Out-of-distribution transfer of PDE foundation models to material dynamics under extreme loading
Authors: Mahindra Rautela, Alexander Most, Siddharth Mansingh, Aleksandra Pachalieva, Bradley Love, Daniel O Malley, Alexander Scheinker, Kyle Hickmann, Diane Oyen, Nathan Debardeleben, Earl Lawrence, Ayan Biswas
Organizations: AOT-IC Group, Los Alamos National Laboratory, Los Alamos, New Mexico, US, 87545 · CAI Division, Los Alamos National Laboratory, Los Alamos, New Mexico, US, 87545 · EES Divison, Los Alamos National Laboratory, Los Alamos, New Mexico, US, 87545 · XCP Division, Los Alamos National Laboratory, Los Alamos, New Mexico, US, 87545 · HPC Division, Los Alamos National Laboratory, Los Alamos, New Mexico, US, 87545
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.
Figures & tables
Dataset/Models
MORPH
POSEIDON
PLI
0.05445
0.13892
FRAC
0.04103
0.03704
Table 1: MSE on the test set
Figure 1: Terminal-state prediction on PLI comparing MORPH-Ti (a) and POSEIDON-T (b). Columns show the input, target terminal state, prediction, and squared error (T−P)2 .
Figure 2: Terminal-state prediction on FRAC comparing MORPH-Ti (a) and POSEIDON-T (b). For each test example, columns show the input (initial state), target terminal state, model prediction, and squared error map (T−P)2 .
Figure 3: Test MSE as a function of training-set size for PLI (a) and FRAC (b), comparing fine-tuning from pretrained weights versus training from scratch for MORPH and POSEIDON. Curves quantify sample efficiency for first-frame → final-frame operator learning.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 4: Representative PLI spatiotemporal evolution over uniformly spaced time-steps. Rows visualize selected per-material density channels.
Figure 5: Representative FRAC trajectories (tungsten subset) showing the evolution of fracture/damage patterns from the initial condition to the terminal state. Each row corresponds to a distinct simulation, with frames annotated by characteristic time.
Figure 6: Additional FRAC terminal-state prediction results comparing MORPH-Ti (a) and POSEIDON-T (b) using the same visualization as Fig. 2 (input, target, prediction, and squared error (T−P)2 ).
Figure 7: Additional PLI terminal-state prediction results comparing MORPH-Ti (a) and POSEIDON-T (b). Columns show input, target, prediction, and squared error (T−P)2 .
Figure 8: Further PLI terminal-state prediction results comparing MORPH-Ti (a) and POSEIDON-T (b). Columns show input, target, prediction, and squared error (T−P)2 .
Department Modeling and Artificial Intelligence Fraunhofer Institute for Integrated Systems and Device Technology IISB Schottkystrasse 10, 91058 Erlangen, Germany
TUM School of Computation, Information and Technology, Technical University of Munich, Garching, Germany · MCML, Munich Center for Machine Learning, Munich, Germany