8 papers
A pullback-corrected scalar auxiliary variable optimizer with momentum and adaptive mobility
Jiahao Zhang, Shiheng Zhang, Guang Lin
Objectives in scientific machine learning are often prescribed as a sum of several terms, such as the residual, boundary, initial, and data losses of a physics-informed neural netw…
FAST-DeepONet: Factor-Augmented Branch Representations for High-Dimensional PDE Inputs in the Small-Sample Regime
Jiyong Kwon, Bongseok Kim, Guang Lin
Deep operator networks can become statistically unstable when partial differential equation inputs are observed at thousands of strongly correlated sensors but only a small number…
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…
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…
Low-Rank Evolutionary Deep Neural Networks via Adaptive Tangent-Space Reduction
Jiahao Zhang, Shiheng Zhang, Guang Lin
Evolutionary deep neural networks (EDNNs) solve time-dependent partial differential equations by evolving the neural-network parameters sequentially in time through a local least-s…
Energy-Dissipative Evolutionary Kolmogorov-Arnold Networks for Complex PDE Systems
Guang Lin, Changhong Mou, Jiahao Zhang
We introduce evolutionary Kolmogorov-Arnold Networks (EvoKAN), a novel framework for solving complex partial differential equations (PDEs). EvoKAN builds on Kolmogorov-Arnold Netwo…
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…
An Element-wise RSAV Algorithm for Unconstrained Optimization Problems
Shiheng Zhang, Jiahao Zhang, Jie Shen +1
We present a novel optimization algorithm, element-wise relaxed scalar auxiliary variable (E-RSAV), that satisfies an unconditional energy dissipation law and exhibits improved ali…