Project Details
Projekt
Deep-learning based modeling and extraction of unknown dynamics in fluid dynamical systems
Applicant
Dr.-Ing. Christian Lagemann
Subject Area
Fluid Mechanics
Term
since 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 525788404
Fluid flows are characterized by high-dimensional, nonlinear dynamical systems that exhibit rich multi-scale phenomena in both space and time. However, they typically evolve on a low-dimensional attractor that may be characterized by spatial-temporal coherent structures. The description of these structures is not straightforward and even for simple fluid dynamical systems it may appear enigmatically complex. For these problems, we usually rely on data-analytics tools and try to find tractable and interpretable reduced-order models. However, most of the frequently used approaches share the main requirement that the underlying set of state variables must be known before any novel low-level system description can be discovered. For many research problems, however, scientists only have access to data which do not directly correspond to the variable space of the underlying system and only represents its evolution. Without prior knowledge or further analysis, there is no possibility to discover the underlying set of ordinary or partial differential equations. Hence, the ability to extract knowledge on the basis of longitudinal observations without prior knowledge, e.g., experimental observations such as particle images or other flow field visualizations, states a game changer for problems where we have no or only restricted access to the variable space of the underlying system. Novel algorithms that specifically tackle these challenges will help scientists to gain insight into underlying, complex phenomena of observed systems, especially when theory and observations do not agree on physical relations. It is thus of great importance to have tools for automated scientific discovery that distil raw sensory perceptions into a compact set of state variables and their relationships. Therefore, the overarching goal of this research proposal is to design robust neural representations that capture and understand temporal dynamics and complex relations from regularly and irregularly sampled real-world observational data without any prior knowledge. That is, no limiting assumptions regarding knowledge and accessibility of the underlying state variables, dynamical system, observation setup, and sampling strategy are imposed. Thus, novel and interpretable models of challenging fluid mechanical applications including new attractors, transients, and intermittent phenomena can be discovered. Moreover, since observational data from experimental measurements are often of sparse nature, the proposed approach has the unique ability to determine unobserved states in-between captured time samples enhancing the temporal resolution up to a continuous representation. The proposed method can further evolve the observed state space to future states going beyond the captured time samples to generate entirely unseen system states. Hence, frequent experimental burdens such as a restricted sampling frequency or a limited camera storage capacity can be mitigated.
DFG Programme
WBP Fellowship
International Connection
USA
