arXiv subjects

Ryne Beeson

Publications and source records attributed to Ryne Beeson.

At least 19 recordsLinked to original sources

arXiv2026

Complexity Bounds and Approaches to Learning Projected Gradient Descent Solver Iterates

Data scarcity poses a fundamental challenge in training generative models to produce initial guesses for parametric optimization problems that are otherwise numerically expensive to solve. We therefore study a $k$-neighborhood data collection strategy that augments datasets of converged solutions with intermediate solver iterates, increasing the amount of training data without additional solver runs. To understand the benefits of this approach, we derive a generalization bound based on Rademacher complexity that reveals the role of the $k$-neighborhoods and related parameters. To achieve this result, we focus on one-sided box-constrained quadratic programs solved by projected gradient descent. We illustrate the behavior of this solver on two examples. The approach proposed in this paper enables a more capable DDDAS paradigm by improving the efficiency of the data-model-optimization loop. We finish by discussing two views of learning solver-iterate data and connect our analysis with GLENS, a new data-efficient global search method.

cs.LG↗

arXiv2026

GLENS: Global Search via Learning from Solver Iterates with Diffusion Models

We consider the problem of generating a large collection of initial guesses for local minima of multimodal non-convex continuous optimization problems. The goal is for these initial guesses to be high-quality (i.e., a numerical solver converges quickly) and diverse (i.e., represent many different local minima). Identifying multiple locally optimal solutions enables flexible downstream decision-making, but typically requires expensive global search. Existing data-driven methods predict initial guesses using only the final converged optima from offline solver runs, which discards information about the local neighborhoods of solutions and limits the available training data. We propose GLENS (Global Search via Learning from Solver Iterates), a data-efficient global search method that leverages intermediate solver iterates as free data augmentation. GLENS consists of two components: a neighborhood structure model that uses diffusion models to learn the local geometry around optima conditioned on problem parameters, and a solver behavior model that learns refinement directions to further guide samples towards nearby optima during diffusion sampling. Experiments on modified non-convex benchmark problems and a two-robot obstacle-avoidance navigation problem show that GLENS generates high-quality initial guesses while preserving the multimodal distribution of diverse local optima. The resulting initial guesses lead to faster solver convergence across different problem settings and solvers. We also analyze how key hyperparameter choices affect the performance.

cs.LG↗

arXiv2026

Transfer Learning of Multiobjective Indirect Low-Thrust Trajectories Using Diffusion Models and Markov Chain Monte Carlo

Preliminary low-thrust spacecraft mission design is a global search problem characterized by a complex solution landscape, multiple objectives, and numerous local minima. During this phase, mission parameters are often not yet fully defined, requiring new solutions to be generated at a high cadence across varying parameter values. When combined with the indirect approach to optimal control, diffusion models can accelerate this search by learning distributions that represent high-quality initial costates. However, generating training data remains expensive, and opportunities exist to better exploit past data. We propose a transfer-learning framework that combines homotopy in a mission parameter with Markov chain Monte Carlo (MCMC) to generate training data more efficiently. The approach reformulates a multiobjective optimization problem as sampling from an unnormalized target distribution in costate space. We compare three MCMC algorithms on a planar multi-revolution transfer in the circular restricted three-body problem, with homotopy in the system mass parameter. The results show that gradient-based MCMC variants achieve the best trade-off between sample quality and computational cost. For the test transfer, the proposed framework generates 40 % more feasible solutions and achieves a higher-quality Pareto front than a state-of-the-art indirect approach based on adjoint control transformations and gradient-based optimization. Finally, the MCMC-generated samples are used to fine-tune a diffusion model conditioned on the mass parameter, enabling it to learn a global representation of the underlying solution distribution and efficiently generate new solutions. These findings establish the transfer-learning framework as a practical method for efficiently solving indirect trajectory optimization problems with varying parameters.

