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KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
Juan Diego Toscano, Li-Lian Wang, George Em Karniadakis
Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a ne…
A Digital Twin for Diesel Engines: Operator-infused Physics-Informed Neural Networks with Transfer Learning for Engine Health Monitoring
Kamaljyoti Nath, Varun Kumar, Daniel J. Smith +1
Improving diesel engine efficiency, reducing emissions, and enabling robust health monitoring have been critical research topics in engine modelling. While recent advancements in t…
HJ-sampler: A Bayesian sampler for inverse problems of a stochastic process by leveraging Hamilton-Jacobi PDEs and score-based generative models
Tingwei Meng, Zongren Zou, Jérôme Darbon +1
The interplay between stochastic processes and optimal control has been extensively explored in the literature. With the recent surge in the use of diffusion models, stochastic pro…
Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations
Jin Song, Ming Zhong, George Em Karniadakis +1
We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterati…
State-space models are accurate and efficient neural operators for dynamical systems
Zheyuan Hu, Nazanin Ahmadi Daryakenari, Qianli Shen +2
Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable soluti…
Physics-Informed Neural Networks and Extensions
Maziar Raissi, Paris Perdikaris, Nazanin Ahmadi +1
In this paper, we review the new method Physics-Informed Neural Networks (PINNs) that has become the main pillar in scientific machine learning, we present recent practical extensi…