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

2026-03-04

AI Summary

This work investigates the out-of-distribution transfer capability of pretrained foundation models for partial differential equations (PDEs) in extreme material dynamics involving nonsmooth fields—such as shock waves, interface evolution, and fracture—where such generalization remains unclear. The authors propose a unified end-state prediction paradigm that directly maps initial snapshots to final states without requiring intermediate supervision. Systematic evaluations are conducted on two canonical discontinuity-dominated problems, PLI and FRAC. Leveraging the open-source models POSEIDON and MORPH, experiments combining fine-tuning and from-scratch training strategies demonstrate that, under few-shot conditions, pretrained models significantly outperform models trained from scratch, thereby confirming their high sample efficiency and effective transferability in extreme loading scenarios.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• out-of-distribution transfer
• PDE foundation models
• material dynamics
• extreme loading
• discontinuity-dominated regimes

Innovation

• out-of-distribution transfer
• PDE foundation models
• terminal-state prediction
• extreme-loading material dynamics
• sample efficiency