Geometric Deep Learning

Geometry-Informed Neural Networks

We introduce geometry-informed neural networks (GINNs) to train shape generative models without any data.

We identify particle clustering originating from tensile instabilities as one of the primary pitfalls. Based on these insights, we enhance both training and rollout inference of GNN-based simulators with varying components from standard SPH solvers, including pressure, viscous, and external force components.

Smoothed particle hydrodynamics (SPH) is omnipresent in modern engineering and scientific disciplines. SPH is a class of Lagrangian schemes that discretize fluid dynamics via finite material points that are tracked through the evolving velocity …

Lie Point Symmetries and Physics-Informed Networks

We present how to use Lie Point Symmetries of PDEs to improve physics-informed neural networks. Published at NeurIPS 2023.

Data-Driven Simulations

I am firmly convinced that AI is on the cusp of disrupting simulations at industry-scale. Therefore, I have started a new group at JKU Linz which has strong computer vision, simulation, and engineering components. My vision is shaped by experience both from university and from industry.

Learning Lagrangian Fluid Mechanics with E(3)-Equivariant Graph Neural Networks

We introduce E(3)-equivariant GNNs to two well-studied fluid-flow systems, namely 3D decaying Taylor-Green vortex and 3D reverse Poiseuille flow. Published at GSI 2023.

Learning Lagrangian Fluid Mechanics with E(3)-Equivariant Graph Neural Networks

We introduce E(3)-equivariant GNNs to two well-studied fluid-flow systems, namely 3D decaying Taylor-Green vortex and 3D reverse Poiseuille flow. Published at GSI 2023.

Clifford Group Equivariant Neural Networks

We introduce a novel method to construct E(n)- and O(n)-equivariant neural networks using Clifford algebras. Published at NeurIPS 2023 (Oral).

Geometric Clifford Algebra Networks

We introduce Geometric Clifford Algebra Networks (GCANs) which parameterize combinations of learnable group actions. Published at ICML 2023.

Clifford Neural Layers for PDE Modeling

We introduce neural network layers based on operations on composite objects of scalars, vectors, and higher order objects such as bivectors. Published at ICLR 2023.

Lie Point Symmetry Data Augmentation for Neural PDE Solvers

We present how to use Lie Point Symmetries of PDEs to improve sample complexity of neural PDE solvers. Published at ICML 2022 (Spotlight).