Deep learning approaches to surrogates for solving the diffusion equation for mechanistic real-world simulations

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. PDE surrogates enable use of larger models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1e3 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application.

Construction and Usage of a Human Body Common Coordinate Framework Comprising Clinical, Semantic, and Spatial Ontologies

The National Institutes of Health's (NIH) Human Biomolecular Atlas Program (HuBMAP) aims to create a comprehensive high-resolution atlas of all the cells in the healthy human body. Multiple laboratories across the United States are collecting tissue specimens from different organs of donors who vary in sex, age, and body size. Integrating and harmonizing the data derived from these samples and 'mapping' them into a common three-dimensional (3D) space is a major challenge. The key to making this possible is a 'Common Coordinate Framework' (CCF), which provides a semantically annotated, 3D reference system for the entire body. The CCF enables contributors to HuBMAP to 'register' specimens and datasets within a common spatial reference system, and it supports a standardized way to query and 'explore' data in a spatially and semantically explicit manner. [...] This paper describes the construction and usage of a CCF for the human body and its reference implementation in HuBMAP. The CCF consists of (1) a CCF Clinical Ontology, which provides metadata about the specimen and donor (the 'who'); (2) a CCF Semantic Ontology, which describes 'what' part of the body a sample came from and details anatomical structures, cell types, and biomarkers (ASCT+B); and (3) a CCF Spatial Ontology, which indicates 'where' a tissue sample is located in a 3D coordinate system. An initial version of all three CCF ontologies has been implemented for the first HuBMAP Portal release. It was successfully used by Tissue Mapping Centers to semantically annotate and spatially register 48 kidney and spleen tissue blocks. The blocks can be queried and explored in their clinical, semantic, and spatial context via the CCF user interface in the HuBMAP Portal.