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cs.LG2026
Agentic Symbolic Search: Characterizing PDEs Beyond Hand-crafted Expressions, Meshes, and Neural Networks
Zongmin Yu, Liu Yang
Mathematicians understand a PDE solution through mathematical structures rather than tables of computed values. Historically, this has been the product of mathematical analysis, ca…
cs.LG2024
PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws
Liu Yang, Stanley J. Osher
Can we build a single large model for a wide range of PDE-related scientific learning tasks? Can this model generalize to new PDEs, even of new forms, without any fine-tuning? In-c…
cs.LG2023
Fine-Tune Language Models as Multi-Modal Differential Equation Solvers
Liu Yang, Siting Liu, Stanley J. Osher
In the growing domain of scientific machine learning, in-context operator learning has shown notable potential in building foundation models, as in this framework the model is trai…