Data-Driven Discovery and Formulation Refines the Quasi-Steady Model of Flapping-Wing Aerodynamics

Insects control unsteady aerodynamic forces on flapping wings to navigate complex environments. While understanding these forces is vital for biology, physics, and engineering, existing evaluation methods face trade-offs: high-fidelity simulations are computationally or experimentally expensive and lack explanatory power, whereas theoretical models based on quasi-steady assumptions offer insights but exhibit low accuracy. To overcome these limitations and thus enhance the accuracy of quasi-steady aerodynamic models, we applied a data-driven approach involving discovery and formulation of previously overlooked critical mechanisms. Through selection from 5,000 candidate kinematic functions, we identified mathematical expressions for three key additional mechanisms -- the effect of advance ratio, effect of spanwise kinematic velocity, and rotational Wagner effect -- which had been qualitatively recognized but were not formulated. Incorporating these mechanisms considerably reduced the prediction errors of the quasi-steady model using the computational fluid dynamics results as the ground truth, both in hawkmoth forward flight (at high Reynolds numbers) and fruit fly maneuvers (at low Reynolds numbers). The data-driven quasi-steady model enables rapid aerodynamic analysis, serving as a practical tool for understanding evolutionary adaptations in insect flight and developing bio-inspired flying robots.

Component-Wise Natural Gradient Descent -- An Efficient Neural Network Optimization

Natural Gradient Descent (NGD) is a second-order neural network training that preconditions the gradient descent with the inverse of the Fisher Information Matrix (FIM). Although NGD provides an efficient preconditioner, it is not practicable due to the expensive computation required when inverting the FIM. This paper proposes a new NGD variant algorithm named Component-Wise Natural Gradient Descent (CW-NGD). CW-NGD is composed of 2 steps. Similar to several existing works, the first step is to consider the FIM matrix as a block-diagonal matrix whose diagonal blocks correspond to the FIM of each layer's weights. In the second step, unique to CW-NGD, we analyze the layer's structure and further decompose the layer's FIM into smaller segments whose derivatives are approximately independent. As a result, individual layers' FIMs are approximated in a block-diagonal form that trivially supports the inversion. The segment decomposition strategy is varied by layer structure. Specifically, we analyze the dense and convolutional layers and design their decomposition strategies appropriately. In an experiment of training a network containing these 2 types of layers, we empirically prove that CW-NGD requires fewer iterations to converge compared to the state-of-the-art first-order and second-order methods.