eess.SY↗

arXiv2026

A Variational Pseudo-Observation Guided Nudged Particle Filter

Nonlinear filtering with standard PF methods requires mitigative techniques to quell weight degeneracy, such as resampling. This is especially true in high-dimensional systems with sparse observations. Unfortunately, such techniques are also fragile when applied to systems with exceedingly rare events. Nonlinear systems with these properties can be assimilated effectively with a control-based PF method known as the nPF, but this method has a high computational cost burden. In this work, we aim to retain this strength of the nudged method while reducing the computational cost by introducing a variational method into the algorithm that acts as a continuous pseudo-observation path. By maintaining a PF representation, the resulting algorithm continues to capture an approximation of the filtering distribution, while reducing computational runtime and improving robustness to the "rare" event of switching phases. Preliminary testing of the new approach is demonstrated on a stochastic variant of the nonlinear and chaotic L63 model, which is used as a surrogate for mimicking "rare" events. The new approach helps to overcome difficulties in applying the nPF for realistic problems and performs favorably with respect to a standard PF with a higher number of particles.

eess.SY↗

arXiv2025

Bi-Level Optimal Control Framework For Missed-Thrust-Design With First-Order Bounds On Maximum Missed-Thrust-Duration

In this paper, we present a bi-level optimal control framework for designing low-thrust spacecraft trajectories with robustness against missed-thrust-events. The upper-level (UL) problem generates a nominal trajectory assuming full control authority, while each lower-level (LL) problem computes the optimal recovery maneuver following a missed-thrust-event along the nominal solution. Under suitable regularity conditions ensuring uniqueness and smoothness of the LL response, the hierarchy admits a single-level reformulation by embedding the LL first-order optimality conditions within the UL constraints. We further establish a robustness certificate, which provides an upper bound on the maximum admissible missed-thrust-duration for which the structural assumptions remain valid for the LL problem. The bound depends explicitly on precomputable dynamical quantities along the nominal solution, enabling rapid evaluation over large ensembles without iterative solves. Numerical experiments show that while the certificate identifies when modeling assumptions are valid, it does not fully characterize recoverability after missed-thrust-events. A finite-horizon controllability-energy analysis is therefore used to interpret recovery beyond the theoretical bounds. Collectively, these results provide a deterministic, certifiable approach for incorporating robustness directly into trajectory design, replacing post-hoc margin allocation techniques with formal guarantees.

math.OC↗

arXiv2025

Gradient-Informed Monte Carlo Fine-Tuning of Diffusion Models for Low-Thrust Trajectory Design

Preliminary mission design of low-thrust spacecraft trajectories in the Circular Restricted Three-Body Problem is a global search characterized by a complex objective landscape and numerous local minima. Formulating the problem as sampling from an unnormalized distribution supported on neighborhoods of locally optimal solutions, provides the opportunity to deploy Markov chain Monte Carlo methods and generative machine learning. In this work, we extend our previous self-supervised diffusion model fine-tuning framework to employ gradient-informed Markov chain Monte Carlo. We compare two algorithms - the Metropolis-Adjusted Langevin Algorithm and Hamiltonian Monte Carlo - both initialized from a distribution learned by a diffusion model. Derivatives of an objective function that balances fuel consumption, time of flight and constraint violations are computed analytically using state transition matrices. We show that incorporating the gradient drift term accelerates mixing and improves convergence of the Markov chain for a multi-revolution transfer in the Saturn-Titan system. Among the evaluated methods, MALA provides the best trade-off between performance and computational cost. Starting from samples generated by a baseline diffusion model trained on a related transfer, MALA explicitly targets Pareto-optimal solutions. Compared to a random walk Metropolis algorithm, it increases the feasibility rate from 17.34% to 63.01% and produces a denser, more diverse coverage of the Pareto front. By fine-tuning a diffusion model on the generated samples and associated reward values with reward-weighted likelihood maximization, we learn the global solution structure of the problem and eliminate the need for a tedious separate data generation phase.

eess.SY↗

arXiv2025

Self-supervised diffusion model fine-tuning for costate initialization using Markov chain Monte Carlo

