Abstract
Machine learning offers unparalleled flexibility and adaptability, excelling at modeling complex systems by learning directly from data. However, data-driven models often face challenges in generalizing beyond their training data, particularly in the presence of noise or limited datasets. Physics-based models, on the other hand, rely on established laws to provide consistency and stability of predictions. Yet, these models often depend on simplifying assumptions, can be computationally demanding, and are less suited to capturing dynamic or evolving behaviors.
Physics-informed machine learning (PIML) is an umbrella term encompassing diverse methods that integrate physics knowledge with machine learning to leverage the strengths of both approaches. In the first chapter of this thesis, we explore the breadth of PIML methodologies. The subsequent chapters focus on three key contributions that demonstrate the potential of PIML in industrial and scientific applications, leading to more accurate and reliable models.
The first contribution focuses on condition monitoring algorithms for industrial systems, where safety and reliability are paramount. We propose a framework for developing fault detection algorithms in which we combine efficient unsupervised machine learning methods with expert validation. The resulting algorithm is validated on real operational data from maritime vessels, demonstrating its capability to identify a range of historical faults and detect a real-time thruster leakage earlier than conventional systems. The algorithm is currently commercially deployed by Brunvoll AS.
The second contribution addresses the challenge of multi-resolution learning in dynamical systems, leveraging the discretization-invariance of deep operator networks with the sequential modeling capabilities of recurrent neural networks.
By combining low-resolution data to model general dynamics with high-resolution data to refine detailed behaviors, the proposed DON-LSTM architecture reduces reliance on large high-resolution data that are often difficult to obtain. DON-LSTM consistently beats single-resolution vanilla models.
The third contribution extends the application of neural operators to long-time horizon predictions and extrapolation beyond the training data, focusing on their ability to ensure stability and accuracy in extended simulations. This capability is particularly relevant for industrial processes that require robust and reliable long-term forecasting.
To further enhance reliability, this thesis examines the integration of soft and hard constraints into neural operators, enforcing conservation laws such as mass and momentum.