Real-time inversion using self-explainable deep learning driven by expert knowledge
Lead Research Organisation:
University of Nottingham
Department Name: Sch of Mathematical Sciences
Abstract
IN-DEEP is a European Doctoral Network composed of nine doctoral candidates (DCs) and top scientists with complementary areas of expertise in applied mathematics, artificial intelligence, high-performance computing, and engineering applications. Its main goal is to provide high-level training to the nine DCs in designing, implementing, and using explainable knowledge-driven Deep Learning (DL) algorithms for rapidly and accurately solving inverse problems governed by partial differential equations (PDEs).
Inverse problems in which the unknown parameters are connected to experimental measurements through PDEs cover from medical applications - like cancer growth assessment - to the safety of civil infrastructures, and green geophysical applications such as geothermal energy production. Their application value is measured in human lives and society's well-being, which goes beyond any quantifiable amount of money. This is why equipping a new generation of specialists with highly-demanded skills for the upcoming transition toward safe and robust AI-based technologies is imperative.
Despite the promising results in many applications, DL for PDEs has severe limitations. The most troublesome is its lack of a solid theoretical background and explainability, which prevents potential users from integrating them into high-risk applications. IN-DEEP aims to remove these constraints to unleash the full potential of DL algorithms for PDEs. We will achieve this by: (a) focusing on emerging applications of DL for PDEs with immense societal and/or industrial value, (b) designing mathematics-infused advanced solvers to address them efficiently, and (c) involving, from the beginning, industrial and technological agents which can monitor, upscale, and exploit this knowledge. On the way, we shall establish the foundations of a better knowledge exchange ecosystem amongst the main academic and industrial actors within Europe, disseminating the results worldwide.
Inverse problems in which the unknown parameters are connected to experimental measurements through PDEs cover from medical applications - like cancer growth assessment - to the safety of civil infrastructures, and green geophysical applications such as geothermal energy production. Their application value is measured in human lives and society's well-being, which goes beyond any quantifiable amount of money. This is why equipping a new generation of specialists with highly-demanded skills for the upcoming transition toward safe and robust AI-based technologies is imperative.
Despite the promising results in many applications, DL for PDEs has severe limitations. The most troublesome is its lack of a solid theoretical background and explainability, which prevents potential users from integrating them into high-risk applications. IN-DEEP aims to remove these constraints to unleash the full potential of DL algorithms for PDEs. We will achieve this by: (a) focusing on emerging applications of DL for PDEs with immense societal and/or industrial value, (b) designing mathematics-infused advanced solvers to address them efficiently, and (c) involving, from the beginning, industrial and technological agents which can monitor, upscale, and exploit this knowledge. On the way, we shall establish the foundations of a better knowledge exchange ecosystem amongst the main academic and industrial actors within Europe, disseminating the results worldwide.
Organisations
People |
ORCID iD |
| Kristoffer Van Der Zee (Principal Investigator) |
| Title | Uzawa algorithm for Minimal Residual problems |
| Description | An Uzawa-type algorithm is proposed and analysed that can be used to solve mathematical problems described by Minimal Residual formulations involving a dual (supremum) norm, applicable to, e.g., weak formulations of general partial differential equations (PDEs). |
| Type Of Material | Computer model/algorithm |
| Year Produced | 2025 |
| Provided To Others? | No |
| Impact | This is a state-of-the-art algorithm that allows the robust solution of a significantly-broader class of partial differential equations (PDEs). It is furthermore designed to be extendable to handle neural-network approximations, thereby providing one of the best-possible algorithms to solve PDEs. |
| Description | EU Consortium Meeting Workshop |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Postgraduate students |
| Results and Impact | All the 8 Marie-Curie Doctoral Candidates (PhD Students) in the Doctoral Network attended this workshop, as well as several of their supervisors and collaborators from their (academic and industrial) institutes. Plenty of questions, discussion and interaction arose because of the presentations given by supervisors and PhD students on their research, as well as from the training given by experts. New ideas were shared and discovered during the meeting, and plans made for future interaction through the planned PhD Student placements (secondments). |
| Year(s) Of Engagement Activity | 2024,2025 |
| URL | https://www.in-deep.science/activities |