A Mechanical Exoskeleton

The purpose of this thesis is to design a 3-D exoskeleton model based on the mechanism of a kind of two degree-of-freedom suspension system. There are two main systems in the exoskeleton, including weight support system and walking assistive system. The weight support system consists a series of linkages, pulleys and springs, which is able to compensate wearer’s weight, make wearer feel much more easier when keeps a crouching posture. The walking assistive system consists clutch system and cable release system, which is able to help exoskeleton walk when led by wearer. In our exoskeleton design, excluding hydraulic and electric systems, we adopt pure mechanical systems, thus the whole system will be simple, light, clean, cheap and easy to build, the power provided by the exoskeleton will not be large. We also introduce the technique of exoskeleton shape optimization, which deserves more research in the future

Learning Dynamics from Data Using Optimal Transport Techniques and Applications

Optimal Transport has been studied widely in recent years, the concept of Wasserstein distance brings a lot of applications in computational mathematics, machine learning, engineering, even finance areas. Meanwhile, people are gradually realizing that as the amount of data as well as the needs of utilizing data increase vastly, data-driven models have great potentials in real-world applications. In this thesis, we apply the theories of OT and design data-driven algorithms to form and compute various OT problems. We also build a framework to learn inverse OT problem. Furthermore, we develop OT and deep learning based models to solve stochastic differential equations, optimal control, mean field games related problems, all in data-driven settings. In Chapter 2, we provide necessary mathematical concepts and results that form the basis of this thesis. It contains brief surveys of optimal transport, stochastic differential equations, Fokker-Planck equations, deep learning, optimal controls and mean field games. Chapter 3 to Chapter 5 present several scalable algorithms to handle optimal transport problems within different settings. Specifically, Chapter 3 shows a new saddle scheme and learning strategy for computing the Wasserstein geodesic, as well as the Wasserstein distance and OT map between two probability distributions in high dimensions. We parametrize the map and Lagrange multipliers as neural networks. We demonstrate the performance of our algorithms through a series of experiments with both synthetic and realistic data. Chapter 4 presents a scalable algorithm for computing the Monge map between two probability distributions since computing the Monge maps remains challenging, in spite of the rapid developments of the numerical methods for optimal transport problems. Similarly, we formulate the problem as a mini-max problem and solve it via deep learning. The performance of our algorithms is demonstrated through a series of experiments with both synthetic and realistic data. In Chapter 5 we study OT problem in an inverse view, which we also call Inverse OT (IOT) problem. IOT also refers to the problem of learning the cost function for OT from observed transport plan or its samples. We derive an unconstrained convex optimization formulation of the inverse OT problem. We provide a comprehensive characterization of the properties of inverse OT, including uniqueness of solutions. We also develop two numerical algorithms, one is a fast matrix scaling method based on the Sinkhorn-Knopp algorithm for discrete OT, and the other one is a learning based algorithm that parameterizes the cost function as a deep neural network for continuous OT. Our numerical results demonstrate promising efficiency and accuracy advantages of the proposed algorithms over existing state-of-the-art methods. In Chapter 6 we propose a novel method using the weak form of Fokker Planck Equation (FPE) --- a partial differential equation --- to describe the density evolution of data in a sampled form, which is then combined with Wasserstein generative adversarial network (WGAN) in the training process. In such a sample-based framework we are able to learn the nonlinear dynamics from aggregate data without explicitly solving FPE. We demonstrate our approach in the context of a series of synthetic and real-world data sets. Chapter 7 introduces the application of OT and neural networks in optimal density control. Particularly, we parametrize the control strategy via neural networks, and provide an algorithm to learn the strategy that can drive samples following one distribution to new locations following target distribution. We demonstrate our method in both synthetic and realistic experiments, where we also consider perturbation fields. Finally Chapter 8 presents applications of mean field game in generative modeling and finance area. With more details, we build a GAN framework upon mean field game to generate desired distribution starting with white noise, we also investigate its connection to OT. Moreover, we apply mean field game theories to study the equilibrium trading price in stock markets, we demonstrate the theoretical result by conducting experiments on real trading data.Ph.D

High-dimensional Optimal Density Control with Wasserstein Metric Matching

We present a novel computational framework for density control in high-dimensional state spaces. The considered dynamical system consists of a large number of indistinguishable agents whose behaviors can be collectively modeled as a time-evolving probability distribution. The goal is to steer the agents from an initial distribution to reach (or approximate) a given target distribution within a fixed time horizon at minimum cost. To tackle this problem, we propose to model the drift as a nonlinear reduced-order model, such as a deep network, and enforce the matching to the target distribution at terminal time either strictly or approximately using the Wasserstein metric. The resulting saddle-point problem can be solved by an effective numerical algorithm that leverages the excellent representation power of deep networks and fast automatic differentiation for this challenging high-dimensional control problem. A variety of numerical experiments were conducted to demonstrate the performance of our method.Comment: 8 pages, 4 figures. Accepted for IEEE Conference on Decision and Control 202

An {\alpha}-Matte Boundary Defocus Model Based Cascaded Network for Multi-focus Image Fusion

Capturing an all-in-focus image with a single camera is difficult since the depth of field of the camera is usually limited. An alternative method to obtain the all-in-focus image is to fuse several images focusing at different depths. However, existing multi-focus image fusion methods cannot obtain clear results for areas near the focused/defocused boundary (FDB). In this paper, a novel {\alpha}-matte boundary defocus model is proposed to generate realistic training data with the defocus spread effect precisely modeled, especially for areas near the FDB. Based on this {\alpha}-matte defocus model and the generated data, a cascaded boundary aware convolutional network termed MMF-Net is proposed and trained, aiming to achieve clearer fusion results around the FDB. More specifically, the MMF-Net consists of two cascaded sub-nets for initial fusion and boundary fusion, respectively; these two sub-nets are designed to first obtain a guidance map of FDB and then refine the fusion near the FDB. Experiments demonstrate that with the help of the new {\alpha}-matte boundary defocus model, the proposed MMF-Net outperforms the state-of-the-art methods both qualitatively and quantitatively.Comment: 10 pages, 8 figures, journal Unfortunately, I cannot spell one of the authors' name coorectl

Real-MFF: A Large Realistic Multi-focus Image Dataset with Ground Truth

Multi-focus image fusion, a technique to generate an all-in-focus image from two or more partially-focused source images, can benefit many computer vision tasks. However, currently there is no large and realistic dataset to perform convincing evaluation and comparison of algorithms in multi-focus image fusion. Moreover, it is difficult to train a deep neural network for multi-focus image fusion without a suitable dataset. In this letter, we introduce a large and realistic multi-focus dataset called Real-MFF, which contains 710 pairs of source images with corresponding ground truth images. The dataset is generated by light field images, and both the source images and the ground truth images are realistic. To serve as both a well-established benchmark for existing multi-focus image fusion algorithms and an appropriate training dataset for future development of deep-learning-based methods, the dataset contains a variety of scenes, including buildings, plants, humans, shopping malls, squares and so on. We also evaluate 10 typical multi-focus algorithms on this dataset for the purpose of illustration