetermined parameters, typically arising from closure relations. To enable re…
CODE: A global approach to ODE dynamics learning
Nils Wildt, Daniel M. Tartakovsky, Sergey Oladyshkin +1
Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, prop…
Numerical Investigation of Preferential Flow Paths in Enzymatically Induced Calcite Precipitation supported by Bayesian Model Analysis
Rebecca Kohlhaas, Johannes Hommel, Felix Weinhardt +3
The usability of enzymatically induced calcium carbonate precipitation (EICP) as a method for altering porous-media properties, soil stabilization, or biocementation depends on our…
Inferring Underwater Topography with FINN
Coşku Can Horuz, Matthias Karlbauer, Timothy Praditia +3
Spatiotemporal partial differential equations (PDEs) find extensive application across various scientific and engineering fields. While numerous models have emerged from both physi…
The Deep Arbitrary Polynomial Chaos Neural Network or how Deep Artificial Neural Networks could benefit from Data-Driven Homogeneous Chaos Theory
Sergey Oladyshkin, Timothy Praditia, Ilja Kröker +3
Artificial Intelligence and Machine learning have been widely used in various fields of mathematical computing, physical modeling, computational science, communication science, and…
A fully Bayesian sparse polynomial chaos expansion approach with joint priors on the coefficients and global selection of terms
Paul-Christian Bürkner, Ilja Kröker, Sergey Oladyshkin +1
Polynomial chaos expansion (PCE) is a versatile tool widely used in uncertainty quantification and machine learning, but its successful application depends strongly on the accuracy…
Composing Partial Differential Equations with Physics-Aware Neural Networks
Matthias Karlbauer, Timothy Praditia, Sebastian Otte +3
We introduce a compositional physics-aware FInite volume Neural Network (FINN) for learning spatiotemporal advection-diffusion processes. FINN implements a new way of combining the…
A Surrogate-Assisted Uncertainty-Aware Bayesian Validation Framework and its Application to Coupling Free Flow and Porous-Medium Flow
Farid Mohammadi, Elissa Eggenweiler, Bernd Flemisch +4
Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a…
Finite Volume Neural Network: Modeling Subsurface Contaminant Transport
Timothy Praditia, Matthias Karlbauer, Sebastian Otte +3
Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of…
Surrogate-based Bayesian Comparison of Computationally Expensive Models: Application to Microbially Induced Calcite Precipitation
Stefania Scheurer, Aline Schäfer Rodrigues Silva, Farid Mohammadi +4
Geochemical processes in subsurface reservoirs affected by microbial activity change the material properties of porous media. This is a complex biogeochemical process in subsurface…
Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario
Markus Köppel, Fabian Franzelin, Ilja Kröker +8
A variety of methods is available to quantify uncertainties arising with\-in the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough compariso…