Max-product'belief propagation' (BP) is a popular distributed heuristic for finding the Maximum A Posteriori (MAP) assignment in a joint probability distribution represented by a Graphical Model (GM). It was recently shown that BP converges to the correct MAP assignment for a class of loopy GMs with the following common feature: the Linear Programming (LP) relaxation to the MAP problem is tight (has no integrality gap). Unfortunately, tightness of the LP relaxation does not, in general, guarantee convergence and correctness of the BP algorithm. The failure of BP in such cases motivates reverse engineering a solution – namely, given a tight LP, can we design a'good' BP algorithm. We prove that the algorithm converges to the correct optimum if the respective LP relaxation, which may include inequalities associated with non-intersecting odd-sized cycles, is tight.

Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalization to the emerging domain of hypergraphs has remained largely unexplored. On graphs, the Ollivier-Ricci curvature measures differences between random walks via Wasserstein distances, thus grounding a geometric concept in ideas from probability theory and optimal transport. We develop ORCHID, a flexible framework generalizing Ollivier-Ricci curvature to hypergraphs, and prove that the resulting curvatures have favorable theoretical properties. Through extensive experiments on synthetic and real-world hypergraphs from different domains, we demonstrate that ORCHID curvatures are both scalable and useful to perform a variety of hypergraph tasks in practice.

Subset weighted-Tempered Gibbs Sampler (wTGS) has been recently introduced by Jankowiak to reduce the computation complexity per MCMC iteration in high-dimensional applications where the exact calculation of the posterior inclusion probabilities (PIP) is not essential. However, the Rao-Backwellized estimator associated with this sampler has a high variance as the ratio between the signal dimension and the number of conditional PIP estimations is large. In this paper, we design a new subset weighted-Tempered Gibbs Sampler (wTGS) where the expected number of computations of conditional PIPs per MCMC iteration can be much smaller than the signal dimension. Different from the subset wTGS and wTGS, our sampler has a variable complexity per MCMC iteration. We provide an upper bound on the variance of an associated Rao-Blackwellized estimator for this sampler at a finite number of iterations, $T$, and show that the variance is $O\big(\big(\frac{P}{S}\big)^2 \frac{\log T}{T}\big)$ for a given dataset where $S$ is the expected number of conditional PIP computations per MCMC iteration. Experiments show that our Rao-Blackwellized estimator can have a smaller variance than its counterpart associated with the subset wTGS.

The aim of this work is to investigate the use of Incrementally Input-to-State Stable ($\delta$ISS) deep Long Short Term Memory networks (LSTMs) for the identification of nonlinear dynamical systems. We show that suitable sufficient conditions on the weights of the network can be leveraged to setup a training procedure able to learn provenly-$\delta$ISS LSTM models from data. The proposed approach is tested on a real brake-by-wire apparatus to identify a model of the system from input-output experimentally collected data. Results show satisfactory modeling performances.

The large amount of data collected in buildings makes energy management smarter and more energy efficient. This study proposes a design and implementation methodology of data-driven heating, ventilation, and air conditioning (HVAC) control. Building thermodynamics is modeled using a symbolic regression model (SRM) built from the collected data. Additionally, an HVAC system model is also developed with a data-driven approach. A model predictive control (MPC) based HVAC scheduling is formulated with the developed models to minimize energy consumption and peak power demand and maximize thermal comfort. The performance of the proposed framework is demonstrated in the workspace in the actual campus building. The HVAC system using the proposed framework reduces the peak power by 16.1\% compared to the widely used thermostat controller.

Although both the public sector and defense agencies are interested in urban uncrewed aerial vehicle (UAV) mission performance, fixed winged aircraft are still incapable of adapting to the complex aerodynamics within a city environment [1, 2, 3, 4, 5, 6]. Currently, the most dynamic environments are dominated by multirotor flight vehicles; however, the highly maneuverable and responsive quadrotor design suffers from substantial weight and power constraints, limiting the operational range and on-board computational capabilities needed for autonomy [7, 8, 9, 10]. Current fixed wing UAVs have greater range but are not as maneuverable [11]. Counter to both rotorcraft and traditional fixed wing UAV design, birds can adapt their wing shape as the environment changes to achieve both efficient and maneuverable flight [12]. This ability supports birds of prey in navigating through complex environments [13], or rejecting perturbations in a gusty environment [14, 15].

