{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:37:00Z","timestamp":1777901820507,"version":"3.51.4"},"reference-count":54,"publisher":"American Institute of Aeronautics and Astronautics (AIAA)","issue":"5","funder":[{"name":"DEVCOM Analysis Center","award":["W911NF-22-2-0001"],"award-info":[{"award-number":["W911NF-22-2-0001"]}]}],"content-domain":{"domain":["arc.aiaa.org"],"crossmark-restriction":true},"short-container-title":["Journal of Aerospace Information Systems"],"published-print":{"date-parts":[[2026,5]]},"abstract":"<jats:p>Systems like aircraft and spacecraft are expensive to operate in the real world. The design, validation, and testing for such systems therefore rely on a combination of mathematical modeling, abundant numerical simulations, and a relatively small set of real-world experiments. Due to modeling errors, simplifications, and uncertainties, the data synthesized by simulation models often do not match data from the system\u2019s real-world operation. We consider the broad research question of whether this model mismatch can be significantly reduced by generative artificial intelligence models (GAIMs). Loosely speaking, a GAIM learns to transform a set of uniformly or normally distributed vectors to a set of outputs with a distribution similar to that of a training dataset. Unlike text or image processing, where generative models have attained recent successes, GAIM development for aerospace engineering applications must not only train with scarce operational data, but their outputs must also satisfy governing equations based on natural laws, e.g., conservation laws. With this motivation, we study GAIMs for dynamic systems. The scope of this paper primarily focuses on two case studies of optimally controlled systems that are commonly understood and employed in aircraft guidance, namely, minimum-time navigation in a wind field and minimum-exposure navigation in a threat field. For these case studies, we report GAIMs that are trained with a relatively small set on the order of a few hundred examples and with underlying governing equations. By focusing on optimally controlled systems, we formulate training loss functions based on invariance of the Hamiltonian function along system trajectories. As an additional case study, we consider GAIMs for high-dimensional linear time-invariant (LTI) systems with process noise of unknown statistics. LTI dynamic systems are widely used for control design in aerospace engineering. We investigate three GAIM architectures, namely, the generative adversarial network and two variants of the variational autoencoder (VAE). We provide architectural details and thorough performance analyses of these models. The main finding is that our new models, especially the VAE-based models, are able to synthesize data that satisfy the governing equations and are statistically similar to the training data despite small volumes of training data.<\/jats:p>","DOI":"10.2514\/1.i011631","type":"journal-article","created":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T17:03:03Z","timestamp":1775408583000},"page":"393-412","update-policy":"https:\/\/doi.org\/10.2514\/aiaa_crossmarkpolicy","source":"Crossref","is-referenced-by-count":0,"title":["Case Studies of Generative Machine Learning Models for Dynamic Systems"],"prefix":"10.2514","volume":"23","author":[{"given":"Nachiket U.","family":"Bapat","sequence":"first","affiliation":[{"name":"Worcester Polytechnic Institute"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Randy C.","family":"Paffenroth","sequence":"additional","affiliation":[{"name":"Worcester Polytechnic Institute"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9365-3021","authenticated-orcid":false,"given":"Raghvendra V.","family":"Cowlagi","sequence":"additional","affiliation":[{"name":"Worcester Polytechnic Institute"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1387","reference":[{"key":"r1","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2017.2773458"},{"key":"r2","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2019.2962338"},{"key":"r3","doi-asserted-by":"crossref","unstructured":"GuptaS.DurakU.EllisO.TorensC. \u201cFrom Operational Scenarios to Synthetic Data: Simulation-Based Data Generation for AI-Based Airborne Systems,\u201d AIAA Paper 2022-2103, 2022. 10.2514\/6.2022-2103","DOI":"10.2514\/6.2022-2103"},{"key":"r4","doi-asserted-by":"crossref","unstructured":"SissonN.MoncayoH. \u201cMachine Learning Based Architecture for Generation of Synthetic Flight Test Data,\u201d AIAA Paper 2023-1814, 2024. 10.2514\/6.2023-1814","DOI":"10.2514\/6.2023-1814"},{"key":"r5","doi-asserted-by":"publisher","DOI":"10.2514\/6.2024-1462"},{"key":"r6","doi-asserted-by":"publisher","DOI":"10.2514\/4.866852"},{"key":"r7","unstructured":"IoannouP.SunJ., Robust Adaptive Control, Dover, Mineola, NY, 2012, pp.\u00a075\u201376."},{"key":"r8","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719376"},{"key":"r9","doi-asserted-by":"publisher","DOI":"10.1561\/2200000071"},{"key":"r10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-75178-4_4"},{"key":"r11","unstructured":"RameshA.DhariwalP.NicholA.ChuC.ChenM. \u201cHierarchical Text-Conditional Image Generation with CLIP Latents,\u201d 2022, https:\/\/arxiv.org\/abs\/2204.06125. 10.48550\/arXiv.2204.06125"},{"key":"r12","first-page":"1","author":"Nguyen N.","year":"2022","journal-title":"Proceedings of the 19th International Conference on Mining Software Repositories"},{"key":"r13","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2024.3350004"},{"issue":"10","key":"r14","first-page":"027836492412736","volume":"44","author":"Chi C.","year":"2023","journal-title":"International Journal of Robotics Research"},{"key":"r15","unstructured":"PresserT.DasguptaA.ErwinD.OberaiA. \u201cDiffusion Models for Generating Ballistic Spacecraft Trajectories,\u201d arXiv preprint arXiv: 2405.11738, 2024. 10.48550\/arXiv.2405.11738."},{"key":"r16","doi-asserted-by":"crossref","unstructured":"BapatN. 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