Authors
Wenrui Hao, Zhipeng Chang, Wenpeng Yin
Published in
Research square. Sep 10, 2026. Epub Sep 10, 2026.
Abstract
Many nonlinear models across physics, chemistry, and biology exhibit multiple solutions for the same parameters, and capturing this entire solution set is essential for understanding pattern-forming systems. Yet existing learned surrogates are fundamentally single-valued: neural operators map each parameter to a single output, and physics-informed neural networks converge to one branch. We develop PatternFormer (PF), a large language model-based framework for learning the multiple solutions of nonlinear partial differential equations. By transforming unordered coexisting solutions into canonical sequences, PF produces structured solution sets in a single autoregressive pass, terminating automatically for finite families and enforcing physical residual constraints for unbounded ones. On nonlinear elliptic problems it recovers all solution branches in one inference step; on Gray--Scott it generates coexisting Turing patterns, including physically valid states absent from the reference data and beyond training. PF can also be sequentially fine-tuned across multistable systems, toward general foundation models for solution landscapes.
PMID:
42818495
Bibliographic data and abstract were imported from PubMed on 01 Oct 2026.
Read full publication at:
Please sign in
to see all details.
Advertisement
Stats
- Recommendations n/a n/a positive of 0 vote(s)
- Views 0
- Comments 0