Encoder-decoder Convolutional Neural Network Research Articles

A deep learning based dual encoder–decoder framework for anatomical structure segmentation in chest X-ray images

Automated multi-organ segmentation plays an essential part in the computer-aided diagnostic (CAD) of chest X-ray fluoroscopy. However, developing a CAD system for the anatomical structure segmentation remains challenging due to several indistinct structures, variations in the anatomical structure shape among different individuals, the presence of medical tools, such as pacemakers and catheters, and various artifacts in the chest radiographic images. In this paper, we propose a robust deep learning segmentation framework for the anatomical structure in chest radiographs that utilizes a dual encoder–decoder convolutional neural network (CNN). The first network in the dual encoder–decoder structure effectively utilizes a pre-trained VGG19 as an encoder for the segmentation task. The pre-trained encoder output is fed into the squeeze-and-excitation (SE) to boost the network’s representation power, which enables it to perform dynamic channel-wise feature calibrations. The calibrated features are efficiently passed into the first decoder to generate the mask. We integrated the generated mask with the input image and passed it through a second encoder–decoder network with the recurrent residual blocks and an attention the gate module to capture the additional contextual features and improve the segmentation of the smaller regions. Three public chest X-ray datasets are used to evaluate the proposed method for multi-organs segmentation, such as the heart, lungs, and clavicles, and single-organ segmentation, which include only lungs. The results from the experiment show that our proposed technique outperformed the existing multi-class and single-class segmentation methods.

An Improved Encoder-Decoder CNN with Region-Based Filtering for Vibrant Colorization

Colorization is the practice of adding appropriate chromatic values to monochrome photographs or videos. A real-valued luminance image can be mapped to a three-dimensional color image. However, it is a severely ill-defined problem and not has a single solution. In this paper, an encoder-decoder Convolutional Neural Network (CNN) model is used for colorizing gray images where the encoder is a Densely Connected Convolutional Network (DenseNet) and the decoder is a conventional CNN. The DenseNet extracts image features from gray images and the conventional CNN outputs a * b * color channels. Due to a large number of desaturated color components compared to saturated color components in the training images, the saturated color components have a strong tendency towards desaturated color components in the predicted a * b * channel. To solve the problems, we rebalance the predicted a * b * color channel by smoothing every subregion individually using the average filter. 2 stage k-means clustering technique is applied to divide the subregions. Then we apply Gamma transformation in the entire a * b * channel to saturate the image. We compare our proposed method with several existing methods. From the experimental results, we see that our proposed method has made some notable improvements over the existing methods and color representation of gray-scale images by our proposed method is more plausible to visualize. Additionally, our suggested approach beats other approaches in terms of Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM) and Histogram.

Direct field-to-pattern monolithic design of holographic metasurface via residual encoder-decoder convolutional neural network

Complex-amplitude holographic metasurfaces (CAHMs) with the flexibility in modulating phase and amplitude profiles have been used to manipulate the propagation of wavefront with an unprecedented level, leading to higher image-reconstruction quality compared with their natural counterparts. However, prevailing design methods of CAHMs are based on Huygens-Fresnel theory, meta-atom optimization, numerical simulation and experimental verification, which results in a consumption of computing resources. Here, we applied residual encoder-decoder convolutional neural network to directly map the electric field distributions and input images for monolithic metasurface design. A pretrained network is firstly trained by the electric field distributions calculated by diffraction theory, which is subsequently migrated as transfer learning framework to map the simulated electric field distributions and input images. The training results show that the normalized mean pixel error is about 3% on dataset. As verification, the metasurface prototypes are fabricated, simulated and measured. The reconstructed electric field of reverse-engineered metasurface exhibits high similarity to the target electric field, which demonstrates the effectiveness of our design. Encouragingly, this work provides a monolithic field-to-pattern design method for CAHMs, which paves a new route for the direct reconstruction of metasurfaces.

