Nonlinear Model
Nonlinear models are mathematical representations of systems where the output is not directly proportional to the input, capturing complex relationships prevalent in numerous scientific domains. Current research emphasizes developing and improving nonlinear model architectures, including neural networks (e.g., autoencoders, GANs), Volterra series, and Koopman operator methods, often incorporating techniques like adaptive sampling and Bayesian inference to enhance efficiency and robustness. These advancements are crucial for addressing challenges in diverse fields such as structural health monitoring, control systems, and machine learning, enabling more accurate predictions and improved decision-making in complex systems.
Papers
KAN/MultKAN with Physics-Informed Spline fitting (KAN-PISF) for ordinary/partial differential equation discovery of nonlinear dynamic systems
Ashish Pal, Satish Nagarajaiah
KAN-Mamba FusionNet: Redefining Medical Image Segmentation with Non-Linear Modeling
Akansh Agrawal, Akshan Agrawal, Shashwat Gupta, Priyanka Bagade