The Alan Turing Insitute redesigns the Finite Element Method (FEM)

Headed by Professor Mark Girolami (Programme Director for Data-Centric Engineering at the Turing, Sir Kirby Laing Professor of Civil Engineering and Royal Academy of Engineering Research Chair at the University of Cambridge) and led by The Alan Turing Institute, an international consortium of researchers including the University of Cambridge and The University of Western Australia (UWA) has redesigned the Finite Element Method (FEM).

The FEM, a tool that provides computer-simulated solutions to otherwise unsolvable mathematical models of complex systems, has been the cornerstone of modern day applied mathematics, numerical analysis and engineering. But the ability to integrate data with the FEM to improve techniques for making physical model predictions has been overlooked – until now.

In redesigning the FEM, the team has laid the theoretical foundations and developed methodologies by which Digital Twins can be realised. They report their findings in the prestigious Proceedings of the National Academy of Sciences (PNAS), one of the world's most-cited and comprehensive multidisciplinary scientific journals.

Recent advances in data acquisition technologies suggested the need to Girolami and his team that the FEM needed to be reconsidered from a statistical perspective. This resulted in a new FEM: a powerful combination of both data and mathematical models that provides enhancements of predictions in engineering and scientific applications.

“By accepting that our mathematical descriptions of complex systems can be wrong, or at best miss-specified, and not capture all aspects of the system, we were able to define a statistical description of the FEM that provided a very natural, entirely novel and extremely powerful way to blend data and mathematical models,” said Professor Girolami.

The research published in PNAS demonstrates the method in the context of internal ocean waves (solitons), which regularly occur on Australia’s North West Shelf and are a threat to critical offshore infrastructure such as wind turbines.

Connor Duffin, PhD student from UWA’s School of Physics, Mathematics and Computing and lead author on the paper, explains that, “These waves have a significant impact on the engineering design, safety and operations of the offshore energy industry, and improved methods of prediction provides significant benefit.”
 
In addition, the research has the potential to impact and transform most areas of the sciences and engineering, with commercial interest a strong possibility.

Professor Girolami highlights the implications of the research for the advancement of Digital Twins: “Digital Twins – the pairing of the physical and virtual world – are of significant current interest to the broader engineering community. By integrating data with FEMs, this new work provides the foundation and methodology by which these Digital Twins can be realised. It lays the mathematical foundations of the Digital Twin revolution.”

“It also serves as an ideal springboard into the forthcoming Australian Research Council Industrial Transformation Research Hub for Transforming Energy Infrastructure through Digital Engineering, hosted at UWA and directed by Shell Professor Phil Watson, with which The Alan Turing Institute and Cambridge Centre for Smart Infrastructure and Construction are very excited to collaborate,” he concludes. 
 
Notes to editors

• Researchers involved in the project include Connor Duffin, Edward Cripps, Thomas Stemler from The University of Western Australia, and Mark Girolami from The Alan Turing Institute and the University of Cambridge.
• Reference: Mark Girolami et al. ‘Statistical finite elements for misspecified models’. Proceedings of the National Academy of Sciences – PNAS (2021). https://www.pnas.org/content/118/2/e2015006118