Enabling efficient and certifiable solutions in diagnostic biomechanics by rephrasing model-based inverse problems.

• Applicant: Professor Phaedon-Stelios Koutsourelakis, Ph.D.
• Subject Area: Mechanics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 499746055

The prodigious advances of recent years in artificial intelligence and machine learning have unavoidably impacted the biomedical sector and have fueled a novel, data-centric paradigm for personalized medicine. Nevertheless andin biomechanics in particular, data alone, cannot lead to satisfactory answers unless the rich and plentiful domain knowledge that is available in the form of physics-based models is incorporated. Consider for example elastography which represents the primary application domain of this proposal and employs imaging data collected during the deformation of tissue in order to produce a diagnosis. This is achieved by using a physics-based model which enables the non-invasiveness of the procedure that is advantageous in terms of ease, cost and reducing the risk of complications to the patient. Furthermore, rather than purely data-based techniques which rely on the raw, imaging and can detect perhaps variations in tissue density, the identification of mechanical properties can lead to earlier and more accurate diagnosis and ultimately enable to patient-specific treatment strategies. The fusion of data with continuum-mechanics' models poses several challenges and the present project aims to make novel contributions along the following three fronts: uncertainty quantification, model errors and computational efficiency. Uncertainty plays a central role in all data-centric problems and it is imperative that it is quantified. The obvious source of uncertainty is the data itself which are invariably noisy, frequently scarce or incomplete. Another source of uncertainty that has been largely ignored in pertinent literature is the one stemming from the model itself. While the models employed encapsulate knowledge accumulated over decades, they are imperfect, idealizations of the physical reality. Even though it is always possible to fit model parameters to data, if the model is incorrect, it can lead to incorrect diagnosis and prognosis. The third challenge that we intend to address pertains to the computational complexity of solving model-based, inverse problems. Practically all pertinent numerical techniques rely on the availability of a well-posed, forward model which needs to be solved millions of times and each of these solves might require several hours on multiple CPUs or bespoke hardware. The project proposes a novel Bayesian framework which overcomes the limitations of traditional, black-box-based formulations. The governing equations are treated as data sources (virtual observables) which are adaptively and hierarchically mined in a self-supervised fashion. In addition, we propose a physically interpretable framework that distinguishes between reliable and unreliable governing equations and can provide quantitative indicators of model errors over the problem domain.Finally, we propose algorithmic advances that address computational scalability issues and draw nearer to real-time, diagnostic capabilities.

• DFG Programme: Research Grants