In recent years, computational power and data availability breakthroughs have revolutionized our ability to analyze complex physical systems through the inverse problem approach. Data-driven techniques like system identification and machine learning play an important role in this field, allowing us to gain insights into previously inaccessible phenomena. However, a major hurdle remains: How can meaningful information from partial measurements be extracted? In the aerospace domain, the challenge of state estimation is particularly pronounced due to the limited availability of observational data and the constraints imposed by sensor capabilities for tracking resident space objects (RSOs). To address these limitations, advanced compensation methodologies are required. Currently, range and bearing measurements obtained from radar and optical systems constitute the primary observational tools in the space situational awareness (SSA) community. In this work, we propose a novel framework that integrates a simplified reference dynamics model with a data-driven surrogate measurement model. This fusion process leverages the strengths of both models to estimate complex dynamical behaviors under conditions of partial observability. Extensive numerical experiments were conducted across multiple datasets to validate the proposed framework. The results demonstrate its efficacy in accurately reconstructing system dynamics from incomplete measurement data. Furthermore, to ensure the robustness of the framework, an initial consistency analysis of the surrogate modeling approach is presented. By addressing the current challenges and refining the integration of data-driven techniques with traditional physics-based modeling, this framework aims to advance state estimation methodologies in the aerospace sector.

This paper presents a comparative case study of wildland fire rate of spread (ROS) estimation, contrasting infrared data from an autonomous unmanned aerial system (UAS) with predictions from the Rothermel fire behavior model during a prescribed burn conducted in Zaleski State Forest, Ohio. In this study, we built and deployed a small UAS platform equipped with infrared sensing to measure the ROS of the fire front in a forest with significant topographic variation. Infrared data from the experiment were reprojected into the three-dimensional world frame, followed by a geometrical analysis of the observed fire intensity contours. Delaunay triangulation was performed to discretize the space around time-separated fire fronts, resulting in local ROS estimates based on fire intensity gradients. The infrared-derived ROS estimates were then compared with widely used Rothermel model predictions. Finally, a vector alignment analysis was conducted to investigate discrepancies between the methods by comparing ROS directionality with local terrain gradients. The results showed a small to negligible correlation, suggesting that the observed fire-front motion was not strongly aligned with terrain-gradient direction alone. These results underscore the complexities of fire behavior shaped by terrain, environmental factors, and the limitations of predictive models in natural fire conditions.

The Resource Constrained Shortest Path Problem (RCSPP) is defined as finding a minimum cost path between two poses while maintaining a path dependent resource consumption below a prescribed limit. The RRT* algorithm operates by generating random vertices and connecting them to each other to find the minimum cost path between two poses. In this work we propose a simple adaptation to RRT* denoted RC-RRT* that guarantees feasible paths with respect to the resource constraint. We prove that RC-RRT* is no longer probabilistically complete when applied to the RCSPP. Additionally we propose a Lagrangian Relaxation based RRT search denoted Lambda-RRT* which minimizes the relaxed cost given some relaxation parameter. We propose a method to update the relaxation parameter with each node added such that the minimum relaxed cost path converges to a feasible path. Finally we test the performance of both RC-RRT* and Lambda-RRT in a set of randomly generated planning scenarios.

Real-time wildfire prediction and estimation is paramount in the practice of wildland fire management. In this paper we propose a method of autonomous wildland fire monitoring via integrated path planning and sensor fusion. Accurate localized measurements made by a Unmanned Aerial System (UAS) equipped with a radiometric infrared camera are fused with a low fidelity Reaction Diffusion fire model using an ensemble Kalman filter (EnKF). We develop a reward function defined by the variance of the EnKF. We pose a fixed-time horizon reward maximization path planning problem to determine what sequence of measurements the UAS is to take, and solve it using a dynamic programming algorithm. We demonstrate the closed loop performance of the path planning and sensor fusion framework using real infrared video of a prescribed prairie burn to simulate a wildland fire.

