| About this Abstract |
| Meeting |
2025 TMS Annual Meeting & Exhibition
|
| Symposium
|
Algorithms Development in Materials Science and Engineering
|
| Presentation Title |
Strongly Physics Constrained Neural Networks: Applications in Solid Mechanics |
| Author(s) |
Andreas E. Robertson, Vivek Oommen, Remi Dingreville |
| On-Site Speaker (Planned) |
Andreas E. Robertson |
| Abstract Scope |
Neural networks with strongly incorporated inductive biases repeatedly display significantly improved performance and stability in suitable applications compared with their generalized alternatives. For example, convolutional neural networks outpace MLPs on image problems by integrating spatial locality. In the sciences, these inductive biases are physical laws (i.e., partial differential equations). However, directly integrating these laws into network architectures proves difficult. Instead, they are commonly imposed via soft-constraints in the loss function which leads to stiff losses and error localization pathologies. In this talk, we introduce a novel construction which strongly incorporates the governing PDE directly into the architecture. The networks generate strain and stress fields constrained by both compatibility and mechanical equilibrium, respectively. We present several examples to explore this addition. For example, we demonstrate that high resolution variants of these networks can be trained on low resolution data, relying on the networks strong inductive bias to stabilize training. |
| Proceedings Inclusion? |
Planned: |
| Keywords |
Machine Learning, ICME, Computational Materials Science & Engineering |