Neural Stress Fields for Reduced-order Elastoplasticity and Fracture
Bibliographic record
Abstract
We propose a hybrid neural network and physics framework for reduced-order modeling of elastoplasticity and fracture. State-of-the-art scientific computing models like the Material Point Method (MPM) faithfully simulate large-deformation elastoplasticity and fracture mechanics. However, their long runtime and large memory consumption render them unsuitable for applications constrained by computation time and memory usage, e.g., virtual reality. To overcome these barriers, we propose a reduced-order framework. Our key innovation is training a low-dimensional manifold for the Kirchhoff stress field via an implicit neural representation. This low-dimensional neural stress field (NSF) enables efficient evaluations of stress values and, correspondingly, internal forces at arbitrary spatial locations. In addition, we also train neural deformation and affine fields to build low-dimensional manifolds for the deformation and affine momentum fields. These neural stress, deformation, and affine fields share the same low-dimensional latent space, which uniquely embeds the high-dimensional simulation state. After training, we run new simulations by evolving in this single latent space, which drastically reduces the computation time and memory consumption. Our general continuum-mechanics-based reduced-order framework is applicable to any phenomena governed by the elastodynamics equation. To showcase the versatility of our framework, we simulate a wide range of material behaviors, including elastica, sand, metal, non-Newtonian fluids, fracture, contact, and collision. We demonstrate dimension reduction by up to 100,000 × and time savings by up to 10 ×.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".