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

近年来，人工智能和机器学习领域的巨大进步不可避免地影响了生物医学领域，并推动了一种以数据为中心的个性化医学新范式。然而，在生物力学方面，除非以基于物理的模型的形式提供的丰富而丰富的领域知识被纳入其中，否则仅凭数据不能得出令人满意的答案。例如，考虑弹性成像，它代表了这一提议的主要应用领域，并使用在组织变形期间收集的成像数据来产生诊断。这是通过使用基于物理的模型来实现的，该模型实现了该过程的非侵入性，在易用性、成本和降低患者的并发症风险方面具有优势。此外，机械特性的识别可以导致更早和更准确的诊断，并最终能够制定针对患者的治疗策略，而不是依赖于原始图像并可能检测到组织密度变化的纯粹基于数据的技术。数据与连续介质力学模型的融合带来了一些挑战，本项目的目标是在以下三个方面做出新的贡献：不确定性量化、模型误差和计算效率。不确定性在所有以数据为中心的问题中扮演着核心角色，因此必须将其量化。不确定性的明显来源是数据本身，这些数据总是有噪音，经常是稀缺的或不完整的。另一个在相关文献中基本上被忽视的不确定性来源是来自模型本身的不确定性。虽然所使用的模型概括了几十年来积累的知识，但它们是物理现实的不完美和理想化。即使总是可以将模型参数与数据进行匹配，但如果模型不正确，可能会导致错误的诊断和预测。我们打算解决的第三个挑战与解决基于模型的逆问题的计算复杂性有关。事实上，所有相关的数值技术都依赖于一个适定的正演模型的可用性，该模型需要求解数百万次，每一次求解都可能需要在多个CPU或定制的硬件上运行几个小时。该项目提出了一个新的贝叶斯框架，它克服了传统的、基于黑盒的配方的局限性。控制方程被视为数据源(虚拟可观测值)，以自监督的方式自适应地和分层地挖掘。此外，我们提出了一个物理可解释的框架，它区分可靠和不可靠的控制方程，并可以提供问题域中模型误差的量化指标。最后，我们提出了算法改进，解决了计算可伸缩性问题，并更接近实时诊断能力。

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.