This paper studies the application of ensembles composed of multi-output models for multi-step ahead forecasting problems. Dynamic ensembles have been commonly used for forecasting. However, these are typically designed for one-step-ahead tasks. On the other hand, the literature regarding the application of dynamic ensembles for multi-step ahead forecasting is scarce. Moreover, it is not clear how the combination rule is applied across the forecasting horizon. We carried out extensive experiments to analyze the application of dynamic ensembles for multi-step forecasting. We resorted to a case study with 3568 time series and an ensemble of 30 multi-output models. We discovered that dynamic ensembles based on arbitrating and windowing present the best performance according to average rank. Moreover, as the horizon increases, most approaches struggle to outperform a static ensemble that assigns equal weights to all models. The experiments are publicly available in a repository.

Vehicle Energy Consumption (VEC) estimation aims to predict the total energy required for a given trip before it starts, which is of great importance to trip planning and transportation sustainability. Existing approaches mainly focus on extracting statistically significant factors from typical trips to improve the VEC estimation. However, the energy consumption of each vehicle may diverge widely due to the personalized driving behavior under varying travel contexts. To this end, this paper proposes a preference-aware meta-optimization framework Meta-Pec for personalized vehicle energy consumption estimation. Specifically, we first propose a spatiotemporal behavior learning module to capture the latent driver preference hidden in historical trips. Moreover, based on the memorization of driver preference, we devise a selection-based driving behavior prediction module to infer driver-specific driving patterns on a given route, which provides additional basis and supervision signals for VEC estimation. Besides, a driver-specific meta-optimization scheme is proposed to enable fast model adaption by learning and sharing transferable knowledge globally. Extensive experiments on two real-world datasets show the superiority of our proposed framework against ten numerical and data-driven machine learning baselines. The source code is available at https://github.com/usail-hkust/Meta-Pec.

The Roller-Quadrotor is a novel quadrotor that combines the maneuverability of aerial drones with the endurance of ground vehicles. This work focuses on the design, modeling, and experimental validation of the Roller-Quadrotor. Flight capabilities are achieved through a quadrotor configuration, with four thrust-providing actuators. Additionally, rolling motion is facilitated by a unicycle-driven and rotor-assisted turning structure. By utilizing terrestrial locomotion, the vehicle can overcome rolling and turning resistance, thereby conserving energy compared to its flight mode. This innovative approach not only tackles the inherent challenges of traditional rotorcraft but also enables the vehicle to navigate through narrow gaps and overcome obstacles by taking advantage of its aerial mobility. We develop comprehensive models and controllers for the Roller-Quadrotor and validate their performance through experiments. The results demonstrate its seamless transition between aerial and terrestrial locomotion, as well as its ability to safely navigate through gaps half the size of its diameter. Moreover, the terrestrial range of the vehicle is approximately 2.8 times greater, while the operating time is about 41.2 times longer compared to its aerial capabilities. These findings underscore the feasibility and effectiveness of the proposed structure and control mechanisms for efficient navigation through challenging terrains while conserving energy.

Implementing accurate Distribution System State Estimation (DSSE) faces several challenges, among which the lack of observability and the high density of the distribution system. While data-driven alternatives based on Machine Learning models could be a choice, they suffer in DSSE because of the lack of labeled data. In fact, measurements in the distribution system are often noisy, corrupted, and unavailable. To address these issues, we propose the Deep Statistical Solver for Distribution System State Estimation (DSS$^2$), a deep learning model based on graph neural networks (GNNs) that accounts for the network structure of the distribution system and for the physical governing power flow equations. DSS$^2$ leverages hypergraphs to represent the heterogeneous components of the distribution systems and updates their latent representations via a node-centric message-passing scheme. A weakly supervised learning approach is put forth to train the DSS$^2$ in a learning-to-optimize fashion w.r.t. the Weighted Least Squares loss with noisy measurements and pseudomeasurements. By enforcing the GNN output into the power flow equations and the latter into the loss function, we force the DSS$^2$ to respect the physics of the distribution system. This strategy enables learning from noisy measurements, acting as an implicit denoiser, and alleviating the need for ideal labeled data. Extensive experiments with case studies on the IEEE 14-bus, 70-bus, and 179-bus networks showed the DSS$^2$ outperforms by a margin the conventional Weighted Least Squares algorithm in accuracy, convergence, and computational time, while being more robust to noisy, erroneous, and missing measurements. The DSS$^2$ achieves a competing, yet lower, performance compared with the supervised models that rely on the unrealistic assumption of having all the true labels.

The increasing size of input graphs for graph neural networks (GNNs) highlights the demand for using multi-GPU platforms. However, existing multi-GPU GNN systems optimize the computation and communication individually based on the conventional practice of scaling dense DNNs. For irregularly sparse and fine-grained GNN workloads, such solutions miss the opportunity to jointly schedule/optimize the computation and communication operations for high-performance delivery. To this end, we propose MGG, a novel system design to accelerate full-graph GNNs on multi-GPU platforms. The core of MGG is its novel dynamic software pipeline to facilitate fine-grained computation-communication overlapping within a GPU kernel. Specifically, MGG introduces GNN-tailored pipeline construction and GPU-aware pipeline mapping to facilitate workload balancing and operation overlapping. MGG also incorporates an intelligent runtime design with analytical modeling and optimization heuristics to dynamically improve the execution performance. Extensive evaluation reveals that MGG outperforms state-of-the-art full-graph GNN systems across various settings: on average 4.41X, 4.81X, and 10.83X faster than DGL, MGG-UVM, and ROC, respectively.

