A mesh-based graph neural network approach for physics simulations with changing domains
Scientific machine learning (SciML), has shown great promise in the context of accelerating classical physics solvers and discovering new governing laws for complex physical systems. However, while the SciML activity in foundational research is growing exponentially, it lags in real-world utility, let alone its reliable, scalable integration into industrial pipelines. To achieve this, current SciML algorithms need to advance in maturity and validation, specifically towards operating in large-scale, three-dimensional, continuously evolving environments marked by noise, sparsity, stochasticity, and other complexities of the natural world problems. 

In this talk, I will highlight some of the current challenges in applying SciML in an industrial context.

I will then focus on a specific approach for the generation of physics surrogates based on Graph Neural Networks (GNNs). Building on DeepMind’s MeshGraphNets, I will introduce two new architectures that address the need for increased interactions in the network’s feature space. Specifically, I will describe Edge Augmented GNNs, where virtual edges are added to the original graph, and Multi-GNNS where a multigrid technique is applied to the graph. Both these architectures perform significantly better than the baseline MeshGraphNets when applied to time-independent, elastic and hyperelastic solid mechanics problems. Furthermore, the proposed architectures generalize well to unseen boundary conditions, materials, and computational domains. The treatment of the latter is facilitated by a novel coordinate transformation that enables rotation and translation invariance.