This project is connected to NTNU AMOS, as a collaboration between NTNU, SINTEF and FFI to develop methods for improved learning of dynamical systems from data. The focus will be on method development based on mathematical theory, and on applying the methods to learn models that may give move accurate control of underwater and surface vehicles.
Dynamical systems are systems that describe how a system changes with time. In classical modelling such systems are typically given by differential equations, which one must solve to predict future behaviour. It is often not possible to solve these equations analytically, in which case one can use numerical methods, or so-called numerical integrators, to approximate the solutions. The differential equations to be solved are typically based on underlying scientific laws, but maybe also assumptions that are necessary simplifications of the reality. This can be due to too high model complexity or because too little is known about the underlying dynamics. However, if there is available data describing the state of the system at various times, these can be used to train a machine learning model of the system.
In DynNoise, an investigation will be performed on how techniques from numerical integration, an established field, can be used and developed further in the new setting of learning dynamical systems from data. Much of the established theory and known methods from numerical integration can be applied in the training of the machine learning models, but the properties of the methods will then have to be seen in a new light. Furthermore, DynNoise will also consider the development of new methods that address the specific challenges of training from noisy data, as this is expected to be prevalent in most applications.
SINTEF Digital and the Norwegian Defence Research Establishment (FFI) are both involved as partners in the Centre for Autonomous Marine Operations and Systems (NTNU AMOS). We are seeking funding for two years of a PhD project within physics-informed machine learning, with applications to underwater robotics. The candidate will be employed at the Department of Mathematics at NTNU. In addition to AMOS, the PhD student will be connected to several other ongoing projects linked to this research area.
Hybrid modeling combines data-driven and analytical modeling. This approach enables the simulation of dynamical systems from data, allowing physical principles and numerical analysis to inform and constrain deep learning models. In particular, Hamiltonian neural networks leverages the energy-preserving Hamiltonian formulation from classical mechanics to obtain a deep learning model that describes the dynamics of a physical system. Geometric numerical integration is a well-established field concerning numerical solutions that preserve geometric structure or follow first principles. Geometric integration and classical mechanics combine centuries of theoretical discoveries. Deep learning serves as an enabling technology allowing a range of complex systems to be modeled from data. A combination of these fields could trigger a revolution in mathematical modeling of dynamical systems. This PhD project aims at combining the mathematical rigor of geometric integration with the approximation capacity of neural networks, allowing neural networks to learn dynamical systems from data while preserving geometric structure. Furthermore, this project will explore how a learned system could support scientific discovery in underwater robotics and be applied in control of autonomous navigation vehicles.