Trajectory optimization methods have achieved an exceptional level of performance on real-world robots in recent years. These methods heavily rely on accurate analytical models of the dynamics, yet some aspects of the physical world can only be captured to a limited extent. An alternative approach is to leverage machine learning techniques to learn a differentiable dynamics model of the system from data. In this work, we use trajectory optimization and model learning for performing highly dynamic and complex tasks with robotic systems in absence of accurate analytical models of the dynamics. We show that a neural network can model highly nonlinear behaviors accurately for large time horizons, from data collected in only 25 minutes of interactions on two distinct robots: (i) the Boston Dynamics Spot and an (ii) RC car. Furthermore, we use the gradients of the neural network to perform gradient-based trajectory optimization. In our hardware experiments, we demonstrate that our learned model can represent complex dynamics for both the Spot and Radio-controlled (RC) car, and gives good performance in combination with trajectory optimization methods.

Despite their ubiquity throughout science and engineering, only a handful of partial differential equations (PDEs) have analytical, or closed-form solutions. This motivates a vast amount of classical work on numerical simulation of PDEs and more recently, a whirlwind of research into data-driven techniques leveraging machine learning (ML). A recent line of work indicates that a hybrid of classical numerical techniques and machine learning can offer significant improvements over either approach alone. In this work, we show that the choice of the numerical scheme is crucial when incorporating physics-based priors. We build upon Fourier-based spectral methods, which are known to be more efficient than other numerical schemes for simulating PDEs with smooth and periodic solutions. Specifically, we develop ML-augmented spectral solvers for three common PDEs of fluid dynamics. Our models are more accurate (2-4x) than standard spectral solvers at the same resolution but have longer overall runtimes (~2x), due to the additional runtime cost of the neural network component. We also demonstrate a handful of key design principles for combining machine learning and numerical methods for solving PDEs.

The paper studies the capabilities of Recurrent-Neural-Network sequence to sequence (RNN seq2seq) models in learning four transduction tasks: identity, reversal, total reduplication, and quadratic copying. These transductions are traditionally well studied under finite state transducers and attributed with increasing complexity. We find that RNN seq2seq models are only able to approximate a mapping that fits the training or in-distribution data, instead of learning the underlying functions. Although attention makes learning more efficient and robust, it does not overcome the out-of-distribution generalization limitation. We establish a novel complexity hierarchy for learning the four tasks for attention-less RNN seq2seq models, which may be understood in terms of the complexity hierarchy of formal languages, instead of string transductions. RNN variants also play a role in the results. In particular, we show that Simple RNN seq2seq models cannot count the input length.

The bulk kinematics and thermodynamics of hot supernovae-driven galactic winds is critically dependent on both the amount of swept up cool clouds and non-spherical collimated flow geometry. However, accurately parameterizing these physics is difficult because their functional forms are often unknown, and because the coupled non-linear flow equations contain singularities. We show that deep neural networks embedded as individual terms in the governing coupled ordinary differential equations (ODEs) can robustly discover both of these physics, without any prior knowledge of the true function structure, as a supervised learning task. We optimize a loss function based on the Mach number, rather than the explicitly solved-for 3 conserved variables, and apply a penalty term towards near-diverging solutions. The same neural network architecture is used for learning both the hidden mass-loading and surface area expansion rates. This work further highlights the feasibility of neural ODEs as a promising discovery tool with mechanistic interpretability for non-linear inverse problems.

Optimal design is a critical yet challenging task within many applications. This challenge arises from the need for extensive trial and error, often done through simulations or running field experiments. Fortunately, sequential optimal design, also referred to as Bayesian optimization when using surrogates with a Bayesian flavor, has played a key role in accelerating the design process through efficient sequential sampling strategies. However, a key opportunity exists nowadays. The increased connectivity of edge devices sets forth a new collaborative paradigm for Bayesian optimization. A paradigm whereby different clients collaboratively borrow strength from each other by effectively distributing their experimentation efforts to improve and fast-track their optimal design process. To this end, we bring the notion of consensus to Bayesian optimization, where clients agree (i.e., reach a consensus) on their next-to-sample designs. Our approach provides a generic and flexible framework that can incorporate different collaboration mechanisms. In lieu of this, we propose transitional collaborative mechanisms where clients initially rely more on each other to maneuver through the early stages with scant data, then, at the late stages, focus on their own objectives to get client-specific solutions. Theoretically, we show the sub-linear growth in regret for our proposed framework. Empirically, through simulated datasets and a real-world collaborative material discovery experiment, we show that our framework can effectively accelerate and improve the optimal design process and benefit all participants.