Inference and Collective Steering for Stochastic and Deterministic Systems

New Directions in Schrödinger Bridges and Optimal Transport
Erscheinungsjahr 2027
ISBN: 978-3-032-43660-3
Verlag: Springer

Buch, Englisch, Format (B × H): 155 mm x 235 mm

Reihe: Springer Theses

This book makes an original and substantial contribution to the mathematical theory of stochastic particle flows in settings where particles may drift, stop, be created, or be killed. The work builds on the classical Schrödinger bridge framework, introduced to reconcile observed statistical data with stochastic dynamics, and extends it in a new and physically meaningful direction. The thesis’ central innovation is the incorporation of spatio-temporal creation and killing into the Schrödinger bridge paradigm. This allows one to model, for instance, particles transported by a flow that may be deposited along the way, or new particles entering the system, while still matching prescribed statistical observations. Beyond this physical intuition, the thesis develops a rigorous Markovian probabilistic framework in which drift, stopping, creation, and killing jointly determine probability laws on sample paths. A particularly important feature of the work is its dual interpretation: as an inference problem, it asks how stochastic dynamics should be updated in light of observed statistics; as a control problem, it asks how drift and creation/killing rates should be chosen to steer a population toward prescribed distributions. By placing this duality on a rigorous foundation and linking it to optimal mass transport, the thesis opens a novel and promising direction.

Zielgruppe

Research

Autoren/Hrsg.

Eldesoukey, Asmaa

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

1. An Overview of Schr¨odinger Bridges and Optimal Transport.- 2. Schr¨odinger Bridges over Stopped Processes.- 3. Schr¨odinger Bridges over Killed Diffusion Processes.- 4. Tracer-Informed Optimal Transport.

Über Autor(innen)

Asmaa Eldesoukey is a postdoctoral Scholar in the Department of Aerospace Engineering at Iowa State University. She received her B.Sc. degree in Aerospace Engineering from Zewail University of Science and Technology, Giza, Egypt, in 2018. She received her M.Sc. and Ph.D. in Mechanical and Aerospace Engineering from the University of California, Irvine in 2021 and 2025, respectively. Asmaa is a co-recipient of the best student paper award at the American Control Conference in 2023, the recipient of the outstanding student paper award from the Control Systems Community at the IEEE Conference on Decision and Control (CDC), 2024, and the Paul and Beverly Holmes Endowed Fellowship from Henri Samueli School of Engineering, 2024. Her research interests are in stochastic control, variational inference, and inverse problems.