Driving simulators have been used in the automotive industry for many years because of their ability to perform tests in a safe, reproducible and controlled immersive virtual environment. The improved performance of the simulator and its ability to recreate in-vehicle experience for the user is established through motion cueing algorithms (MCA). Such algorithms have constantly been developed with model predictive control (MPC) acting as the main control technique. Currently, available MPC-based methods either compute the optimal controller online or derive an explicit control law offline. These approaches limit the applicability of the MCA for real-time applications due to online computational costs and/or offline memory storage issues. This research presents a solution to deal with issues of offline and online solving through a hybrid approach. For this, an explicit MPC is used to generate a look-up table to provide an initial guess as a warm-start for the implicit MPC-based MCA. From the simulations, it is observed that the presented hybrid approach is able to reduce online computation load by shifting it offline using the explicit controller. Further, the algorithm demonstrates a good tracking performance with a significant reduction of computation time in a complex driving scenario using an emulator environment of a driving simulator.

ABSTRACT: In this study, we have shown autonomous long-term prediction with a spintronic physical reservoir. Due to the short-term memory property of the magnetization dynamics, non-linearity arises in the reservoir states which could be used for long-term prediction tasks using simple linear regression for online training. During the prediction stage, the output is directly fed to the input of the reservoir for autonomous prediction. We employ our proposed reservoir for the modeling of the chaotic time series such as Mackey-Glass and dynamic time-series data, such as household building energy loads. Since only the last layer of a RC needs to be trained with linear regression, it is well suited for learning in real time on edge devices. Here we show that a skyrmion based magnetic tunnel junction can potentially be used as a prototypical RC but any nanomagnetic magnetic tunnel junction with nonlinear magnetization behavior can implement such a RC. By comparing our spintronic physical RC approach with state-of-the-art energy load forecasting algorithms, such as LSTMs and RNNs, we conclude that the proposed framework presents good performance in achieving high predictions accuracy, while also requiring low memory and energy both of which are at a premium in hardware resource and power constrained edge applications. Further, the proposed approach is shown to require very small training datasets and at the same time being at least 16X energy efficient compared to the state-of-the-art sequence to sequence LSTM for accurate household load predictions. I. INTRODUCTION Recurrent neural networks (RNNs) [1,2] are shown to be more suitable in temporal data processing tasks than the traditional feedforward neural networks (FNNs) because of the recurrent connections among constituent neurons. However, RNNs often suffers from vanishing and exploding gradients problem due to the long-term dependencies that could arise in the recurrent layers. To circumvent these issues variations of RNN is proposed, i.e., long short-term memory (LSTM) [3] and reservoir computing (RC) [4,5].

Automated machine learning (AutoML) methods improve upon existing models by optimizing various aspects of their design. While present methods focus on hyperparameters and neural network topologies, other aspects of neural network design can be optimized as well. To further the state of the art in AutoML, this dissertation introduces techniques for discovering more powerful activation functions and establishing more robust weight initialization for neural networks. These contributions improve performance, but also provide new perspectives on neural network optimization. First, the dissertation demonstrates that discovering solutions specialized to specific architectures and tasks gives better performance than reusing general approaches. Second, it shows that jointly optimizing different components of neural networks is synergistic, and results in better performance than optimizing individual components alone. Third, it demonstrates that learned representations are easier to optimize than hard-coded ones, creating further opportunities for AutoML. The dissertation thus makes concrete progress towards fully automatic machine learning in the future.

A combustion chemistry acceleration scheme is developed based on deep operator networks (DeepONets). The scheme is based on the identification of combustion reaction dynamics through a modified DeepOnet architecture such that the solutions of thermochemical scalars are projected to new solutions in small and flexible time increments. The approach is designed to efficiently implement chemistry acceleration without the need for computationally expensive integration of stiff chemistry. An additional framework of latent-space dynamics identification with modified DeepOnet is also proposed which enhances the computational efficiency and widens the applicability of the proposed scheme. The scheme is demonstrated on simple chemical kinetics of hydrogen oxidation to more complex chemical kinetics of n-dodecane high- and low-temperature oxidations. The proposed framework accurately learns the chemical kinetics and efficiently reproduces species and temperature temporal profiles corresponding to each application. In addition, a very large speed-up with a great extrapolation capability is also observed with the proposed scheme.