Effective airfoil geometry optimization requires exploring a diverse range of designs using as few design variables as possible. This study introduces AirDbM, a Design-by-Morphing (DbM) approach specialized for airfoil optimization that systematically reduces design-space dimensionality. AirDbM selects an optimal set of 12 baseline airfoils from the UIUC airfoil database, which contains over 1,600 shapes, by sequentially adding the baseline that most increases the design capacity. With these baselines, AirDbM reconstructs 99 % of the database with a mean absolute error below 0.005, which matches the performance of a previous DbM approach that used more baselines. In multi-objective aerodynamic optimization, AirDbM demonstrates rapid convergence and achieves a Pareto front with a greater hypervolume than that of the previous larger-baseline study, where new Pareto-optimal solutions are discovered with enhanced lift-to-drag ratios at moderate stall tolerances. Furthermore, AirDbM demonstrates outstanding adaptability for reinforcement learning (RL) agents in generating airfoil geometry when compared to conventional airfoil parameterization methods, implying the broader potential of DbM in machine learning-driven design.

Unlike conventional approaches that focus on the spatial domain, FreD employs frequency-based transforms to optimize the frequency representations of each data instance.

Thompson sampling (TS) is an effective method to explore parametric uncertainties and can therefore be used for active learning-based controller design. However, TS relies on finite parametric representations, which limits its applicability to more general spaces, which are more commonly encountered in control system design. To address this issue, this work pro poses a parameterization method for control law learning using reproducing kernel Hilbert spaces and designs a data-driven active learning control approach. Specifically, the proposed method treats the control law as an element in a function space, allowing the design of control laws without imposing restrictions on the system structure or the form of the controller. A TS framework is proposed in this work to explore potential optimal control laws, and the convergence guarantees are further provided for the learning process. Theoretical analysis shows that the proposed method learns the relationship between control laws and closed-loop performance metrics at an exponential rate, and the upper bound of control regret is also derived. Numerical experiments on controlling unknown nonlinear systems validate the effectiveness of the proposed method.

Utilizing a large-scale dataset is essential for training high-performance deep learning models, but it also comes with substantial computation and storage costs. To overcome these challenges, dataset distillation has emerged as a promising solution by compressing the large-scale dataset into a smaller synthetic dataset that retains the essential information needed for training. This paper proposes a novel parameterization framework for dataset distillation, coined Distilling Dataset into Neural Field (DDiF), which leverages the neural field to store the necessary information of the large-scale dataset. Due to the unique nature of the neural field, which takes coordinates as input and output quantity, DDiF effectively preserves the information and easily generates various shapes of data. We theoretically confirm that DDiF exhibits greater expressiveness than some previous literature when the utilized budget for a single synthetic instance is the same. Through extensive experiments, we demonstrate that DDiF achieves superior performance on several benchmark datasets, extending beyond the image domain to include video, audio, and 3D voxel.

Airfoil shape optimization plays a critical role in the design of high-performance aircraft. However, the high-dimensional nature of airfoil representation causes the challenging problem known as the "curse of dimensionality". To overcome this problem, numerous airfoil parameterization methods have been developed, which can be broadly classified as polynomial-based and data-driven approaches. Each of these methods has desirable characteristics such as flexibility, parsimony, feasibility, and intuitiveness, but a single approach that encompasses all of these attributes has yet to be found. For example, polynomial-based methods struggle to balance parsimony and flexibility, while data-driven methods lack in feasibility and intuitiveness. In recent years, generative models, such as generative adversarial networks and variational autoencoders, have shown promising potential in airfoil parameterization. However, these models still face challenges related to intuitiveness due to their black-box nature. To address this issue, we developed a novel airfoil parameterization method using physics-aware variational autoencoder. The proposed method not only explicitly separates the generation of thickness and camber distributions to produce smooth and non-intersecting airfoils, thereby improving feasibility, but it also directly aligns its latent dimensions with geometric features of the airfoil, significantly enhancing intuitiveness. Finally, extensive comparative studies were performed to demonstrate the effectiveness of our approach.

The current dominant paradigm for robotic manipulation involves two separate stages: manipulator design and control. Because the robot's morphology and how it can be controlled are intimately linked, joint optimization of design and control can significantly improve performance. Existing methods for co-optimization are limited and fail to explore a rich space of designs. The primary reason is the trade-off between the complexity of designs that is necessary for contact-rich tasks against the practical constraints of manufacturing, optimization, contact handling, etc. We overcome several of these challenges by building an end-to-end differentiable framework for contact-aware robot design. The two key components of this framework are: a novel deformation-based parameterization that allows for the design of articulated rigid robots with arbitrary, complex geometry, and a differentiable rigid body simulator that can handle contact-rich scenarios and computes analytical gradients for a full spectrum of kinematic and dynamic parameters. On multiple manipulation tasks, our framework outperforms existing methods that either only optimize for control or for design using alternate representations or co-optimize using gradient-free methods.

Deep neural networks are typically highly over-parameterized with pruning techniques able to remove a significant fraction of network parameters with little loss in accuracy. Recently, techniques based on dynamic re-allocation of non-zero parameters have emerged for training sparse networks directly without having to train a large dense model beforehand. We present a parameter re-allocation scheme that addresses the limitations of previous methods such as their high computational cost and the fixed number of parameters they allocate to each layer. We investigate the performance of these dynamic re-allocation methods in deep convolutional networks and show that our method outperforms previous static and dynamic parameterization methods, yielding the best accuracy for a given number of training parameters, and performing on par with networks obtained by iteratively pruning a trained dense model. We further investigated the mechanisms underlying the superior performance of the resulting sparse networks. We found that neither the structure, nor the initialization of the sparse networks discovered by our parameter reallocation scheme are sufficient to explain their superior generalization performance. Rather, it is the continuous exploration of different sparse network structures during training that is critical to effective learning. We show that it is more fruitful to explore these structural degrees of freedom than to add extra parameters to the network.

This paper introduces an interpolation-based method, called the reconstruction approach, for function estimation in nonparametric models. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction approach uses an interpolator to parameterize the unknown function with its values at finite knots, and then estimates these values by minimizing a regularized empirical risk function. Some popular methods including kernel ridge regression and kernel support vector machines can be viewed as its special cases. It is shown that, the reconstruction idea not only provides different angles to look into existing methods, but also produces new effective experimental design and estimation methods for nonparametric models.