Increased drone proliferation in civilian and professional settings has created new threat vectors for airports and national infrastructures. The economic damage for a single major airport from drone incursions is estimated to be millions per day. Du
e to the lack of diverse drone training data, accurate training of deep learning detection algorithms under scarce data is an open challenge. Existing methods largely rely on collecting diverse and comprehensive experimental drone footage data, artificially induced data augmentation, transfer and meta-learning, as well as physics-informed learning. However, these methods cannot guarantee capturing diverse drone designs and fully understanding the deep feature space of drones. Here, we show how understanding the general distribution of the drone data via a Generative Adversarial Network (GAN) and explaining the missing features using Topological Data Analysis (TDA) - can allow us to acquire missing data to achieve rapid and more accurate learning. We demonstrate our results on a drone image dataset, which contains both real drone images as well as simulated images from computer-aided design. When compared to random data collection (usual practice - discriminator accuracy of 94.67% after 200 epochs), our proposed GAN-TDA informed data collection method offers a significant 4% improvement (99.42% after 200 epochs). We believe that this approach of exploiting general data distribution knowledge form neural networks can be applied to a wide range of scarce data open challenges.
In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotr
opic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).
Modern deep learning methods have achieved great success in machine learning and computer vision fields by learning a set of pre-defined datasets. Howerver, these methods perform unsatisfactorily when applied into real-world situations. The reason of
this phenomenon is that learning new tasks leads the trained model quickly forget the knowledge of old tasks, which is referred to as catastrophic forgetting. Current state-of-the-art incremental learning methods tackle catastrophic forgetting problem in traditional classification networks and ignore the problem existing in embedding networks, which are the basic networks for image retrieval, face recognition, zero-shot learning, etc. Different from traditional incremental classification networks, the semantic gap between the embedding spaces of two adjacent tasks is the main challenge for embedding networks under incremental learning setting. Thus, we propose a novel class-incremental method for embedding network, named as zero-shot translation class-incremental method (ZSTCI), which leverages zero-shot translation to estimate and compensate the semantic gap without any exemplars. Then, we try to learn a unified representation for two adjacent tasks in sequential learning process, which captures the relationships of previous classes and current classes precisely. In addition, ZSTCI can easily be combined with existing regularization-based incremental learning methods to further improve performance of embedding networks. We conduct extensive experiments on CUB-200-2011 and CIFAR100, and the experiment results prove the effectiveness of our method. The code of our method has been released.
Achieving transparency in black-box deep learning algorithms is still an open challenge. High dimensional features and decisions given by deep neural networks (NN) require new algorithms and methods to expose its mechanisms. Current state-of-the-art
NN interpretation methods (e.g. Saliency maps, DeepLIFT, LIME, etc.) focus more on the direct relationship between NN outputs and inputs rather than the NN structure and operations itself. In current deep NN operations, there is uncertainty over the exact role played by neurons with fixed activation functions. In this paper, we achieve partially explainable learning model by symbolically explaining the role of activation functions (AF) under a scalable topology. This is carried out by modeling the AFs as adaptive Gaussian Processes (GP), which sit within a novel scalable NN topology, based on the Kolmogorov-Arnold Superposition Theorem (KST). In this scalable NN architecture, the AFs are generated by GP interpolation between control points and can thus be tuned during the back-propagation procedure via gradient descent. The control points act as the core enabler to both local and global adjustability of AF, where the GP interpolation constrains the intrinsic autocorrelation to avoid over-fitting. We show that there exists a trade-off between the NNs expressive power and interpretation complexity, under linear KST topology scaling. To demonstrate this, we perform a case study on a binary classification dataset of banknote authentication. By quantitatively and qualitatively investigating the mapping relationship between inputs and output, our explainable model can provide interpretation over each of the one-dimensional attributes. These early results suggest that our model has the potential to act as the final interpretation layer for deep neural networks.
This paper is concerned with the time-dependent acoustic-elastic interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above an unbounded rough surface. The well-posedness and stability of the problem are f
irst established by using the Laplace transform and the energy method. A perfectly matched layer (PML) is then introduced to truncate the interaction problem above a finite layer containing the elastic body, leading to a PML problem in a finite strip domain. We further establish the existence, uniqueness and stability estimate of solutions to the PML problem. Finally, we prove the exponential convergence of the PML problem in terms of the thickness and parameter of the PML layer, based on establishing an error estimate between the DtN operators of the original problem and the PML problem.
In this paper, a perfectly matched layer (PML) method is proposed to solve the time-domain electromagnetic scattering problems in 3D effectively. The PML problem is defined in a spherical layer and derived by using the Laplace transform and real coor
dinate stretching in the frequency domain. The well-posedness and the stability estimate of the PML problem are first proved based on the Laplace transform and the energy method. The exponential convergence of the PML method is then established in terms of the thickness of the layer and the PML absorbing parameter. As far as we know, this is the first convergence result for the time-domain PML method for the three-dimensional Maxwell equations. Our proof is mainly based on the stability estimates of solutions of the truncated PML problem and the exponential decay estimates of the stretched dyadic Greens function for the Maxwell equations in the free space.
This paper is concerned with the mathematical analysis of time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded scatterin
g problem into an equivalent initial-boundary value problem defined in a bounded domain by proposing a transparent boundary condition (TBC) on a hemisphere. Analyzing the reduced problem with Lax-Milgram lemma and abstract inversion theorem of Laplace transform, we prove the well-posedness and stability for the reduced problem. Moreover, an a priori estimate is established directly in the time domain for the acoustic wave and elastic displacement with using the energy method.
