CGNSDE: Conditional Gaussian Neural Stochastic Differential Equation for Modeling Complex Systems and Data Assimilation

A new knowledge-based and machine learning hybrid modeling approach, called conditional Gaussian neural stochastic differential equation (CGNSDE), is developed to facilitate modeling complex dynamical systems and implementing analytic formulae of the associated data assimilation (DA). In contrast to the standard neural network predictive models, the CGNSDE is designed to effectively tackle both forward prediction tasks and inverse state estimation problems. The CGNSDE starts by exploiting a systematic causal inference via information theory to build a simple knowledge-based nonlinear model that nevertheless captures as much explainable physics as possible. Then, neural networks are supplemented to the knowledge-based model in a specific way, which not only characterizes the remaining features that are challenging to model with simple forms but also advances the use of analytic formulae to efficiently compute the nonlinear DA solution. These analytic formulae are used as an additional computationally affordable loss to train the neural networks that directly improve the DA accuracy. This DA loss function promotes the CGNSDE to capture the interactions between state variables and thus advances its modeling skills. With the DA loss, the CGNSDE is more capable of estimating extreme events and quantifying the associated uncertainty. Furthermore, crucial physical properties in many complex systems, such as the translate-invariant local dependence of state variables, can significantly simplify the neural network structures and facilitate the CGNSDE to be applied to high-dimensional systems. Numerical experiments based on chaotic systems with intermittency and strong non-Gaussian features indicate that the CGNSDE outperforms knowledge-based regression models, and the DA loss further enhances the modeling skills of the CGNSDE.

Benchmarking Data Science Agents

In the era of data-driven decision-making, the complexity of data analysis necessitates advanced expertise and tools of data science, presenting significant challenges even for specialists. Large Language Models (LLMs) have emerged as promising aids as data science agents, assisting humans in data analysis and processing. Yet their practical efficacy remains constrained by the varied demands of real-world applications and complicated analytical process. In this paper, we introduce DSEval -- a novel evaluation paradigm, as well as a series of innovative benchmarks tailored for assessing the performance of these agents throughout the entire data science lifecycle. Incorporating a novel bootstrapped annotation method, we streamline dataset preparation, improve the evaluation coverage, and expand benchmarking comprehensiveness. Our findings uncover prevalent obstacles and provide critical insights to inform future advancements in the field.

Integrating Active Learning in Causal Inference with Interference: A Novel Approach in Online Experiments

In the domain of causal inference research, the prevalent potential outcomes framework, notably the Rubin Causal Model (RCM), often overlooks individual interference and assumes independent treatment effects. This assumption, however, is frequently misaligned with the intricate realities of real-world scenarios, where interference is not merely a possibility but a common occurrence. Our research endeavors to address this discrepancy by focusing on the estimation of direct and spillover treatment effects under two assumptions: (1) network-based interference, where treatments on neighbors within connected networks affect one's outcomes, and (2) non-random treatment assignments influenced by confounders. To improve the efficiency of estimating potentially complex effects functions, we introduce an novel active learning approach: Active Learning in Causal Inference with Interference (ACI). This approach uses Gaussian process to flexibly model the direct and spillover treatment effects as a function of a continuous measure of neighbors' treatment assignment. The ACI framework sequentially identifies the experimental settings that demand further data. It further optimizes the treatment assignments under the network interference structure using genetic algorithms to achieve efficient learning outcome. By applying our method to simulation data and a Tencent game dataset, we demonstrate its feasibility in achieving accurate effects estimations with reduced data requirements. This ACI approach marks a significant advancement in the realm of data efficiency for causal inference, offering a robust and efficient alternative to traditional methodologies, particularly in scenarios characterized by complex interference patterns.

FlowHON: Representing Flow Fields Using Higher-Order Networks

Flow fields are often partitioned into data blocks for massively parallel computation and analysis based on blockwise relationships. However, most of the previous techniques only consider the first-order dependencies among blocks, which is insufficient in describing complex flow patterns. In this work, we present FlowHON, an approach to construct higher-order networks (HONs) from flow fields. FlowHON captures the inherent higher-order dependencies in flow fields as nodes and estimates the transitions among them as edges. We formulate the HON construction as an optimization problem with three linear transformations. The first two layers correspond to the node generation and the third one corresponds to edge estimation. Our formulation allows the node generation and edge estimation to be solved in a unified framework. With FlowHON, the rich set of traditional graph algorithms can be applied without any modification to analyze flow fields, while leveraging the higher-order information to understand the inherent structure and manage flow data for efficiency. We demonstrate the effectiveness of FlowHON using a series of downstream tasks, including estimating the density of particles during tracing, partitioning flow fields for data management, and understanding flow fields using the node-link diagram representation of networks.

