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A Hyperbolic Neural Closure for M1 Radiation Transfer
Bongseok Kim, Jiahao Zhang, Johannes Krotz +3
In radiation transfer simulations, an M1 method achieves substantial computational savings by replacing the full angular transport equation with a low-order moment system. Because…
Weak-Form Evolutionary Kolmogorov-Arnold Networks for Solving Partial Differential Equations
Bongseok Kim, Jiahao Zhang, Guang Lin
Partial differential equations (PDEs) form a central component of scientific computing. Among recent advances in deep learning, evolutionary neural networks have been developed to…
Muon with Spectral Guidance: Efficient Optimization for Scientific Machine Learning
Binghang Lu, Jiahao Zhang, Guang Lin
Physics-informed neural networks and neural operators often suffer from severe optimization difficulties caused by ill-conditioned gradients, multi-scale spectral behavior, and sti…
BEKAN: Boundary condition-guaranteed evolutionary Kolmogorov-Arnold networks with radial basis functions for solving PDE problems
Bongseok Kim, Jiahao Zhang, Guang Lin
Deep learning has gained attention for solving PDEs, but the black-box nature of neural networks hinders precise enforcement of boundary conditions. To address this, we propose a b…
An Energy-Based Self-Adaptive Learning Rate for Stochastic Gradient Descent: Enhancing Unconstrained Optimization with VAV method
Jiahao Zhang, Christian Moya, Guang Lin
Optimizing the learning rate remains a critical challenge in machine learning, essential for achieving model stability and efficient convergence. The Vector Auxiliary Variable (VAV…