6D Phase space diagnostics based on adaptively tuned physics-informed generative convolutional neural networks

A physics-informed generative convolutional neural network (CNN)-based 6D phase space diagnostic is presented which generates all 15 unique 2D projections (x, y), (x, y′),...,(z, E) of a charged particle beam’s 6D phase space (x, y, z, x′, y′, E). The CNN is trained by supervised learning over a wide range of input beam distributions, accelerator parameters, and the associated 6D beam phase spaces at multiple accelerator locations. The CNN is applied in an un-supervised adaptive manner without knowledge of the input beam distribution or accelerator parameters and is robust to their unknown time variation. Adaptive feedback automatically tunes the low-dimensional latent space of the encoder-decoder CNN to predict the 6D phase space based only on 2D (z, E) longitudinal phase space measurements from a device such as a transverse deflecting RF cavity (TCAV). This method has the potential to provide diagnostics beyond the existing state of the art at many accelerator facilities. Studies are presented for two very different accelerators: the 5-meter-long ultra-fast electron diffraction (UED) HiRES compact accelerator at LBNL and the kilometer long plasma wakefield accelerator FACET-II at SLAC.

Robust automatic hexahedral cartilage meshing framework enables population-based computational studies of the knee.

Osteoarthritis of the knee is increasingly prevalent as our population ages, representing an increasing financial burden, and severely impacting quality of life. The invasiveness of in vivo procedures and the high cost of cadaveric studies has left computational tools uniquely suited to study knee biomechanics. Developments in deep learning have great potential for efficiently generating large-scale datasets to enable researchers to perform population-sized investigations, but the time and effort associated with producing robust hexahedral meshes has been a limiting factor in expanding finite element studies to encompass a population. Here we developed a fully automated pipeline capable of taking magnetic resonance knee images and producing a working finite element simulation. We trained an encoder-decoder convolutional neural network to perform semantic image segmentation on the Imorphics dataset provided through the Osteoarthritis Initiative. The Imorphics dataset contained 176 image sequences with varying levels of cartilage degradation. Starting from an open-source swept-extrusion meshing algorithm, we further developed this algorithm until it could produce high quality meshes for every sequence and we applied a template-mapping procedure to automatically place soft-tissue attachment points. The meshing algorithm produced simulation-ready meshes for all 176 sequences, regardless of the use of provided (manually reconstructed) or predicted (automatically generated) segmentation labels. The average time to mesh all bones and cartilage tissues was less than 2min per knee on an AMD Ryzen 5600X processor, using a parallel pool of three workers for bone meshing, followed by a pool of four workers meshing the four cartilage tissues. Of the 176 sequences with provided segmentation labels, 86% of the resulting meshes completed a simulated flexion-extension activity. We used a reserved testing dataset of 28 sequences unseen during network training to produce simulations derived from predicted labels. We compared tibiofemoral contact mechanics between manual and automated reconstructions for the 24 pairs of successful finite element simulations from this set, resulting in mean root-mean-squared differences under 20% of their respective min-max norms. In combination with further advancements in deep learning, this framework represents a feasible pipeline to produce population sized finite element studies of the natural knee from subject-specific models.

Noise Suppression of Computed Tomography (CT) Images Using Residual Encoder-Decoder Convolutional Neural Network (RED-CNN)

