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Physics-Informed Foresight Pruning for Sparse PINN Solvers of Nonlinear PDEs
Ahmad Ishaque Karimi, Uvini Balasuriya Mudiyanselage, Kookjin Lee
Physics-informed neural networks (PINNs) often rely on over-parameterized models to optimize coupled solution and differential-residual objectives, leaving unclear how much capacit…
Extending Fourier Neural Operators for Modeling Parameterized and Coupled PDEs
Cheng Jing, Uvini Balasuriya Mudiyanselage, Abhishek Verma +3
Parameterized and coupled partial differential equations (PDEs) are central to modeling phenomena in science and engineering, yet neural operator methods that address both aspects…
Meta-learning Structure-Preserving Dynamics
Cheng Jing, Uvini Balasuriya Mudiyanselage, Woojin Cho +3
Structure-preserving approaches to dynamics discovery have demonstrated great potential for modeling physical systems due to their use of strong inductive biases, which enforce key…
PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling
Minju Jo, Woojin Cho, Uvini Balasuriya Mudiyanselage +3
Scientific machine learning often involves representing complex solution fields that exhibit high-frequency features such as sharp transitions, fine-scale oscillations, and localiz…
Unveiling the Potential of Superexpressive Networks in Implicit Neural Representations
Uvini Balasuriya Mudiyanselage, Woojin Cho, Minju Jo +2
In this study, we examine the potential of one of the ``superexpressive'' networks in the context of learning neural functions for representing complex signals and performing machi…