Neural rendering enables dynamic tomography

Interrupted X-ray computed tomography (X-CT) has been the common way to observe the deformation of materials during an experiment. While this approach is effective for quasi-static experiments, it has never been possible to reconstruct a full 3d tomography during a dynamic experiment which cannot be interrupted. In this work, we propose that neural rendering tools can be used to drive the paradigm shift to enable 3d reconstruction during dynamic events. First, we derive theoretical results to support the selection of projections angles. Via a combination of synthetic and experimental data, we demonstrate that neural radiance fields can reconstruct data modalities of interest more efficiently than conventional reconstruction methods. Finally, we develop a spatio-temporal model with spline-based deformation field and demonstrate that such model can reconstruct the spatio-temporal deformation of lattice samples in real-world experiments.

Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work we present a higher-order GNN model trained to predict the fourth-order stiffness tensor of periodic strut-based lattices. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate the benefits of the encoded equivariance and energy conservation in terms of predictive performance and reduced training requirements.