Swashplateless-elevon Actuation for a Dual-rotor Tail-sitter VTOL UAV

In this paper, we propose a novel swashplateless-elevon actuation (SEA) for dual-rotor tail-sitter vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs). In contrast to the conventional elevon actuation (CEA) which controls both pitch and yaw using elevons, the SEA adopts swashplateless mechanisms to generate an extra moment through motor speed modulation to control pitch and uses elevons solely for controlling yaw, without requiring additional actuators. This decoupled control strategy mitigates the saturation of elevons' deflection needed for large pitch and yaw control actions, thus improving the UAV's control performance on trajectory tracking and disturbance rejection performance in the presence of large external disturbances. Furthermore, the SEA overcomes the actuation degradation issues experienced by the CEA when the UAV is in close proximity to the ground, leading to a smoother and more stable take-off process. We validate and compare the performances of the SEA and the CEA in various real-world flight conditions, including take-off, trajectory tracking, and hover flight and position steps under external disturbance. Experimental results demonstrate that the SEA has better performances than the CEA. Moreover, we verify the SEA's feasibility in the attitude transition process and fixed-wing-mode flight of the VTOL UAV. The results indicate that the SEA can accurately control pitch in the presence of high-speed incoming airflow and maintain a stable attitude during fixed-wing mode flight. Video of all experiments can be found in youtube.com/watch?v=Sx9Rk4Zf7sQ

A Survey of Imbalanced Learning on Graphs: Problems, Techniques, and Future Directions

Graphs represent interconnected structures prevalent in a myriad of real-world scenarios. Effective graph analytics, such as graph learning methods, enables users to gain profound insights from graph data, underpinning various tasks including node classification and link prediction. However, these methods often suffer from data imbalance, a common issue in graph data where certain segments possess abundant data while others are scarce, thereby leading to biased learning outcomes. This necessitates the emerging field of imbalanced learning on graphs, which aims to correct these data distribution skews for more accurate and representative learning outcomes. In this survey, we embark on a comprehensive review of the literature on imbalanced learning on graphs. We begin by providing a definitive understanding of the concept and related terminologies, establishing a strong foundational understanding for readers. Following this, we propose two comprehensive taxonomies: (1) the problem taxonomy, which describes the forms of imbalance we consider, the associated tasks, and potential solutions; (2) the technique taxonomy, which details key strategies for addressing these imbalances, and aids readers in their method selection process. Finally, we suggest prospective future directions for both problems and techniques within the sphere of imbalanced learning on graphs, fostering further innovation in this critical area.

Snapp: An Agile Robotic Fish with 3-D Maneuverability for Open Water Swim

Fish exhibit impressive locomotive performance and agility in complex underwater environments, using their undulating tails and pectoral fins for propulsion and maneuverability. Replicating these abilities in robotic fish is challenging; existing designs focus on either fast swimming or directional control at limited speeds, mainly within a confined environment. To address these limitations, we designed Snapp, an integrated robotic fish capable of swimming in open water with high speeds and full 3-dimensional maneuverability. A novel cyclic-differential method is layered on the mechanism. It integrates propulsion and yaw-steering for fast course corrections. Two independent pectoral fins provide pitch and roll control. We evaluated Snapp in open water environments. We demonstrated significant improvements in speed and maneuverability, achieving swimming speeds of 1.5 m/s (1.7 Body Lengths per second) and performing complex maneuvers, such as a figure-8 and S-shape trajectory. Instantaneous yaw changes of 15$^{\circ}$ in 0.4 s, a minimum turn radius of 0.85 m, and maximum pitch and roll rates of 3.5 rad/s and 1 rad/s, respectively, were recorded. Our results suggest that Snapp's swimming capabilities have excellent practical prospects for open seas and contribute significantly to developing agile robotic fishes.

CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting

Regime switching is ubiquitous in many complex dynamical systems with multiscale features, chaotic behavior, and extreme events. In this paper, a causation entropy boosting (CEBoosting) strategy is developed to facilitate the detection of regime switching and the discovery of the dynamics associated with the new regime via online model identification. The causation entropy, which can be efficiently calculated, provides a logic value of each candidate function in a pre-determined library. The reversal of one or a few such causation entropy indicators associated with the model calibrated for the current regime implies the detection of regime switching. Despite the short length of each batch formed by the sequential data, the accumulated value of causation entropy corresponding to a sequence of data batches leads to a robust indicator. With the detected rectification of the model structure, the subsequent parameter estimation becomes a quadratic optimization problem, which is solved using closed analytic formulae. Using the Lorenz 96 model, it is shown that the causation entropy indicator can be efficiently calculated, and the method applies to moderately large dimensional systems. The CEBoosting algorithm is also adaptive to the situation with partial observations. It is shown via a stochastic parameterized model that the CEBoosting strategy can be combined with data assimilation to identify regime switching triggered by the unobserved latent processes. In addition, the CEBoosting method is applied to a nonlinear paradigm model for topographic mean flow interaction, demonstrating the online detection of regime switching in the presence of strong intermittency and extreme events.

Trajectory Generation and Tracking Control for Aggressive Tail-Sitter Flights

We address the theoretical and practical problems related to the trajectory generation and tracking control of tail-sitter UAVs. Theoretically, we focus on the differential flatness property with full exploitation of actual UAV aerodynamic models, which lays a foundation for generating dynamically feasible trajectory and achieving high-performance tracking control. We have found that a tail-sitter is differentially flat with accurate aerodynamic models within the entire flight envelope, by specifying coordinate flight condition and choosing the vehicle position as the flat output. This fundamental property allows us to fully exploit the high-fidelity aerodynamic models in the trajectory planning and tracking control to achieve accurate tail-sitter flights. Particularly, an optimization-based trajectory planner for tail-sitters is proposed to design high-quality, smooth trajectories with consideration of kinodynamic constraints, singularity-free constraints and actuator saturation. The planned trajectory of flat output is transformed to state trajectory in real-time with consideration of wind in environments. To track the state trajectory, a global, singularity-free, and minimally-parameterized on-manifold MPC is developed, which fully leverages the accurate aerodynamic model to achieve high-accuracy trajectory tracking within the whole flight envelope. The effectiveness of the proposed framework is demonstrated through extensive real-world experiments in both indoor and outdoor field tests, including agile SE(3) flight through consecutive narrow windows requiring specific attitude and with speed up to 10m/s, typical tail-sitter maneuvers (transition, level flight and loiter) with speed up to 20m/s, and extremely aggressive aerobatic maneuvers (Wingover, Loop, Vertical Eight and Cuban Eight) with acceleration up to 2.5g.

MARSIM: A light-weight point-realistic simulator for LiDAR-based UAVs

The emergence of low-cost, small form factor and light-weight solid-state LiDAR sensors have brought new opportunities for autonomous unmanned aerial vehicles (UAVs) by advancing navigation safety and computation efficiency. Yet the successful developments of LiDAR-based UAVs must rely on extensive simulations. Existing simulators can hardly perform simulations of real-world environments due to the requirements of dense mesh maps that are difficult to obtain. In this paper, we develop a point-realistic simulator of real-world scenes for LiDAR-based UAVs. The key idea is the underlying point rendering method, where we construct a depth image directly from the point cloud map and interpolate it to obtain realistic LiDAR point measurements. Our developed simulator is able to run on a light-weight computing platform and supports the simulation of LiDARs with different resolution and scanning patterns, dynamic obstacles, and multi-UAV systems. Developed in the ROS framework, the simulator can easily communicate with other key modules of an autonomous robot, such as perception, state estimation, planning, and control. Finally, the simulator provides 10 high-resolution point cloud maps of various real-world environments, including forests of different densities, historic building, office, parking garage, and various complex indoor environments. These realistic maps provide diverse testing scenarios for an autonomous UAV. Evaluation results show that the developed simulator achieves superior performance in terms of time and memory consumption against Gazebo and that the simulated UAV flights highly match the actual one in real-world environments. We believe such a point-realistic and light-weight simulator is crucial to bridge the gap between UAV simulation and experiments and will significantly facilitate the research of LiDAR-based autonomous UAVs in the future.