In this study, an in-house residual encoder-decoder convolutional neural network (RED-CNN)-based algorithm was composed and trained using images of cylindrical polymethyl-methacrylate (PMMA) phantom with a diameter of 26 cm at different simulated noise levels. The model was tested on 21 × 26 cm elliptical PMMA computed tomography (CT) phantom images with simulated noise to evaluate its denoising capability using signal to noise ratio (SNR), comparative peak signal-to-noise ratio (cPSNR), structural similarity (SSIM) index, modulation transfer function frequencies (MTF 10 %) and noise power spectra (NPS) values as parameters. Evaluation of a possible decrease of image quality was also performed by testing the model using homogenous water phantom and wire phantom images acquired using different mAs values. Results show that the model was able to consistently increase SNR, cPSNR, SSIM values, and decrease the integral noise power spectra (NPS). However, the noise level on either training or testing data affects the model’s final denoising performance. The lower noise level on testing data images tends to result in over-smoothed images, as indicated by the shift of the NPS curves. In contrast, higher simulated noise level tends to result in less satisfactory denoising performance, as indicated by lower SNR, cPSNR, and SSIM values. Meanwhile, the higher noise level on training data images tends to produce denoised images with reduced sharpness, as indicated by the decrease of the MTF 10 % values. Further studies are required to better understand the character of RED-CNN for CT noise suppression regarding the optimum parameters for best results.

Streamlined single-molecule RNA-FISH of core clock mRNAs in clock neurons in whole mount Drosophila brains.

Circadian clocks are ∼24-h timekeepers that control rhythms in almost all aspects of our behavior and physiology. While it is well known that subcellular localization of core clock proteins plays a critical role in circadian regulation, very little is known about the spatiotemporal organization of core clock mRNAs and its role in generating ∼24-h circadian rhythms. Here we describe a streamlined single molecule Fluorescence In Situ Hybridization (smFISH) protocol and a fully automated analysis pipeline to precisely quantify the number and subcellular location of mRNAs of Clock, a core circadian transcription factor, in individual clock neurons in whole mount Drosophila adult brains. Specifically, we used ∼48 fluorescent oligonucleotide probes that can bind to an individual Clock mRNA molecule, which can then be detected as a diffraction-limited spot. Further, we developed a machine learning-based approach for 3-D cell segmentation, based on a pretrained encoder-decoder convolutional neural network, to automatically identify the cytoplasm and nuclei of clock neurons. We combined our segmentation model with a spot counting algorithm to detect Clock mRNA spots in individual clock neurons. Our results demonstrate that the number of Clock mRNA molecules cycle in large ventral lateral clock neurons (lLNvs) with peak levels at ZT4 (4h after lights are turned on) with ∼80 molecules/neuron and trough levels at ZT16 with ∼30 molecules/neuron. Our streamlined smFISH protocol and deep learning-based analysis pipeline can be employed to quantify the number and subcellular location of any mRNA in individual clock neurons in Drosophila brains. Further, this method can open mechanistic and functional studies into how spatiotemporal localization of clock mRNAs affect circadian rhythms.

Deep Cascade Residual Networks (DCRNs): Optimizing an Encoder–Decoder Convolutional Neural Network for Low-Dose CT Imaging

To suppress noise and artifacts caused by the reduced radiation exposure in low-dose computed tomography, several deep learning (DL)-based image restoration methods have been proposed over the past few years. Many of these popular DL-based methods adopt an encoder–decoder framework, for instance, the residual encoder–decoder convolutional neural network. However, this popular framework may suffer from information loss for continual downsampling operations. In this article, deep cascaded residual networks (DCRNs) are proposed to optimize the popular encoder–decoder network. First, cross up- and downsampling operations as well as attention extraction are substitutes for the strict “downsampling and then upping” principle. What is more, four hybrid loss functions, namely, mean absolute error, edge loss, perceptual loss and adversarial loss, are engaged to achieve better visual effects and suppress noise. The experiments are conducted on three individual clinical CT datasets: dental CT data collected with a scanner manufactured by Zhongke Tianyue Company (ZTC), data from the American Association of Physicists in Medicine (AAPM) Challenge, and data collected with a commercial CT scanner from United Imaging Healthcare (UIH). The experimental results indicate the effective noise reduction and detail preservation capabilities of the proposed methods under different radiation dose-reduction strategies.

Minimizing Image Quality Loss After Channel Count Reduction for Plane Wave Ultrasound via Deep Learning Inference.

