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Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chemical reaction modeling and mathematical analysis. A quadratization reveals new variables and structures of a model, which may be easier to analyze, simulate, control, and provides a convenient parametrization for learning. This paper presents novel theory, algorithms and software capabilities for quadratization of non-autonomous ODEs. We provide existence results, depending on the regularity of the input function, for cases when a quadratic-bilinear system can be obtained through quadratization. We further develop existence results and an algorithm that generalizes the process of quadratization for systems with arbitrary dimension that retain the nonlinear structure when the dimension grows. For such systems, we provide dimension-agnostic quadratization. An example is semi-discretized PDEs, where the nonlinear terms remain symbolically identical when the discretization size increases. As an important aspect for practical adoption of this research, we extended the capabilities of the QBee software towards both non-autonomous systems of ODEs and ODEs with arbitrary dimension. We present several examples of ODEs that were previously reported in the literature, and where our new algorithms find quadratized ODE systems with lower dimension than the previously reported lifting transformations. We further highlight an important area of quadratization: reduced-order model learning. This area can benefit significantly from working in the optimal lifting variables, where quadratic models provide a direct parametrization of the model that also avoids additional hyperreduction for the nonlinear terms. A solar wind example highlights these advantages.

In this paper we discuss how to evaluate the differences between fitted logistic regression models across sub-populations. Our motivating example is in studying computerized diagnosis for learning disabilities, where sub-populations based on gender may or may not require separate models. In this context, significance tests for hypotheses of no difference between populations may provide perverse incentives, as larger variances and smaller samples increase the probability of not-rejecting the null. We argue that equivalence testing for a prespecified tolerance level on population differences incentivizes accuracy in the inference. We develop a cascading set of equivalence tests, in which each test addresses a different aspect of the model: the way the phenomenon is coded in the regression coefficients, the individual predictions in the per example log odds ratio and the overall accuracy in the mean square prediction error. For each equivalence test, we propose a strategy for setting the equivalence thresholds. The large-sample approximations are validated using simulations. For diagnosis data, we show examples for equivalent and non-equivalent models.

Finding the initial conditions that led to the current state of the universe is challenging because it involves searching over a vast input space of initial conditions, along with modeling their evolution via tools such as N-body simulations which are computationally expensive. Deep learning has emerged as an alternate modeling tool that can learn the mapping between the linear input of an N-body simulation and the final nonlinear displacements at redshift zero, which can significantly accelerate the forward modeling. However, this does not help reduce the search space for initial conditions. In this paper, we demonstrate for the first time that a deep learning model can be trained for the reverse mapping. We train a V-Net based convolutional neural network, which outputs the linear displacement of an N-body system, given the current time nonlinear displacement and the cosmological parameters of the system. We demonstrate that this neural network accurately recovers the initial linear displacement field over a wide range of scales ($<1$-$2\%$ error up to nearly $k = 1\ \mathrm{Mpc}^{-1}\,h$), despite the ill-defined nature of the inverse problem at smaller scales. Specifically, smaller scales are dominated by nonlinear effects which makes the backward dynamics much more susceptible to numerical and computational errors leading to highly divergent backward trajectories and a one-to-many backward mapping. The results of our method motivate that neural network based models can act as good approximators of the initial linear states and their predictions can serve as good starting points for sampling-based methods to infer the initial states of the universe.

Human-machine interaction (HMI) and human-robot interaction (HRI) can assist structural monitoring and structural dynamics testing in the laboratory and field. In vibratory experimentation, one mode of generating vibration is to use electrodynamic exciters. Manual control is a common way of setting the input of the exciter by the operator. To measure the structural responses to these generated vibrations sensors are attached to the structure. These sensors can be deployed by repeatable robots with high endurance, which require on-the-fly control. If the interface between operators and the controls was augmented, then operators can visualize the experiments, exciter levels, and define robot input with a better awareness of the area of interest. Robots can provide better aid to humans if intelligent on-the-fly control of the robot is: (1) quantified and presented to the human; (2) conducted in real-time for human feedback informed by data. Information provided by the new interface would be used to change the control input based on their understanding of real-time parameters. This research proposes using Augmented Reality (AR) applications to provide humans with sensor feedback and control of actuators and robots. This method improves cognition by allowing the operator to maintain awareness of structures while adjusting conditions accordingly with the assistance of the new real-time interface. One interface application is developed to plot sensor data in addition to voltage, frequency, and duration controls for vibration generation. Two more applications are developed under similar framework, one to control the position of a mediating robot and one to control the frequency of the robot movement. This paper presents the proposed model for the new control loop and then compares the new approach with a traditional method by measuring time delay in control input and user efficiency.

