An Application to the Kinetic Chemotaxis Inverse Problem
Buch, Englisch, 231 Seiten, Format (B × H): 155 mm x 235 mm
ISBN: 978-3-032-24016-3
Verlag: Springer Nature Switzerland AG
Experimental design is a central task in inverse problems that concerns the planning of data collection in accordance with a specific reconstruction goal. In general, not all data are equally informative. Choices made when setting up an experiment - such as how measurements are taken or how the physical test system is designed - alongside other factors, determine whether the resulting data contain useful information for the inference problem. In practice, where only a limited amount of data can be collected, it is therefore crucial to focus on highly informative experiments in order to enable reconstruction and improve its quality. With this in mind, we hope to encourage an interdisciplinary perspective on inverse problems, in which planning, experimentation, and inference are carried out in collaboration between practitioners and mathematicians.
Traditionally, experimental design has been formulated as an optimization problem: identifying the “best” experiments according to a chosen mathematical criterion. This approach is often ambitious, and the associated computational costs can be substantial. In this book, we advocate for a broader notion of experimental design that incorporates additional nuances. In particular, we adopt a qualitative perspective: rather than searching for optimal experiments, the goal is to identify experiments that enable reliable reconstruction. This viewpoint has gained increasing attention in recent years, and we review two methods that are rooted in identifiability analysis and sensitivity analysis: a theory-based approach and a sampling-based approach. Both shall be illustrated on an example from mathematical biology: chemotaxis, the directed movement of bacteria in response to chemical signals, along with the associated inverse problem of reconstructing motion parameters.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
Weitere Infos & Material
Introduction.- Inverse Problems.- Identifiability analysis.- Experimental Design.- The Inverse Problem for Chemotaxis. Structural Identifiability.- Theory-based Experimental Design.- Numerical experiments.- Experimental Design through Sampling.- Discussion, Appendix.
