Graph Neural Networks

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 …

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.

Message Passing Neural PDE Solvers

In this work, we introduce a message passing neural PDE solver that replaces all heuristically designed components in numerical PDE solvers with backprop-optimized neural function approximators. Published at ICLR 2022 (Spotlight).

Geometric and Physical Quantities Improve E(3) Equivariant Message Passing

We generalise steerable E(3) equivariant graph neural networks such that node and edge updates are able to leverage covariant information. Published at ICLR 2022 (Spotlight).

Boundary Graph Neural Networks for 3D Simulations

We generalize graph neural network based simulations of Lagrangian dynamics to complex boundaries as encountered in daily life engineering setups. Published at AAAI 2023.

Geometric Deep Learning

My passion for Geometric Deep Learning can be unmistakenly traced back to my physics background. I have contributed to the fields of graph neural networks, equivariant architectures, and neural PDE solvers. Furthermore, I have lead efforts to introduce Lie Point Symmetries, and, most recently, Clifford (Geometric) Algebras into the Deep Learning community.