Global search and optimization of long-duration, low-thrust spacecraft trajectories with the indirect method is challenging due to a complex solution space and the difficulty of generating good initial guesses for the costate variables. This is particularly true in multibody environments. Given data that reveals a partial Pareto optimal front, it is desirable to find a flexible manner in which the Pareto front can be completed and fronts for related trajectory problems can be found. In this work we use conditional diffusion models to represent the distribution of candidate optimal trajectory solutions. We then introduce into this framework the novel approach of using Markov Chain Monte Carlo algorithms with self-supervised fine-tuning to achieve the aforementioned goals. Specifically, a random walk Metropolis algorithm is employed to propose new data that can be used to fine-tune the diffusion model using a reward-weighted training based on efficient evaluations of constraint violations and missions objective functions. The framework removes the need for separate focused and often tedious data generation phases. Numerical experiments are presented for two problems demonstrating the ability to improve sample quality and explicitly target Pareto optimality based on the theory of Markov chains. The first problem does so for a transfer in the Jupiter-Europa circular restricted three-body problem, where the MCMC approach completes a partial Pareto front. The second problem demonstrates how a dense and superior Pareto front can be generated by the MCMC self-supervised fine-tuning method for a Saturn-Titan transfer starting from the Jupiter-Europa case versus a separate dedicated global search.

astro-ph.EP↗

arXiv2025

Aligning Diffusion Model with Problem Constraints for Trajectory Optimization

Diffusion models have recently emerged as effective generative frameworks for trajectory optimization, capable of producing high-quality and diverse solutions. However, training these models in a purely data-driven manner without explicit incorporation of constraint information often leads to violations of critical constraints, such as goal-reaching, collision avoidance, and adherence to system dynamics. To address this limitation, we propose a novel approach that aligns diffusion models explicitly with problem-specific constraints, drawing insights from the Dynamic Data-driven Application Systems (DDDAS) framework. Our approach introduces a hybrid loss function that explicitly measures and penalizes constraint violations during training. Furthermore, by statistically analyzing how constraint violations evolve throughout the diffusion steps, we develop a re-weighting strategy that aligns predicted violations to ground truth statistics at each diffusion step. Evaluated on a tabletop manipulation and a two-car reach-avoid problem, our constraint-aligned diffusion model significantly reduces constraint violations compared to traditional diffusion models, while maintaining the quality of trajectory solutions. This approach is well-suited for integration into the DDDAS framework for efficient online trajectory adaptation as new environmental data becomes available.

cs.RO↗

arXiv2025

Nudged Particle Filter with Optimal Resampling Applied to the Duffing Oscillator

Efficiently solving the continuous-time signal and discrete-time observation filtering problem for chaotic dynamical systems presents unique challenges in that the advected distribution between observations may encounter a separatrix structure that results in the prior distribution being far from the observation or the distribution may become split into multiple disjoint components. In an attempt to sense and overcome these dynamical issues, as well as approximate a non-Gaussian distribution, a nudged particle filtering approach has been introduced. In the nudged particle filter method a control term is added, but has the potential drawback of degenerating the weights of the particles. To counter this issue, we introduce an intermediate resampling approach based on the modified Cram\'er-von Mises distance. The new method is applied to a challenging scenario of the non-chaotic, unforced nonlinear Duffing oscillator, which possesses a separatrix structure. Our results show that it consistently outperforms the standard particle filter with resampling and original nudged particle filter.

nlin.CD↗

arXiv2025

Predictive Planner for Autonomous Driving with Consistency Models

Trajectory prediction and planning are essential for autonomous vehicles to navigate safely and efficiently in dynamic environments. Traditional approaches often treat them separately, limiting the ability for interactive planning. While recent diffusion-based generative models have shown promise in multi-agent trajectory generation, their slow sampling is less suitable for high-frequency planning tasks. In this paper, we leverage the consistency model to build a predictive planner that samples from a joint distribution of ego and surrounding agents, conditioned on the ego vehicle's navigational goal. Trained on real-world human driving datasets, our consistency model generates higher-quality trajectories with fewer sampling steps than standard diffusion models, making it more suitable for real-time deployment. To enforce multiple planning constraints simultaneously on the ego trajectory, a novel online guided sampling approach inspired by the Alternating Direction Method of Multipliers (ADMM) is introduced. Evaluated on the Waymo Open Motion Dataset (WOMD), our method enables proactive behavior such as nudging and yielding, and also demonstrates smoother, safer, and more efficient trajectories and satisfaction of multiple constraints under a limited computational budget.

