Few-Shot Learning by Explicit Physics Integration: An Application to Groundwater Heat Transport

Machine learning methods often struggle with real-world applications in science and engineering due to limited or low-quality training data. In this work, the example of groundwater flow with heat transport is considered; this corresponds to an advection-diffusion process under heterogeneous flow conditions, that is, spatially distributed material parameters and heat sources. Classical numerical simulations are costly and challenging due to high spatio-temporal resolution requirements and large domains. While often computationally more efficient, purely data-driven surrogate models face difficulties, particularly in predicting the advection process, which is highly sensitive to input variations and involves long-range spatial interactions. Therefore, in this work, a Local-Global Convolutional Neural Network (LGCNN) approach is introduced. It combines a lightweight numerical surrogate for the transport process (global) with convolutional neural networks for the groundwater velocity and heat diffusion processes (local). With the LGCNN, a city-wide subsurface temperature field is modeled, involving a heterogeneous groundwater flow field and one hundred groundwater heat pump injection points forming interacting heat plumes over long distances. The model is first systematically analyzed based on random subsurface input fields. Then, the model is trained on a handful of cut-outs from a real-world subsurface map of the Munich region in Germany, and it scales to larger cut-outs without retraining. All datasets, our code, and trained models are published for reproducibility.

Deep learning based surrogate modeling for thermal plume prediction of groundwater heat pumps

The ability for groundwater heat pumps to meet space heating and cooling demands without relying on fossil fuels, has prompted their mass roll out in dense urban environments. In regions with high subsurface groundwater flow rates, the thermal plume generated from a heat pump's injection well can propagate downstream, affecting surrounding users and reducing their heat pump efficiency. To reduce the probability of interference, regulators often rely on simple analytical models or high fidelity groundwater simulations to determine the impact that a heat pump has on the subsurface aquifer and surrounding heat pumps. These are either too inaccurate or too computationally expensive for everyday use. In this work, a surrogate model was developed to provide a quick, high accuracy prediction tool of the thermal plume generated by a heat pump within heterogeneous subsurface aquifers. Three variations of a convolutional neural network were developed that accepts the known groundwater Darcy velocities as discrete two-dimensional inputs and predicts the temperature within the subsurface aquifer around the heat pump. A data set consisting of 800 numerical simulation samples, generated from random permeability fields and pressure boundary conditions, was used to provide pseudo-randomized Darcy velocity fields as input fields and the temperature field solution for training the network. The subsurface temperature field output from the network provides a more realistic temperature field that follows the Darcy velocity streamlines, while being orders of magnitude faster than conventional high fidelity solvers

CLAIRE -- Parallelized Diffeomorphic Image Registration for Large-Scale Biomedical Imaging Applications

We study the performance of CLAIRE -- a diffeomorphic multi-node, multi-GPU image-registration algorithm, and software -- in large-scale biomedical imaging applications with billions of voxels. At such resolutions, most existing software packages for diffeomorphic image registration are prohibitively expensive. As a result, practitioners first significantly downsample the original images and then register them using existing tools. Our main contribution is an extensive analysis of the impact of downsampling on registration performance. We study this impact by comparing full-resolution registrations obtained with CLAIRE to lower-resolution registrations for synthetic and real-world imaging datasets. Our results suggest that registration at full resolution can yield a superior registration quality -- but not always. For example, downsampling a synthetic image from $1024^3$ to $256^3$ decreases the Dice coefficient from 92% to 79%. However, the differences are less pronounced for noisy or low-contrast high-resolution images. CLAIRE allows us not only to register images of clinically relevant size in a few seconds but also to register images at unprecedented resolution in a reasonable time. The highest resolution considered is CLARITY images of size $2816\times3016\times1162$. To the best of our knowledge, this is the first study on image registration quality at such resolutions.

A Deep Learning Approach for Thermal Plume Prediction of Groundwater Heat Pumps

Climate control of buildings makes up a significant portion of global energy consumption, with groundwater heat pumps providing a suitable alternative. To prevent possibly negative interactions between heat pumps throughout a city, city planners have to optimize their layouts in the future. We develop a novel data-driven approach for building small-scale surrogates for modelling the thermal plumes generated by groundwater heat pumps in the surrounding subsurface water. Building on a data set generated from 2D numerical simulations, we train a convolutional neural network for predicting steady-state subsurface temperature fields from a given subsurface velocity field. We show that compared to existing models ours can capture more complex dynamics while still being quick to compute. The resulting surrogate is thus well-suited for interactive design tools by city planners.

Partitioned Deep Learning of Fluid-Structure Interaction

We present a partitioned neural network-based framework for learning of fluid-structure interaction (FSI) problems. We decompose the simulation domain into two smaller sub-domains, i.e., fluid and solid domains, and incorporate an independent neural network for each. A library is used to couple the two networks which takes care of boundary data communication, data mapping and equation coupling. Simulation data are used for training of the both neural networks. We use a combination of convolutional and recurrent neural networks (CNN and RNN) to account for both spatial and temporal connectivity. A quasi-Newton method is used to accelerate the FSI coupling convergence. We observe a very good agreement between the results of the presented framework and the classical numerical methods for simulation of 1d fluid flow inside an elastic tube. This work is a preliminary step for using neural networks to speed-up the FSI coupling convergence by providing an accurate initial guess in each time step for classical numerical solvers