Reducing the Sensitivity of Neural Physics Simulators to Mesh Topology via Pretraining

TL;DR

The paper addresses the sensitivity of neural physics simulators to mesh topology, a barrier to using mesh augmentations for training. It evaluates pretraining strategies on large mesh datasets and shows that autoencoder-based pretraining of graph-based face embeddings reduces topology-induced performance degradation, using radar simulation and the newly introduced Basic Shapes dataset for controlled topology variation. Key results show that graph-based and tokenization embeddings with autoencoder pretraining are more robust to topology changes than direct embeddings or scratch-training, though there remains a gap to ideal topology-augmented data. The work provides a practical path toward more topology-robust neural simulators and suggests future research directions, including larger-scale pretraining, topology-aware losses, and equivariant mesh representations, with potential applicability across radar, optics, and fluid simulations.

Abstract

Meshes are used to represent complex objects in high fidelity physics simulators across a variety of domains, such as radar sensing and aerodynamics. There is growing interest in using neural networks to accelerate physics simulations, and also a growing body of work on applying neural networks directly to irregular mesh data. Since multiple mesh topologies can represent the same object, mesh augmentation is typically required to handle topological variation when training neural networks. Due to the sensitivity of physics simulators to small changes in mesh shape, it is challenging to use these augmentations when training neural network-based physics simulators. In this work, we show that variations in mesh topology can significantly reduce the performance of neural network simulators. We evaluate whether pretraining can be used to address this issue, and find that employing an established autoencoder pretraining technique with graph embedding models reduces the sensitivity of neural network simulators to variations in mesh topology. Finally, we highlight future research directions that may further reduce neural simulator sensitivity to mesh topology.

Figures (3)

• Figure 1: Example radar responses generated by a first principles radar simulator. balanis2012advanced Fig. \ref{['aug:fig:a']} and Fig. \ref{['aug:fig:c']} show the mesh and radar response. Fig. \ref{['aug:fig:b']} shows the mesh after scaling and vertex jitter, which are both standard augmentations. Both augmentations significantly alter the radar response (Fig.\ref{['aug:fig:d']}).
• Figure 2: Example object from the Basic Shapes dataset with randomly colored faces. Fig. \ref{['basic:fig:a']} shows the simple mesh representation and Fig. \ref{['basic:fig:b']} - Fig. \ref{['basic:fig:c']} show examples of shape preserving augmentations with more complex topologies.
• Figure 3: Example predictions from graph embedding model pretrained via the auto-encoding objective. The model accurately predicts the targets response for simple meshes, and predicts a similar response for complex mesh variants despite significantly increased complexity.