cs.RO↗

arXiv2025

Global Search for Optimal Low Thrust Spacecraft Trajectories using Diffusion Models and the Indirect Method

Long time-duration low-thrust nonlinear optimal spacecraft trajectory global search is a computationally and time expensive problem characterized by clustering patterns in locally optimal solutions. During preliminary mission design, mission parameters are subject to frequent changes, necessitating that trajectory designers efficiently generate high-quality control solutions for these new scenarios. Generative machine learning models can be trained to learn how the solution structure varies with respect to a conditional parameter, thereby accelerating the global search for missions with updated parameters. In this work, state-of-the-art diffusion models are integrated with the indirect approach for trajectory optimization within a global search framework. This framework is tested on two low-thrust transfers of different complexity in the circular restricted three-body problem. By generating and analyzing a training data set, we develop mathematical relations and techniques to understand the complex structures in the costate domain of locally optimal solutions for these problems. A diffusion model is trained on this data and successfully accelerates the global search for both problems. The model predicts how the costate solution structure changes, based on the maximum spacecraft thrust magnitude. Warm-starting a numerical solver with diffusion model samples for the costates at the initial time increases the number of solutions generated per minute for problems with unseen thrust magnitudes by one to two orders of magnitude in comparison to samples from a uniform distribution and from an adjoint control transformation.

eess.SY↗

arXiv2025

Initial Guess Generation for Low-Thrust Trajectory Design with Robustness to Missed-Thrust-Events

The growing interest in cislunar space exploration in recent years has driven an increasing demand for efficient low-thrust missions to key cislunar orbits. These missions, typically possessing long thrust arcs, are particularly susceptible to operational uncertainties such as missed thrust events. Addressing these challenges requires efficient robust trajectory design frameworks during the preliminary mission design phase, where it is necessary to explore the solution space at a rapid cadence under evolving operational constraints. However, existing methods for missed thrust design rely on solving high-dimensional nonlinear programs, where generating effective initial guesses becomes challenging. To enhance computational efficiency, quality, and depth of robustness of solutions from global search, we compare two initial guess strategies: a baseline non-conditional global search, which samples from a static distribution with global support, and a conditional global search, which generates initial guesses conditioned on solutions to problems with less depth of robustness. The conditional search provides a sequential procedure for solving increasingly robust problems. We validate the improvements in the conditional approach using a low-thrust case study for the Lunar Gateway Power and Propulsion Element, where our results demonstrate that it significantly improves convergence rate and solution quality, highlighting its potential in preliminary robust trajectory design.

math.OC↗

arXiv2024

Global Search of Optimal Spacecraft Trajectories using Amortization and Deep Generative Models

Preliminary spacecraft trajectory optimization is a parameter dependent global search problem that aims to provide a set of solutions that are of high quality and diverse. In the case of numerical solution, it is dependent on the original optimal control problem, the choice of a control transcription, and the behavior of a gradient based numerical solver. In this paper we formulate the parameterized global search problem as the task of sampling a conditional probability distribution with support on the neighborhoods of local basins of attraction to the high quality solutions. The conditional distribution is learned and represented using deep generative models that allow for prediction of how the local basins change as parameters vary. The approach is benchmarked on a low thrust spacecraft trajectory optimization problem in the circular restricted three-body problem, showing significant speed-up over a simple multi-start method and vanilla machine learning approaches. The paper also provides an in-depth analysis of the multi-modal funnel structure of a low-thrust spacecraft trajectory optimization problem.

math.OC↗

arXiv2024

Learning Optimal Control and Dynamical Structure of Global Trajectory Search Problems with Diffusion Models

