4 papers
Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction
Jiaquan Zhang, Shuxu Chen, Haifan Meng +6
Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs). However, long-horizon autoregressive prediction remains chall…
HERO: History-Enriched Rollout Training for Long-Horizon Autoregressive Neural Operators
Jiaquan Zhang, Shuxu Chen, Haifan Meng +6
Neural operators provide fast surrogates for time-dependent partial differential equations (PDEs) by applying a learned evolution operator recursively to its own predictions, but t…
Autoregression-Free Neural Operators for Time-Dependent PDEs
Jiaquan Zhang, Caiyan Qin, Haoyu Bian +7
Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent…
Understanding Chain-of-Thought in Large Language Models via Topological Data Analysis
Chenghao Li, Chaoning Zhang, Yi Lu +10
With the development of large language models (LLMs), particularly with the introduction of the long reasoning chain technique, the reasoning ability of LLMs in complex problem-sol…