Real-time inversion using self-explainable deep learning driven by expert knowledge

In-Deep是一个欧洲博士网络，由9名博士生(DC)和顶尖科学家组成，他们在应用数学、人工智能、高性能计算和工程应用方面具有互补的专业知识。它的主要目标是为九个DC提供设计、实施和使用可解释的知识驱动的深度学习(DL)算法的高级培训，以快速和准确地解决由偏微分方程(PDE)控制的反问题。在这些反问题中，未知参数通过偏微分方程与实验测量相联系，涵盖从医疗应用(如癌症生长评估)到民用基础设施的安全，以及绿色地球物理应用(如地热能生产)。它们的应用价值是以人的生命和社会福祉来衡量的，这超出了任何可以量化的金钱数量。这就是为什么为即将到来的向安全和健壮的基于人工智能的技术过渡而配备具有高要求技能的新一代专家是当务之急。尽管在许多应用中取得了令人振奋的结果，但PDE的DL具有严重的局限性。最麻烦的是它缺乏坚实的理论背景和可解释性，这使得潜在用户无法将其集成到高风险应用程序中。In-Deep的目标是消除这些限制，以释放偏微分方程组的DL算法的全部潜力。我们将通过以下方式实现这一点：(A)专注于具有巨大社会和/或工业价值的PDE的数字逻辑的新兴应用；(B)设计数学灌输的高级解算器，以有效地解决这些问题；以及(C)从一开始就让能够监测、升级和利用这些知识的工业和技术机构参与进来。在此过程中，我们将为欧洲主要学术和工业参与者之间更好的知识交流生态系统奠定基础，并将成果传播到世界各地。

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.