6 papers
Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning
Salah A Faroughi, Farinaz Mostajeran, Amirhossein Arzani +1
Symbolic discovery of governing equations is a long-standing goal in scientific machine learning, yet a fundamental trade-off persists between interpretability and scalable learnin…
MINPO: Memory-Informed Neural Pseudo-Operator to Resolve Nonlocal Spatiotemporal Dynamics
Farinaz Mostajeran, Aruzhan Tleubek, Salah A Faroughi
Many physical systems exhibit nonlocal spatiotemporal behaviors described by integro-differential equations (IDEs). Classical methods for solving IDEs require repeatedly evaluating…
Scientific Machine Learning with Kolmogorov-Arnold Networks
Salah A. Faroughi, Farinaz Mostajeran, Amin Hamed Mashhadzadeh +1
The field of scientific machine learning, which originally utilized multilayer perceptrons (MLPs), is increasingly adopting Kolmogorov-Arnold Networks (KANs) for data encoding. Thi…
Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs
Salah A. Faroughi, Farinaz Mostajeran
Physics-informed Kolmogorov-Arnold Networks (PIKANs), and in particular their Chebyshev-based variants (cPIKANs), have recently emerged as promising models for solving partial diff…
Scaled-cPIKANs: Domain Scaling in Chebyshev-based Physics-informed Kolmogorov-Arnold Networks
Farinaz Mostajeran, Salah A Faroughi
Partial Differential Equations (PDEs) are integral to modeling many scientific and engineering problems. Physics-informed Neural Networks (PINNs) have emerged as promising tools fo…
EPi-cKANs: Elasto-Plasticity Informed Kolmogorov-Arnold Networks Using Chebyshev Polynomials
Farinaz Mostajeran, Salah A Faroughi
Multilayer perceptron (MLP) networks are predominantly used to develop data-driven constitutive models for granular materials. They offer a compelling alternative to traditional ph…