Machine learning-based modeling of physical systems has attracted significant interest in recent years. Based solely on the underlying physical equations and initial and boundary conditions, these new approaches allow to approximate, for example, the complex flow of blood in the case of fluid dynamics. Physics-informed neural networks offer certain advantages compared to conventional computational fluid dynamics methods as they avoid the need for discretized meshes and allow to readily solve inverse problems and integrate additional data into the algorithms. Today, the majority of published reports on learning-based flow modeling relies on fully-connected neural networks. However, many different network architectures are introduced into deep learning each year, each with specific benefits for certain applications. In this paper, we present the first comprehensive comparison of various state-of-the-art networks and evaluate their performance in terms of computational cost and accuracy relative to numerical references. We found that while fully-connected networks offer an attractive balance between training time and accuracy, more elaborate architectures (e.g., Deep Galerkin Method) generated superior results. Moreover, we observed high accuracy in simple cylindrical geometries, but slightly poorer estimates in complex aneurysms. This paper provides quantitative guidance for practitioners interested in complex flow modeling using physics-based deep learning.

In burn medicine, the percentage of the burned body surface area (TBSA-B) to the total body surface area (TBSA) is a crucial parameter to ensure adequate treatment and therapy. Inaccurate estimations of the burn extent can lead to wrong medical decisions resulting in considerable consequences for patients. These include, for instance, over-resuscitation, complications due to fluid aggregation from burn edema, or non-optimal distribution of patients. Due to the frequent inaccurate TBSA-B estimation in practice, objective methods allowing for precise assessments are required. Over time, various methods have been established whose development has been influenced by contemporary technical standards. This article provides an overview of the history of burn size estimation and describes existing methods with a critical view of their benefits and limitations. Traditional methods that are still of great practical relevance were developed from the middle of the 20th century. These include the “Lund Browder Chart”, the “Rule of Nines”, and the “Rule of Palms”. These methods have in common that they assume specific values for different body parts’ surface as a proportion of the TBSA. Due to the missing consideration of differences regarding sex, age, weight, height, and body shape, these methods have practical limitations. Due to intensive medical research, it has been possible to develop three-dimensional computer-based systems that consider patients’ body characteristics and allow a very realistic burn size assessment. To ensure high-quality burn treatment, comprehensive documentation of the treatment process, and wound healing is essential. Although traditional paper-based documentation is still used in practice, it no longer meets modern requirements. Instead, adequate documentation is ensured by electronic documentation systems. An illustrative software already being used worldwide is “BurnCase 3D”. It allows for an accurate burn size assessment and a complete medical documentation.