Konstantinos E. Tatsis

Alberto Miño Calero, Luis Salamanca, Konstantinos E. Tatsis

Physics-Informed Neural Networks (PINNs) incorporate physics into neural networks by embedding partial differential equations (PDEs) into their loss function. Despite their success in learning the underlying physics, PINN models remain difficult to train and interpret. In this work, a novel modeling approach is proposed, which relies on the use of Domain-aware Fourier Features (DaFFs) for the positional encoding of the input space. These features encapsulate all the domain-specific characteristics, such as the geometry and boundary conditions, and unlike Random Fourier Features (RFFs), eliminate the need for explicit boundary condition loss terms and loss balancing schemes, while simplifying the optimization process and reducing the computational cost associated with training. We further develop an LRP-based explainability framework tailored to PINNs, enabling the extraction of relevance attribution scores for the input space. It is demonstrated that PINN-DaFFs achieve orders-of-magnitude lower errors and allow faster convergence compared to vanilla PINNs and RFFs-based PINNs. Furthermore, LRP analysis reveals that the proposed leads to more physically consistent feature attributions, while PINN-RFFs and vanilla PINNs display more scattered and less physics-relevant patterns. These results demonstrate that DaFFs not only enhance PINNs' accuracy and efficiency but also improve interpretability, laying the ground for more robust and informative physics-informed learning.

Diego Machain Rivera, Selen Ercan Jenny, Ping Hsun Tsai et al.

This work proposes a Graph Neural Network (GNN) modeling approach to predict the resulting surface from a particle based fabrication process. The latter consists of spray-based printing of cementitious plaster on a wall and is facilitated with the use of a robotic arm. The predictions are computed using the robotic arm trajectory features, such as position, velocity and direction, as well as the printing process parameters. The proposed approach, based on a particle representation of the wall domain and the end effector, allows for the adoption of a graph-based solution. The GNN model consists of an encoder-processor-decoder architecture and is trained using data from laboratory tests, while the hyperparameters are optimized by means of a Bayesian scheme. The aim of this model is to act as a simulator of the printing process, and ultimately used for the generation of the robotic arm trajectory and the optimization of the printing parameters, towards the materialization of an autonomous plastering process. The performance of the proposed model is assessed in terms of the prediction error against unseen ground truth data, which shows its generality in varied scenarios, as well as in comparison with the performance of an existing benchmark model. The results demonstrate a significant improvement over the benchmark model, with notably better performance and enhanced error scaling across prediction steps.