Out-of-distribution transfer of PDE foundation models to material dynamics under extreme loading

Most PDE foundation models are pretrained and fine-tuned on fluid-centric benchmarks. Their utility under extreme-loading material dynamics remains unclear. We benchmark out-of-distribution transfer on two discontinuity-dominated regimes in which shocks, evolving interfaces, and fracture produce highly non-smooth fields: shock-driven multi-material interface dynamics (perturbed layered interface or PLI) and dynamic fracture/failure evolution (FRAC). We formulate the downstream task as terminal-state prediction, i.e., learning a long-horizon map that predicts the final state directly from the first snapshot without intermediate supervision. Using a unified training and evaluation protocol, we evaluate two open-source pretrained PDE foundation models, POSEIDON and MORPH, and compare fine-tuning from pretrained weights against training from scratch across training-set sizes to quantify sample efficiency under distribution shift.

How Robust Are Energy-Based Models Trained With Equilibrium Propagation?

Deep neural networks (DNNs) are easily fooled by adversarial perturbations that are imperceptible to humans. Adversarial training, a process where adversarial examples are added to the training set, is the current state-of-the-art defense against adversarial attacks, but it lowers the model's accuracy on clean inputs, is computationally expensive, and offers less robustness to natural noise. In contrast, energy-based models (EBMs), which were designed for efficient implementation in neuromorphic hardware and physical systems, incorporate feedback connections from each layer to the previous layer, yielding a recurrent, deep-attractor architecture which we hypothesize should make them naturally robust. Our work is the first to explore the robustness of EBMs to both natural corruptions and adversarial attacks, which we do using the CIFAR-10 and CIFAR-100 datasets. We demonstrate that EBMs are more robust than transformers and display comparable robustness to adversarially-trained DNNs on gradient-based (white-box) attacks, query-based (black-box) attacks, and natural perturbations without sacrificing clean accuracy, and without the need for adversarial training or additional training techniques.