3 papers
cs.LG2025
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation
Rui Zhang, Qi Meng, Rongchan Zhu +5
In scenarios with limited available data, training the function-to-function neural PDE solver in an unsupervised manner is essential. However, the efficiency and accuracy of existi…
cs.LG2024
Provable Adaptivity of Adam under Non-uniform Smoothness
Bohan Wang, Yushun Zhang, Huishuai Zhang +6
Adam is widely adopted in practical applications due to its fast convergence. However, its theoretical analysis is still far from satisfactory. Existing convergence analyses for Ad…
cs.LG2024
LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data
Xinquan Huang, Wenlei Shi, Xiaotian Gao +5
Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of…