Machine Learning for Data Driven Sound Propagation Modelling - Ref 43


This PhD project is part of the CDT in Distributed Algorithms: The What, How and where of Next-Generation Data Science.

The University of Liverpool’s Centre for Doctoral Training in Distributed Algorithms (CDT) is working in partnership with the STFC Hartree Centre and 20+ external partners from the manufacturing, defence and security sectors to provide a 4-year innovative PhD training course that will equip over 60 students with: the essential skills needed to become future leaders in distributed algorithms; the technical and professional networks needed to launch a career in next generation data science and future computing; and the confidence to make a positive difference in society, the economy and beyond.

The successful PhD student will be co-supervised by Dr Daniel Colquitt and work alongside our external partner Dstl. The industry supervisor will be Dr Duncan Williams: Chief Scientist Acoustics.  

Sound is the primary method used for a wide variety of underwater activities, including communication, sonar, navigation, exploration, and monitoring. These activities span a broad spectrum of domains from marine biology and climatology, to defence, navigation, and transport.  Future concepts for monitoring of the underwater environment include distributed acoustic sensors. Effective exploitation of distributed acoustic sensors relies on our ability to understand the differences in propagation between the individual sensors, resulting from complex and dynamic ocean processes, allowing for example coherent processing. Understanding the propagation of sound in ocean environments is not a new problem but we still lack a comprehensive understanding of the complex processes that are involved. Indeed, sound propagation is itself highly complex depending on a wide range of factors that change both spatially and temporally, across disparate scales – even on the calmest days, the sea is constantly changing, which affects how sound propagates. However, presently, only the simplest factors are included in existing propagation models and developing new frameworks presents several interrelated challenges.

The mechanisms associated with these phenomena are rarely studied and remain poorly understood, particularly from a mathematical and physical perspective; the majority of studies in this area are stochastic in nature and, although these models provide useful predictive capability, by their very nature, they cannot offer real physical insight into the processes involved. The present project will address these deficiencies by developing models that are simultaneously data-driven and physically realistic in order to enhance the understanding of complex and critical dynamic phenomena that have substantial impact on the propagation of sound through our oceans.

This project will develop a series of high-fidelity digital twins capable of encapsulating a number of critical dynamic phenomena, which affect the propagation of sound waves through ocean environments, including internal waves, multi-scale structural thermal and temporal variations and fluctuations, scattering by non-smooth interfaces and boundaries (e.g. semi-submerged structures, sea bed, surface), currents, eddies, and fronts.

The resulting sound propagation models, and advanced understanding embodied within these models, will enable the Royal Navy and other users of the ocean, the means to improve the effectiveness of their sonar systems and achieve the best results from sonar deployments and operations.

The project will develop high-fidelity digital twins using new adaptive hybrid numerical-analytical approaches, which incorporate real-world data. The models will be capable of intelligently adapting their approach and selecting the best solution method based on the input data, computational and operational constraints, desired  outputs, and physical configuration. These models will incorporate advances in Finite Element Methods, via GPU parallel computing capability that has been largely untapped for underwater acoustics, along with hybrid semi-analytic coupling methods. Stochastic analysis of physical scattering models, incorporating real-world data, will provide a major step forward in the capability available to investigate dynamic ocean mechanisms. Analysis of simulated and measured oceanographic and acoustic data, including the use of artificial intelligence and machine learning techniques, will be supported by a parallel PhD project In the Department of Mathematical Sciences on Advances in mathematical modelling to study complex sound propagation in an inhomogeneous moving ocean,. This will help to identify the properties and behaviour of different mechanisms. New ways of representing the specified mechanisms will be developed, and environment-specific modelling tools and innovative mathematical representations will be implemented.

The focus of the project will be on machine learning models that can characterise successfully sound propagation in dynamic ocean environments, in the presence of multi-scale processes which are computationally or mathematically difficult to represent in physical models, in order to efficiently and intelligently estimate sound propagation for any sonar deployment.

This studentship is open to  British and EU nationals who are willing and able to obtain  UK gov security clearance.

This studentship is due to commence on 1 October 2023.

Students will be based at the University of Liverpool and will be part of the CDT and Signal Processing  research community - a large, social and creative research group that works together solving tough research problems.  Students have two academic supervisors and an industrial partner who provide co-supervision, placements and the opportunity to work on real world challenges. In addition, students attend technical and professional training to gain unparalleled expertise to make a difference now and in the future.

The CDT is committed to providing an inclusive environment in which diverse students can thrive. The CDT particularly encourages applications from women, disabled and Black, Asian and Minority Ethnic candidates, who are currently under-represented in the sector.  We can also consider part time PhD students.  We also encourage talented individuals from various backgrounds, with either an UG or MSc in a numerate subject and people with ambition and an interest in making a difference. 

Please visit the Distributed Algorithms CDT website to discover more about the research work and the people who make it happen.

Contact the named supervisors in the first instance or visit the CDT website for Director, Student Ambassador and Centre Manager details.

Name and email address to direct enquiries to:

Application Web Address:
Visit the CDT website for application instructions, FAQs, interview timelines and guidance.


Open to EU/UK applicants

Funding information

Funded studentship

This project is a funded Studentship for 4 years in total and will provide UK tuition fees and maintenance at the UKRI Doctoral Stipend rate £17,668 per annum, 2022/23 rate).

Please enter the following information on your application:

  • Admission Term: 2023/2024
  • Application Type: Research Degree (MPhil/PhD/MD) – Full time
  • Programme of Study: Electrical Engineering and Electronics – Doctor in Philosophy (PhD)

The remainder of the guidance is found in the CDT application instructions on our website.

Visit the CDT website for further funding and eligibility information.