Spacecraft trajectory design is a global search problem, where previous work has revealed specific solution structures that can be captured with data-driven methods. This paper explores two global search problems in the circular restricted three-body problem: hybrid cost function of minimum fuel/time-of-flight and transfers to energy-dependent invariant manifolds. These problems display a fundamental structure either in the optimal control profile or the use of dynamical structures. We build on our prior generative machine learning framework to apply diffusion models to learn the conditional probability distribution of the search problem and analyze the model's capability to capture these structures.

cs.LG↗

arXiv2024

Algorithmic Considerations for Effective Global Search of Robust Low-Thrust Trajectories

The growing interest in the cislunar domain over the past decade has led to an increasing demand for low-thrust missions to key orbits within this region. These low-thrust missions, typically characterized by long thrust arcs, are highly susceptible to operational disruptions such as unforeseen thruster outages or missed thrust events. Consequently, there is a critical need for efficient trajectory design frameworks which incorporate robustness against such anomalies. In this study, we utilize a robust trajectory design framework to explore the solution space for the Power and Propulsion Element (PPE) module to the Earth-Moon L2 Southern 9:2 Near Rectilinear Halo Orbit. We propose algorithmic enhancements to improve the global search for robust solutions, and present a comprehensive analysis of two approaches: a nonconditional approach which involves a purely random search for robust solutions versus a conditional approach which involves warm-starting the search for robust solutions using the non-robust solutions. Our results indicate that by using non-robust solutions as initial guesses for the robust solutions, it is possible to achieve significant improvements in both the rate of convergence and the robustness of the final solutions.

math.NA↗

arXiv2024

Statistical Analysis of the Role of Invariant Manifolds on Robust Trajectories

As low-thrust space missions increase in prevalence, it is becoming increasingly important to design robust trajectories against unforeseen thruster outages or missed thrust events. Accounting for such events is particularly important in multibody systems, such as the cislunar realm, where the dynamics are chaotic and the dynamical flow is constrained by pertinent dynamical structures. Yet the role of these dynamical structures in robust trajectory design is unclear. This paper provides the first comprehensive statistical study of robust and non-robust trajectories in relation to the invariant manifolds of resonant orbits in a circular restricted three-body problem. For both the non-robust and robust solutions analyzed in this study, the optimal subset demonstrates a closer alignment with the invariant manifolds, while the overall feasible set frequently exhibits considerable deviations. Robust optimal trajectories shadow the invariant manifolds as closely as the non-robust optimal trajectories, and in some cases, demonstrate closer alignment than the non-robust solutions. By maintaining proximity to these structures, low-thrust solutions are able to efficiently utilize the manifolds to achieve optimality even under operational uncertainties.

math.OC↗

arXiv2024

Constraint-Aware Diffusion Models for Trajectory Optimization

The diffusion model has shown success in generating high-quality and diverse solutions to trajectory optimization problems. However, diffusion models with neural networks inevitably make prediction errors, which leads to constraint violations such as unmet goals or collisions. This paper presents a novel constraint-aware diffusion model for trajectory optimization. We introduce a novel hybrid loss function for training that minimizes the constraint violation of diffusion samples compared to the groundtruth while recovering the original data distribution. Our model is demonstrated on tabletop manipulation and two-car reach-avoid problems, outperforming traditional diffusion models in minimizing constraint violations while generating samples close to locally optimal solutions.

cs.LG↗

arXiv2024

DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization

Optimal trajectory design is computationally expensive for nonlinear and high-dimensional dynamical systems. The challenge arises from the non-convex nature of the optimization problem with multiple local optima, which usually requires a global search. Traditional numerical solvers struggle to find diverse solutions efficiently without appropriate initial guesses. In this paper, we introduce DiffuSolve, a general diffusion model-based solver for non-convex trajectory optimization. An expressive diffusion model is trained on pre-collected locally optimal solutions and efficiently samples initial guesses, which then warm-starts numerical solvers to fine-tune the feasibility and optimality. We also present DiffuSolve+, a novel constrained diffusion model with an additional loss in training that further reduces the problem constraint violations of diffusion samples. Experimental evaluations on three tasks verify the improved robustness, diversity, and a 2$\times$ to 11$\times$ increase in computational efficiency with our proposed method, which generalizes well to trajectory optimization problems of varying challenges.

cs.RO↗