The Deep Arbitrary Polynomial Chaos Neural Network or how Deep Artificial Neural Networks could benefit from Data-Driven Homogeneous Chaos Theory

no code implementations • 26 Jun 2023 • Sergey Oladyshkin, Timothy Praditia, Ilja Kröker, Farid Mohammadi, Wolfgang Nowak, Sebastian Otte

However, for a majority of deep learning approaches based on DANNs, the kernel structure of neural signal processing remains the same, where the node response is encoded as a linear superposition of neural activity, while the non-linearity is triggered by the activation functions.

PDEBENCH: An Extensive Benchmark for Scientific Machine Learning

2 code implementations • 13 Oct 2022 • Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Dan MacKinlay, Francesco Alesiani, Dirk Pflüger, Mathias Niepert

With those metrics we identify tasks which are challenging for recent ML methods and propose these tasks as future challenges for the community.

Composing Partial Differential Equations with Physics-Aware Neural Networks

1 code implementation • 23 Nov 2021 • Matthias Karlbauer, Timothy Praditia, Sebastian Otte, Sergey Oladyshkin, Wolfgang Nowak, Martin V. Butz

We introduce a compositional physics-aware FInite volume Neural Network (FINN) for learning spatiotemporal advection-diffusion processes.

Out-of-Distribution Generalization

Finite Volume Neural Network: Modeling Subsurface Contaminant Transport

1 code implementation • 13 Apr 2021 • Timothy Praditia, Matthias Karlbauer, Sebastian Otte, Sergey Oladyshkin, Martin V. Butz, Wolfgang Nowak

To tackle this issue, we introduce a new approach called the Finite Volume Neural Network (FINN).