Geometric Deep Learning

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.

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

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.

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.

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.

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

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

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.

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