A Prefixed Patch Time Series Transformer for Two-Point Boundary Value Problems in Three-Body Problems
Authors: Akira Hatakeyama, Shota Ito, Toshihiko Yanase, Naoya Ozaki
Abstract
Two-point boundary value problems for cislunar trajectories present significant challenges in circler restricted three body problem, making traditional analytical methods like Lambert's problem inapplicable. This study proposes a novel approach using a prefixed patch time series Transformer model that automates the solution of two-point boundary value problems from lunar flyby to arbitrary terminal conditions. Using prefix tokens of terminal conditions in our deep generative model enables solving boundary value problems in three-body dynamics. The training dataset consists of trajectories obtained through forward propagation rather than solving boundary value problems directly. The model demonstrates potential practical utility for preliminary trajectory design in cislunar mission scenarios.
The papers around it, by date and closeness
Higher is closer to this paper; left is older. Lines join papers close to each other: groups of lines are sub-topics. Select a point to see why it is there. Back to the summary of this paper
Papers around this one
Ranked by how close their title and abstract are to this paper’s. Select some to read them together.
Closest papers
-
A Time Series is Worth 64 Words: Long-term Forecasting with TransformersYuqi Nie, Nam H. Nguyen, Phanwadee Sinthong et al. · 2022 · Machine Learning · cited 5,238 times · AI summary available
Abstract
We propose an efficient design of Transformer-based models for multivariate time series forecasting and self-supervised representation learning. It is based on two key components: (i) segmentation of time series into subseries-level patches which are served as input tokens to Transformer; (ii) channel-independence where each channel contains a single univariate time series that shares the same embedding and Transformer weights across all the series. Patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend long…
-
Transformers for Trajectory Optimization with Application to Spacecraft RendezvousT. Guffanti, Daniele Gammelli, Simone D'Amico et al. · 2023 · IEEE Aerospace Conference · cited 38 times · Not summarized yet
Abstract
Reliable and efficient trajectory optimization methods are a fundamental need for autonomous dynamical systems, effectively enabling applications including rocket landing, hypersonic reentry, spacecraft rendezvous, and docking. Within such safety-critical application areas, the complexity of the emerging trajectory optimization problems has motivated the application of AI-based techniques to enhance the performance of traditional approaches. However, current AI-based methods either attempt to fully replace traditional control algorithms, thus lacking constraint satisfaction guarantees and incurring in expensive simulation, or aim to solely imitate the behavior of traditional methods via supe…
-
Diffusion Policies for Generative Modeling of Spacecraft TrajectoriesJulia Briden, Breanna Johnson, Richard Linares et al. · 2025 · AIAA SCITECH 2025 Forum · cited 10 times · Not summarized yet
Abstract
Machine learning has demonstrated remarkable promise for solving the trajectory generation problem and in paving the way for online use of trajectory optimization for resource-constrained spacecraft. However, a key shortcoming in current machine learning-based methods for trajectory generation is that they require large datasets and even small changes to the original trajectory design requirements necessitate retraining new models to learn the parameter-to-solution mapping. In this work, we leverage compositional diffusion modeling to efficiently adapt out-of-distribution data and problem variations in a few-shot framework for 6 degree-of-freedom (DoF) powered descent trajectory generation. …
-
Physics-Constrained Convolutional Recurrent Neural Networks for Solving Spatial-Temporal PDEs With Arbitrary Boundary ConditionsGuangfa Li, Yanglong Lu, De-Hao Liu · 2024 · Conference on Computability in Europe · Not summarized yet
Abstract
The inception of physics-constrained or physics-informed machine learning represents a paradigm shift, addressing the challenges associated with data scarcity and enhancing model interpretability. This innovative approach incorporates the fundamental laws of physics as constraints, guiding the training process of machine learning models. In this work, the physics-constrained convolutional recurrent neural network is further extended for solving spatial-temporal partial differential equations with arbitrary boundary conditions. Two notable advancements are introduced: the implementation of boundary conditions as soft constraints through finite difference-based differentiation, and the establi…
-
Amortized Global Search for Efficient Preliminary Trajectory Design with Deep Generative ModelsAnjian Li, Amlan Sinha, Ryne T. Beeson · 2023 · arXiv.org · preprint, not peer reviewed · cited 13 times · Not summarized yet
Abstract
Preliminary trajectory design is a global search problem that seeks multiple qualitatively different solutions to a trajectory optimization problem. Due to its high dimensionality and non-convexity, and the frequent adjustment of problem parameters, the global search becomes computationally demanding. In this paper, we exploit the clustering structure in the solutions and propose an amortized global search (AmorGS) framework. We use deep generative models to predict trajectory solutions that share similar structures with previously solved problems, which accelerates the global search for unseen parameter values. Our method is evaluated using De Jong's 5th function and a low-thrust circular r…
-
Cislunar navigation is an observability problem: arc-length thresholds, Gramian conditioning, and the Doppler leverChakshu Baweja · 2026 · Signal Processing · AI summary available
In short
For the studied cislunar configurations, range-only navigation requires dynamical observability over time, while Doppler enables instantaneous full-state observability and interferometry resolves a small-constellation joint-estimation deficiency.
