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In this paper, we propose, analyze and implement efficient time parallel methods for the Cahn-Hilliard (CH) equation. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of the CH equation has. The CH equation generally needs to be simulated for a very long time to get the solution of phase coarsening stage. Therefore it is desirable to accelerate the computation using parallel method in time. We present linear and nonlinear Parareal methods for the CH equation depending on the choice of fine approximation. We illustrate our results by numerical experiments.

In this paper, we study zeroth-order algorithms for nonconvex-concave minimax problems, which have attracted widely attention in machine learning, signal processing and many other fields in recent years. We propose a zeroth-order alternating randomized gradient projection (ZO-AGP) algorithm for smooth nonconvex-concave minimax problems, and its iteration complexity to obtain an $\varepsilon$-stationary point is bounded by $\mathcal{O}(\varepsilon^{-4})$, and the number of function value estimation is bounded by $\mathcal{O}(d_{x}+d_{y})$ per iteration. Moreover, we propose a zeroth-order block alternating randomized proximal gradient algorithm (ZO-BAPG) for solving block-wise nonsmooth nonconvex-concave minimax optimization problems, and the iteration complexity to obtain an $\varepsilon$-stationary point is bounded by $\mathcal{O}(\varepsilon^{-4})$ and the number of function value estimation per iteration is bounded by $\mathcal{O}(K d_{x}+d_{y})$. To the best of our knowledge, this is the first time that zeroth-order algorithms with iteration complexity gurantee are developed for solving both general smooth and block-wise nonsmooth nonconvex-concave minimax problems. Numerical results on data poisoning attack problem validate the efficiency of the proposed algorithms.

This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending first-order methods for multiobjective problems without scalarization has been widely studied, but providing accelerated methods with accurate proofs of convergence rates remains an open problem. Our proposed method is a multiobjective generalization of the accelerated proximal gradient method, also known as the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), for scalar optimization. The key to this successful extension is solving a subproblem with terms exclusive to the multiobjective case. This approach allows us to demonstrate the global convergence rate of the proposed method ($O(1 / k^2)$), using a merit function to measure the complexity. Furthermore, we present an efficient way to solve the subproblem via its dual representation, and we confirm the validity of the proposed method through some numerical experiments.

Time Series Classification (TSC) involved building predictive models for a discrete target variable from ordered, real valued, attributes. Over recent years, a new set of TSC algorithms have been developed which have made significant improvement over the previous state of the art. The main focus has been on univariate TSC, i.e. the problem where each case has a single series and a class label. In reality, it is more common to encounter multivariate TSC (MTSC) problems where multiple series are associated with a single label. Despite this, much less consideration has been given to MTSC than the univariate case. The UEA archive of 30 MTSC problems released in 2018 has made comparison of algorithms easier. We review recently proposed bespoke MTSC algorithms based on deep learning, shapelets and bag of words approaches. The simplest approach to MTSC is to ensemble univariate classifiers over the multivariate dimensions. We compare the bespoke algorithms to these dimension independent approaches on the 26 of the 30 MTSC archive problems where the data are all of equal length. We demonstrate that the independent ensemble of HIVE-COTE classifiers is the most accurate, but that, unlike with univariate classification, dynamic time warping is still competitive at MTSC.

We consider the computations of the action ground state for a rotating nonlinear Schr\"odinger equation. It reads as a minimization of the action functional under the Nehari constraint. In the focusing case, we identify an equivalent formulation of the problem which simplifies the constraint. Based on it, we propose a normalized gradient flow method with asymptotic Lagrange multiplier and establish the energy-decaying property. Popular optimization methods are also applied to gain more efficiency. In the defocusing case, we prove that the ground state can be obtained by the unconstrained minimization. Then the direct gradient flow method and unconstrained optimization methods are applied. Numerical experiments show the convergence and accuracy of the proposed methods in both cases, and comparisons on the efficiency are discussed. Finally, the relation between the action and the energy ground states are numerically investigated.

Typical algorithms for point cloud registration such as Iterative Closest Point (ICP) require a favorable initial transform estimate between two point clouds in order to perform a successful registration. State-of-the-art methods for choosing this starting condition rely on stochastic sampling or global optimization techniques such as branch and bound. In this work, we present a new method based on Bayesian optimization for finding the critical initial ICP transform. We provide three different configurations for our method which highlights the versatility of the algorithm to both find rapid results and refine them in situations where more runtime is available such as offline map building. Experiments are run on popular data sets and we show that our approach outperforms state-of-the-art methods when given similar computation time. Furthermore, it is compatible with other improvements to ICP, as it focuses solely on the selection of an initial transform, a starting point for all ICP-based methods.

In this paper, we use composite optimization algorithms to solve sigmoid networks. We equivalently transfer the sigmoid networks to a convex composite optimization and propose the composite optimization algorithms based on the linearized proximal algorithms and the alternating direction method of multipliers. Under the assumptions of the weak sharp minima and the regularity condition, the algorithm is guaranteed to converge to a globally optimal solution of the objective function even in the case of non-convex and non-smooth problems. Furthermore, the convergence results can be directly related to the amount of training data and provide a general guide for setting the size of sigmoid networks. Numerical experiments on Franke's function fitting and handwritten digit recognition show that the proposed algorithms perform satisfactorily and robustly.

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.

In recent years, there has been an exponential growth in the number of complex documents and texts that require a deeper understanding of machine learning methods to be able to accurately classify texts in many applications. Many machine learning approaches have achieved surpassing results in natural language processing. The success of these learning algorithms relies on their capacity to understand complex models and non-linear relationships within data. However, finding suitable structures, architectures, and techniques for text classification is a challenge for researchers. In this paper, a brief overview of text classification algorithms is discussed. This overview covers different text feature extractions, dimensionality reduction methods, existing algorithms and techniques, and evaluations methods. Finally, the limitations of each technique and their application in the real-world problem are discussed.