Academic Journal
Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schrödinger Bridge, and Reaction-Diffusion PDEs.
| Τίτλος: | Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schrödinger Bridge, and Reaction-Diffusion PDEs. |
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| Συγγραφείς: | Teter, Alexis M. H., Nodozi, Iman, Halder, Abhishek |
| Πηγή: | SIAM Journal on Applied Dynamical Systems; 2025, Vol. 24 Issue 1, p16-43, 28p |
| Θεματικοί όροι: | Boundary value problems, Orbital mechanics, Probability density function, Time perspective, Machine learning |
| Περίληψη: | The Lambert problem originated in orbital mechanics. It is concerned with determining the initial velocity for a boundary value problem involving the dynamical constraint due to gravitational potential with additional time horizon and endpoint position constraints. Its solution has application in transferring a spacecraft from a given initial to a given terminal position within a prescribed flight time via velocity control. We consider a probabilistic variant of the Lambert problem where the knowledge of the endpoint constraints in position vectors is replaced by the knowledge of their respective joint probability density functions. We show that the Lambert problem with endpoint joint probability density constraints is a generalized optimal mass transport (OMT) problem, thereby connecting this classical astrodynamics problem with a burgeoning area of research in modern stochastic control and stochastic machine learning. This newfound connection allows us to rigorously establish the existence and uniqueness of solution for the probabilistic Lambert problem. The same connection also helps to numerically solve the probabilistic Lambert problem via diffusion regularization, i.e., by leveraging further connection of the OMT with the Schrödinger bridge problem (SBP). This also shows that the probabilistic Lambert problem with additive dynamic process noise is a generalized SBP and can be solved numerically using the so-called Schrödinger factors, as we do in this work. Our analysis leads to solving a system of reaction-diffusion PDEs where the gravitational potential appears as the reaction rate. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Applied Dynamical Systems is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: edb DbLabel: Complementary Index An: 183533385 RelevancyScore: 984 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 983.694702148438 |
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| Items | – Name: Title Label: Title Group: Ti Data: Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schrödinger Bridge, and Reaction-Diffusion PDEs. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Teter%2C+Alexis+M%2E+H%2E%22">Teter, Alexis M. H.</searchLink><br /><searchLink fieldCode="AR" term="%22Nodozi%2C+Iman%22">Nodozi, Iman</searchLink><br /><searchLink fieldCode="AR" term="%22Halder%2C+Abhishek%22">Halder, Abhishek</searchLink> – Name: TitleSource Label: Source Group: Src Data: SIAM Journal on Applied Dynamical Systems; 2025, Vol. 24 Issue 1, p16-43, 28p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Orbital+mechanics%22">Orbital mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Probability+density+function%22">Probability density function</searchLink><br /><searchLink fieldCode="DE" term="%22Time+perspective%22">Time perspective</searchLink><br /><searchLink fieldCode="DE" term="%22Machine+learning%22">Machine learning</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The Lambert problem originated in orbital mechanics. It is concerned with determining the initial velocity for a boundary value problem involving the dynamical constraint due to gravitational potential with additional time horizon and endpoint position constraints. Its solution has application in transferring a spacecraft from a given initial to a given terminal position within a prescribed flight time via velocity control. We consider a probabilistic variant of the Lambert problem where the knowledge of the endpoint constraints in position vectors is replaced by the knowledge of their respective joint probability density functions. We show that the Lambert problem with endpoint joint probability density constraints is a generalized optimal mass transport (OMT) problem, thereby connecting this classical astrodynamics problem with a burgeoning area of research in modern stochastic control and stochastic machine learning. This newfound connection allows us to rigorously establish the existence and uniqueness of solution for the probabilistic Lambert problem. The same connection also helps to numerically solve the probabilistic Lambert problem via diffusion regularization, i.e., by leveraging further connection of the OMT with the Schrödinger bridge problem (SBP). This also shows that the probabilistic Lambert problem with additive dynamic process noise is a generalized SBP and can be solved numerically using the so-called Schrödinger factors, as we do in this work. Our analysis leads to solving a system of reaction-diffusion PDEs where the gravitational potential appears as the reaction rate. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of SIAM Journal on Applied Dynamical Systems is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/24M1646145 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 28 StartPage: 16 Subjects: – SubjectFull: Boundary value problems Type: general – SubjectFull: Orbital mechanics Type: general – SubjectFull: Probability density function Type: general – SubjectFull: Time perspective Type: general – SubjectFull: Machine learning Type: general Titles: – TitleFull: Probabilistic Lambert Problem: Connections with Optimal Mass Transport, Schrödinger Bridge, and Reaction-Diffusion PDEs. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Teter, Alexis M. H. – PersonEntity: Name: NameFull: Nodozi, Iman – PersonEntity: Name: NameFull: Halder, Abhishek IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 15360040 Numbering: – Type: volume Value: 24 – Type: issue Value: 1 Titles: – TitleFull: SIAM Journal on Applied Dynamical Systems Type: main |
| ResultId | 1 |