-
iTransformer: Inverted Transformers Are Effective for Time Series ForecastingYong Liu, Tengge Hu, Haoran Zhang et al. · 2023 · Machine Learning · cited 2,727 times · AI summary available
Abstract
The recent boom of linear forecasting models questions the ongoing passion for architectural modifications of Transformer-based forecasters. These forecasters leverage Transformers to model the global dependencies over temporal tokens of time series, with each token formed by multiple variates of the same timestamp. However, Transformers are challenged in forecasting series with larger lookback windows due to performance degradation and computation explosion. Besides, the embedding for each temporal token fuses multiple variates that represent potential delayed events and distinct physical measurements, which may fail in learning variate-centric representations and result in meaningless atte…
-
Smooth multi-patch scaled boundary isogeometric analysis for Kirchhoff-Love shellsMathias Reichle, Jeremias Arf, Bernd Simeon et al. · 2023 · Numerical Analysis · cited 16 times · AI summary available
Abstract
In this work, a linear Kirchhoff-Love shell formulation in the framework of scaled boundary isogeometric analysis is presented that aims to provide a simple approach to trimming for NURBS-based shell analysis. To obtain a global C1-regular test function space for the shell discretization, an inter-patch coupling is applied with adjusted basis functions in the vicinity of the scaling center to ensure the approximation ability. Doing so, the scaled boundary geometries are related to the concept of analysis-suitable G1 parametrizations. This yields a coupling of patch boundaries in a strong sense that is restricted to G1-smooth surfaces. The proposed approach is advantageous to trimmed geometri…
Prior work it builds on
-
Diffusion Models for Generating Ballistic Spacecraft TrajectoriesTyler Presser, Agnimitra Dasgupta, Daniel Erwin et al. · 2024 · arXiv.org · preprint, not peer reviewed · cited 6 times · Not summarized yet
Abstract
Generative modeling has drawn much attention in creative and scientific data generation tasks. Score-based Diffusion Models, a type of generative model that iteratively learns to denoise data, have shown state-of-the-art results on tasks such as image generation, multivariate time series forecasting, and robotic trajectory planning. Using score-based diffusion models, this work implements a novel generative framework to generate ballistic transfers from Earth to Mars. We further analyze the model's ability to learn the characteristics of the original dataset and its ability to produce transfers that follow the underlying dynamics. Ablation studies were conducted to determine how model perfor…
-
Robust interplanetary trajectory design under multiple uncertainties via meta-reinforcement learningL. Federici, A. Zavoli · 2023 · Acta Astronautica · cited 23 times · Not summarized yet
-
Real-Time Guidance for Low-Thrust Transfers Using Deep Neural NetworksD. Izzo, Ekin Öztürk · 2021 · Journal of Guidance Control and Dynamics · cited 112 times · Not summarized yet
Abstract
We consider the Earth–Venus mass-optimal interplanetary transfer of a low-thrust spacecraft and show that the optimal guidance can be represented by deep networks in a large portion of the state sp...
-
EQUULEUS Trajectory DesignK. Oguri, K. Oshima, S. Campagnola et al. · 2020 · The Journal of the Astronautical Sciences · cited 54 times · Not summarized yet
-
N-BEATS: Neural basis expansion analysis for interpretable time series forecastingBoris N. Oreshkin, Dmitri Carpov, Nicolas Chapados et al. · 2019 · International Conference on Learning Representations · cited 1,894 times · Not summarized yet
Abstract
We focus on solving the univariate times series point forecasting problem using deep learning. We propose a deep neural architecture based on backward and forward residual links and a very deep stack of fully-connected layers. The architecture has a number of desirable properties, being interpretable, applicable without modification to a wide array of target domains, and fast to train. We test the proposed architecture on several well-known datasets, including M3, M4 and TOURISM competition datasets containing time series from diverse domains. We demonstrate state-of-the-art performance for two configurations of N-BEATS for all the datasets, improving forecast accuracy by 11% over a statisti…
Papers that cite it
-
Multi-constraint spacecraft close-range observation effectiveness evaluation and optimization via a feedback-coefficient scheduled RLNNAHong-Sheng Hu, Yu-Fei Luo, Yun-He Meng · 2026 · Astrodynamics · Not summarized yet
Go further
How are these papers found?
We compare the title and abstract of this paper with those of every paper summarized on this site, and with the papers Semantic Scholar recommends, those it cites and those citing it (for a much-cited paper, its most recent citations and, from OpenAlex, the most cited ones). Among the prior work and the follow-ups, the papers that use each other in depth, a method it uses and the much-cited follow-ups come a little higher. The levels (very close, close, related) come from the similarity of the texts, not from a judgment of quality; * marks a paper without an abstract, compared by its title. The sentence under a paper is written by an AI from the two abstracts: check it in the papers. A paper marked not relevant by three readers leaves the list.
Updated on 1 November 2026.