New knowledge originates from the old. The various types of elements, deposited in the training history, are a large amount of wealth for improving learning deep models. In this survey, we comprehensively review and summarize the topic--``Historical Learning: Learning Models with Learning History'', which learns better neural models with the help of their learning history during its optimization, from three detailed aspects: Historical Type (what), Functional Part (where) and Storage Form (how). To our best knowledge, it is the first survey that systematically studies the methodologies which make use of various historical statistics when training deep neural networks. The discussions with related topics like recurrent/memory networks, ensemble learning, and reinforcement learning are demonstrated. We also expose future challenges of this topic and encourage the community to pay attention to the think of historical learning principles when designing algorithms. The paper list related to historical learning is available at \url{//github.com/Martinser/Awesome-Historical-Learning.}

Many recent pattern recognition applications rely on complex distributed architectures in which sensing and computational nodes interact together through a communication network. Deep neural networks (DNNs) play an important role in this scenario, furnishing powerful decision mechanisms, at the price of a high computational effort. Consequently, powerful state-of-the-art DNNs are frequently split over various computational nodes, e.g., a first part stays on an embedded device and the rest on a server. Deciding where to split a DNN is a challenge in itself, making the design of deep learning applications even more complicated. Therefore, we propose Split-Et-Impera, a novel and practical framework that i) determines the set of the best-split points of a neural network based on deep network interpretability principles without performing a tedious try-and-test approach, ii) performs a communication-aware simulation for the rapid evaluation of different neural network rearrangements, and iii) suggests the best match between the quality of service requirements of the application and the performance in terms of accuracy and latency time.

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.

Catastrophic forgetting refers to the tendency that a neural network "forgets" the previous learned knowledge upon learning new tasks. Prior methods have been focused on overcoming this problem on convolutional neural networks (CNNs), where the input samples like images lie in a grid domain, but have largely overlooked graph neural networks (GNNs) that handle non-grid data. In this paper, we propose a novel scheme dedicated to overcoming catastrophic forgetting problem and hence strengthen continual learning in GNNs. At the heart of our approach is a generic module, termed as topology-aware weight preserving~(TWP), applicable to arbitrary form of GNNs in a plug-and-play fashion. Unlike the main stream of CNN-based continual learning methods that rely on solely slowing down the updates of parameters important to the downstream task, TWP explicitly explores the local structures of the input graph, and attempts to stabilize the parameters playing pivotal roles in the topological aggregation. We evaluate TWP on different GNN backbones over several datasets, and demonstrate that it yields performances superior to the state of the art. Code is publicly available at \url{//github.com/hhliu79/TWP}.

There is a resurgent interest in developing intelligent open-domain dialog systems due to the availability of large amounts of conversational data and the recent progress on neural approaches to conversational AI. Unlike traditional task-oriented bots, an open-domain dialog system aims to establish long-term connections with users by satisfying the human need for communication, affection, and social belonging. This paper reviews the recent works on neural approaches that are devoted to addressing three challenges in developing such systems: semantics, consistency, and interactiveness. Semantics requires a dialog system to not only understand the content of the dialog but also identify user's social needs during the conversation. Consistency requires the system to demonstrate a consistent personality to win users trust and gain their long-term confidence. Interactiveness refers to the system's ability to generate interpersonal responses to achieve particular social goals such as entertainment, conforming, and task completion. The works we select to present here is based on our unique views and are by no means complete. Nevertheless, we hope that the discussion will inspire new research in developing more intelligent dialog systems.