Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

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

Abstract

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.

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

Abstract

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.
Paper Structure (15 sections, 8 figures, 1 table)

This paper contains 15 sections, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Datasets
  4. Perturbed Layered Interface.
  5. Dynamic fracture and failure evolution.
  6. Models
  7. POSEIDON PDE-FM
  8. MORPH PDE-FM
  9. Experiments
  10. Settings
  11. Terminal-state prediction
  12. Data-level Scaling
  13. Conclusions
  14. Datasets
  15. Extended Results

Figures (8)

  • 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 $\rightarrow$ final-frame operator learning.
  • 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.
  • ...and 3 more figures