7 papers
Invariant Guided PINN for Fluid Flow Computation
Zheng Lu, Jiwei Jia, Bora Aniruddha +2
The paper introduces an invariant‑guided physics‑informed neural network (IG‑PINN) that trains on spatial subdomains or temporal slabs and then applies a global correction to impro…
ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems
Zheng Lu, Jiwei Jia, Young Ju Lee
Inverse problems governed by partial differential equations are difficult when observations are sparse and the unknown coefficient field contains both large- and small-scale struct…
Beyond binary scission: a generalized three-species cascade breakage model for wormlike micellar solutions
Rongxin Lu, Jiwei Jia, Young Ju Lee
Wormlike micellar fluids exhibit complex rheological behavior driven by the continuous breakage and recombination of self-assembled micellar networks. Existing two-species models p…
fOGA: An Orthogonal Greedy Algorithm for Fractional Laplacian Problems
Ruitong Shan, Young Ju Lee, Jiwei Jia
In this paper, we propose a numerical method for fractional Laplace equations that combines finite difference discretization with shallow neural network approximation. The fraction…
Boundary neuron method for solving partial differential equations
Ye Lin, Wentao Liu, Young Ju Lee +1
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow net…
R-PINN: Recovery-type a-posteriori estimator enhanced adaptive PINN
Rongxin Lu, Jiwei Jia, Young Ju Lee +2
In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread appli…