Physics-informed neural networks for data-efficient learning

Thesis

The physical world around us is profoundly complex and for centuries we have sought to develop a deeper understanding of how it functions. Building models capable of forecasting the long term dynamics of multi-physics systems such as complex blood flow, chaotic oscillators and quantum mechanical systems thus continues to be a critical challenge within the sciences. While traditional and computational tools have dramatically improved to address parts of this open problem, they face numerous challenges, remain computationally resource intensive, and are susceptible to severe error accumulation. Now, modern machine learning techniques, augmented by a plethora of sensor data, are driving significant progress in this direction, helping us uncover sophisticated relationships from underlying physical processes. An emergent area within this domain is hybrid physics-informed machine learning where partial prior knowledge of the physical system is integrated into the machine learning pipeline to improve predictive performance and data-efficiency. In this thesis, we investigate how existing knowledge about the physical world can be used to improve and augment predictive performance of neural networks. First, we show that learning biases designed to preserve structure, connectivity and energy such as graphs, integrators and Hamiltonians can be effectively combined to learn the dynamics of complex many-body energy-conserving systems from sparse, noisy data. Secondly, by embedding a generalized formalism of port-Hamiltonians into neural networks, we accurately recover the dynamics of irreversible physical systems from data. Furthermore, we highlight how our models, by design, can discover the underlying force and damping terms from sparse data as well as reconstruct the Poincar\'e section of chaotic systems. Lastly, we show that physics-informed neural networks can be effectively exploited for efficient and accurate transfer learning - achieving orders of magnitude speed-up while maintaining high-fidelity on numerous well studied differential equations. Collectively, these innovations show case a new direction for scientific machine learning - one where existing knowledge is combined with machine learning methods. Many benefits naturally arise as a consequence of this including (1) accurate learning and long-term predictions (2) data-efficiency (3) reliability and (4) scalability. Such hybrid models are paramount to developing robust machine learning methods capable of modeling and forecasting complex multi-fidelity, multi-scale physical processes.

Authors: Desai, S

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: digital twins; artificial intelligence; physics; machine learning; surrogates
• Subjects: Physics; Computer Science