The focus of this work is on examining the sense of belonging within aerospace engineering students across an undergraduate curriculum. Sense of belonging is typically viewed as being respected, valued, and accepted [1] and is a complex topic that includes many different features [2] [3]. It is also commonly viewed as a topic that is extremely important when considering inclusion and diversity initiatives. Gender specifically has been shown to impact sense of belonging in STEM disciplines with women reporting lower sense of belonging than men [4]. The Aerospace Engineering Program at The Ohio State University (OSU) is interested in examining sense of belonging as a way to investigate recruitment and retention efforts in their program. The retention of students in Aerospace Engineering, previously investigated by Kecskemety and Kajfez [5], found that at Ohio State, 21% of students in the Aerospace pre-major left engineering compared to only 15% of Mechanical engineering pre-majors. These two majors are part of the same department at Ohio State and thus have access to similar faculty, advisors, and other resources. Additionally, that study found that there were differences in retention trends for minoritized populations. In order to investigate this further, initial baseline data needs to be collected with respect to student sense of belonging and that is the goal of this work.

This paper employs belief function theory (also known as evidential reasoning) to infer the probable intentions behind close proximity maneuvers in orbit using only relative range and angle measurements. The problem is motivated by limited sensing capabilities in the space domain and a lack of known correlations between physical movements in space and the reasoning behind them. This work uses simulated range and angle measurements to approximate the dynamic movements of a deputy satellite classified as different maneuvers in the Hill reference frame. These maneuvers form a basis of physical characteristics that make up different potential intent trajectories. The basis maneuvers are then fused to formulate beliefs in said intentions. Two methods of maneuver classification are considered, which can modify the intention update method. These methods allow for the future propagation of credible intentions driving particular actions, and are tested via numerical simulation.

This paper discusses the predictive capability of Dynamic Mode Decomposition (DMD) in the context of orbital mechanics. The focus is specifically on the Hankel variant of DMD which uses a stacked set of time-delayed observations for system identification and subsequent prediction. A theory on the minimum number of time delays required for accurate reconstruction of periodic trajectories of nonlinear systems is presented and corroborated using experimental analysis. In addition, the window size for training and prediction regions, respectively, is presented. The need for a meticulous approach while using DMD is emphasized by comparing its performance on two candidate satellites, the ISS and MOLNIYA-3-50. Experiments are also presented for quasi-periodic scenarios with applied perturbing forces.

Collecting and annotating images for the purpose of training segmentation models is often cost prohibitive. In the domain of wildland fire science, this challenge is further compounded by the scarcity of reliable public datasets with labeled ground truth. This paper presents the Centralized Copy-Paste Data Augmentation (CCPDA) method, for the purpose of assisting with the training of deep-learning multiclass segmentation models, with special focus on improving segmentation outcomes for the fire-class. CCPDA has three main steps: (i) identify fire clusters in the source image, (ii) apply a centralization technique to focus on the core of the fire area, and (iii) paste the refined fire clusters onto a target image. This method increases dataset diversity while preserving the essential characteristics of the fire class. The effectiveness of this augmentation technique is demonstrated via numerical analysis and comparison against various other augmentation methods using a weighted sum-based multi-objective optimization approach. This approach helps elevate segmentation performance metrics specific to the fire class, which carries significantly more operational significance than other classes (fuel, ash, or background). Numerical performance assessment validates the efficacy of the presented CCPDA method in alleviating the difficulties associated with small, manually labeled training datasets. It also illustrates that CCPDA outperforms other augmentation strategies in the application scenario considered, particularly in improving fire-class segmentation performance.

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the temporally consistent Koopman autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE's superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.

In recent years, the development of the Lunar Gateway and Artemis missions has renewed interest in lunar exploration, including both manned and unmanned missions. This interest necessitates accurate initial orbit determination (IOD) and orbit prediction (OP) in this domain, which faces significant challenges such as severe nonlinearity, sensitivity to initial conditions, large state-space volume, and sparse, faint, and unreliable measurements. This paper explores the capability of data-driven Koopman operator-based approximations for OP in these scenarios. Three stable periodic trajectories from distinct cislunar families are analyzed. The analysis includes theoretical justification for using a linear time-invariant system as the data-driven surrogate. This theoretical framework is supported by experimental validation. Furthermore, the accuracy is assessed by comparing the spectral content captured to period estimates derived from the fast Fourier transform (FFT) and Poincare-like sections.

