3 papers
cs.AI2025
DeePoly: A High-Order Accuracy Scientific Machine Learning Framework for Function Approximation and Solving PDEs
Li Liu, Heng Yong
Recently, machine learning methods have gained significant traction in scientific computing, particularly for solving Partial Differential Equations (PDEs). However, methods based…
cs.LG2025
A general physics-constrained method for the modelling of equation's closure terms with sparse data
Tian Chen, Shengping Liu, Li Liu +1
Accurate modeling of closure terms is a critical challenge in engineering and scientific research, particularly when data is sparse (scarse or incomplete), making widely applicable…
cs.LG2024
Numerical Approximation Capacity of Neural Networks with Bounded Parameters: Do Limits Exist, and How Can They Be Measured?
Li Liu, Tengchao Yu, Heng Yong
The Universal Approximation Theorem posits that neural networks can theoretically possess unlimited approximation capacity with a suitable activation function and a freely chosen o…