6 papers
Adaptive multi-resolution Gaussian processes: Scalable exact inference with naturally data-sparse covariance matrices
Yanchuang Cao, Jun Liu, Tengchao Yu +1
Gaussian processes constitute a cornerstone of probabilistic machine learning, yet scaling them to large datasets typically forces a trade-off between computational efficiency and…
pcNN-SN: a physics-enhanced predictor-corrector neural network algorithm coupled with the discrete ordinates method for neutron transport equations
Cong Liu, Junxia Wei, Shuai Wang +1
Super-resolution machine learning methods hold promise for addressing the high computational costs associated with high-dimensional features in traditional transport simulations. T…
Gaussian process surrogate with physical law-corrected prior for multi-coupled PDEs defined on irregular geometry
Pucheng Tang, Hongqiao Wang, Wenzhou Lin +2
Parametric partial differential equations (PDEs) serve as fundamental mathematical tools for modeling complex physical phenomena, yet repeated high-fidelity numerical simulations a…
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…
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…
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…