The Resource Constrained Shortest Path Problem (RCSPP) requires a minimum-cost simple path between two nodes that is subject to a resource consumption constraint. In this paper, we consider the Backtracking A* algorithm presented in previous works applied to the general RCSPP. Backtracking A* attempts to solve the RCSPP by iterative modification of paths generated by a shortest path algorithm such as A*. We consider the completeness of Backtracking A* and demonstrate that it cannot be a complete algorithm. Then we propose a complete, modified version of Backtracking A*. Finally, we give a result for the time complexity of Backtracking A*, and demonstrate it under worst-case conditions applied to randomly generated graphs.

We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particlein-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD-based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. We demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.

Accurate simulations of nonlinear kinetic plasma-wave interactions are essential for the design and analysis of high-power microwave devices, fusion energy devices, terahertz and directed energy devices, as well as for studying a host of ionosphere and magnetosphere phenomena and their impact on space assets. However, large-scale kinetic plasma simulations that rely on popular electromagnetic particle-in-cell (EMPIC) algorithms face a significant computational burden due to the need to individually simulate thousands to millions of charged particles (ions, electrons). To address this, reduced order models such as proper orthogonal decomposition (POD) [1] and dynamic mode decomposition (DMD) have proved especially useful [2].

Data-driven modeling of high-dimensional spatio-temporal dynamical systems, which are often governed by nonlinear partial differential equations (PDEs), poses a serious challenge in the absence of sufficient or high-quality training data. Recently developed Koopman autoencoders (KAEs) leverage the expressivity of deep neural networks (DNNs) and the spectral structure of Koopman operator to learn a reduced-order feature space exhibiting simpler linear dynamics. However, limited and noisy training datasets present a significant roadblock and results in a lack of generalizability due to inconsistency in training data. In this paper we propose the prediction-consistent Koopman autoencoder (pcKAE) which is capable of generating accurate long-term predictions even with limited and noisy training data. We introduce a consistency regularization term that enforces consistency among predictions at different time-steps, making pcKAE more robust and generalizable compared to its counterparts. An analytical justification is presented for such consistency regularization using the Koopman spectral theory. Experimentally, we demonstrate that with limited training data, pcKAE outperforms existing state-of-the-art KAE models for several test-cases, ranging from simple pendulum to kinetic plasmas, fluid flows and sea surface temperature data.

This short paper describes the potential for use of autonomous multi-UAS teams during all stages of a prescribed burn. The current state of practice of prescribed burning is labor intensive and based on numerous simplifying assumptions. UAS teams promise to increase efficiency and effectiveness, while creating the opportunity to develop new science related to fire behavior. Ingrained in the proposed UAS mission profiles is bi-directional feedback between sensing and computational components at multiple timescales, which is a hallmark of the Dynamic Data Driven Applications Systems (DDDAS) framework.

This paper presents a case study of wildland fire rate of spread estimation using an autonomous unmanned aerial system (UAS), deployed in a prescribed burn conducted in the Zaleski State Forest in South Ohio. In recent years, UAS have seen increasing use to measure the fire perimeter in active wildland burns. In this case study, we build and deploy a small UAS platform equipped with infrared sensing to measure the rate of spread of the fire front in a prescribed burn conducted in a forest environment with significant topographic expression. Infrared data retrieved from the experiment is re-projected into the three-dimensional world frame, followed by a novel geometrical analysis of the observed fire intensity contours. A Delaunay triangulation is conducted to discretize the space around time-separated fire fronts, resulting in local rate of spread estimates based on fire intensity gradients. The infrared data-based rate of spread estimates are compared against the output of a widely used fire behavior model called the Rothermel model. While the data-based calculations show a good match with the Rothermel model's mean predictions, the latter is shown to exhibit large sensitivity to topographic and environmental parameters, especially slope steepness of the terrain.

Electromagnetic particle-in-cell (EMPIC) algorithms have been a popular choice for simulating kinetic plasmas due to their ability to accurately capture complex transient nonlinear plasma phenomena. Despite the accuracy of EMPIC simulations, they incur high very high computational costs. This is a direct consequence of the large number of particles necessary to obtain accurate results. In this chapter, we discuss the use of Koopman autoencoders as effective machine learning based reduced-order models to mitigate the computational burden of traditional EMPIC algorithms. We discuss how deep learning architectures provide a natural data-driven route for approximating finite-dimensional Koopman invariant subspaces associated with kinetic plasma problems. We also provide a framework for the inclusion of physics-informed constraints into Koopman autoencoders models for this class of problems.