Physics-informed machine learning: from concepts to real-world applications

Thesis

Machine learning (ML) has caused a fundamental shift in how we practice science, with many now placing learning from data at the focal point of their research. As the complexity of the scientific problems we want to study increases, and the amount of data generated by today's scientific experiments grows, ML is helping to automate, accelerate and enhance traditional workflows.

Emerging at the forefront of this revolution is a field called scientific machine learning (SciML). The central goal of SciML is to more tightly combine existing scientific understanding with ML, generating powerful ML algorithms which are informed by our prior knowledge.

A plethora of approaches exist for incorporating scientific principles into ML and expectations are rising for SciML to address some of the biggest challenges in science. However, the field is burgeoning and many questions are still arising. A major one is whether SciML approaches can scale to more complex, real-world problems. Much SciML research is at a proof-of-concept stage, where techniques are validated on simplified, toy problems. Yet, understanding how well they scale to more complex problems is essential for them to become widely applicable.

This question is of central focus in this thesis. Firstly, multiple different physics-informed ML approaches are designed for three complex, real-world, domain-specific case studies taken from the fields of lunar science and geophysics, and their performance and scalability is assessed. Secondly, the scalability of physics-informed neural networks, a popular and general SciML approach, for solving differential equations with large domains and high frequency solutions is evaluated and improved. Common observations across these studies are discussed, and significant advantages and underlying limitations are identified, highlighting the importance of designing scalable SciML techniques.

Authors: Moseley, B

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: differential equations; real-world problems; domain decomposition; geophysics; scientific machine learning; physics-informed machine learning; lunar science; machine learning; scientific computing; physics-informed neural networks; deep learning; seismic simulation; permanently shadowed regions; neural networks
• Subjects: Physics; Machine learning; Moon; Differential equations, Partial; Seismology; Deep learning (Machine learning); Geophysics; Neural networks (Computer science)