Advancements in Physics-Informed Neural Networks and Kolmogorov-Arnold Networks

The field of physics-informed neural networks and Kolmogorov-Arnold networks is rapidly advancing, with a focus on improving the accuracy, efficiency, and interpretability of these models. Recent developments have introduced new architectures, such as Lyapunov-based physics-informed deep neural networks and distance-aware error for Kurkova-Kolmogorov networks, which have shown improved performance in various applications. The incorporation of physical principles and symmetry considerations has also been explored, leading to more robust and reliable models. Furthermore, the combination of Kolmogorov-Arnold networks with other techniques, such as graph convolutional networks and transformers, has opened up new avenues for modeling complex systems. Noteworthy papers include: Lyapunov-Based Physics-Informed Deep Neural Networks with Skew Symmetry Considerations, which introduces a new physics-informed DNN controller for Euler-Lagrange dynamic systems. K-DAREK: Distance Aware Error for Kurkova Kolmogorov Networks, which develops a novel learning algorithm for efficient and interpretable function approximation with uncertainty quantification. Towards Deep Physics-Informed Kolmogorov-Arnold Networks, which proposes a basis-agnostic initialization scheme and Residual-Gated Adaptive KANs to improve stability and accuracy in deep physics-informed KANs.

Sources

Lyapunov-Based Physics-Informed Deep Neural Networks with Skew Symmetry Considerations

K-DAREK: Distance Aware Error for Kurkova Kolmogorov Networks

Towards Deep Physics-Informed Kolmogorov-Arnold Networks

Stiff Circuit System Modeling via Transformer

KAN-GCN: Combining Kolmogorov-Arnold Network with Graph Convolution Network for an Accurate Ice Sheet Emulator

A Practitioner's Guide to Kolmogorov-Arnold Networks

A New Type of Axis-Angle Attitude Control Law for Rotational Systems: Synthesis, Analysis, and Experiments

Command-filter-based trajectory-tracking control of quadrotor subject to internal and external disturbances

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