High-frame-rate ultrasound imaging uses unfocused transmissions to insonify an entire imaging view for each transmit event, thereby enabling frame rates over 1000 frames per second (fps). At these high frame rates, it is naturally challenging to realize real-time transfer of channel-domain raw data from the transducer to the system back end. Our work seeks to halve the total data transfer rate by uniformly decimating the receive channel count by 50% and, in turn, doubling the array pitch. We show that despite the reduced channel count and the inevitable use of a sparse array aperture, the resulting beamformed image quality can be maintained by designing a custom convolutional encoder-decoder neural network to infer the radio frequency (RF) data of the nullified channels. This deep learning framework was trained with in vivo human carotid data (5-MHz plane wave imaging, 128 channels, 31 steering angles over a 30° span, and 62 799 frames in total). After training, the network was tested on an in vitro point target scenario that was dissimilar to the training data, in addition to in vivo carotid validation datasets. In the point target phantom image beamformed from inferred channel data, spatial aliasing artifacts attributed to array pitch doubling were found to be reduced by up to 10 dB. For carotid imaging, our proposed approach yielded a lumen-to-tissue contrast that was on average within 3 dB compared to the full-aperture image, whereas without channel data inferencing, the carotid lumen was obscured. When implemented on an RTX-2080 GPU, the inference time to apply the trained network was 4 ms, which favors real-time imaging. Overall, our technique shows that with the help of deep learning, channel data transfer rates can be effectively halved with limited impact on the resulting image quality.

Simulation and prediction of three-dimensional rotating flows based on convolutional neural networks

Two deep learning models to reconstruct three-dimensional (3D) steady-state rotating flows are proposed to capture the spatial information: the 3D convolutional encoder–decoder and the 3D convolutional long short-term memory model. They are based on deep learning methods such as the encoder–decoder convolutional neural network and recurrent neural network. Their common components are an encoder, a middle layer, and a decoder. The rotating flows in a stirred tank with four inclined blades are calculated for the dataset to train and test the two models. A workflow for the flow field reconstruction is established and all variants made up of various components are executed according to the flow. The optimal networks of the two models are selected by comparing performance measures. The results show that both models have the excellent ability to fit the 3D rotating flow field. Performance measures of the second model are better than those of the first one, but its running time is slower than that of the first one. In practice, this method can be used in the design and optimization of stirred tanks, centrifugal pumps, and other machines with rotating parts.

White Matter Perivascular Space Burden Is Associated With Mild Traumatic Brain Injury History In Soldiers

Mild traumatic brain injury (mTBI) exposure in military Service Members may lead to impaired brain waste clearance which increases neurological disease risk including amyloidopathies. Perivascular spaces (PVS) are part of the glymphatic pathway which support brain waste clearance, especially during sleep. Greater magnetic resonance imaging (MRI)-visible PVS burden has been previously observed in patients with neurodegenerative diseases and animal TBI models. PURPOSE: To determine the association between PVS burden (number and volume) and mTBI history in Special Operations Forces (SOF) combat Soldiers. METHODS: In this cross-sectional study, participants underwent neuroimaging to capture T2-weighted (T2w) whole brain three dimensional volumes obtained on a Siemens 3T Biograph mMR or 3T MAGNETOM Prisma scanner (TR/TE = 3200/400ms, slice thickness = 1mm, FoV = 256mm x 256 mm). The PVS segmentation was performed using a previously validated, multi-scale deep convolutional encoder-decoder neural network. All T2w images were skull stripped and a custom T2w atlas with segmented cerebral white matter and subcortical gray matter labels was registered to each subject using Advanced Normalization Tools to minimize misidentifying thin tubular structures in the skull, brainstem, cerebellum, and cortex as PVS. Only PVS clusters within the white matter mask were quantified for analyses. Binary mTBI history was self-reported (“yes” or “no”). Due to non-normal PVS metric distribution, non-parametric Mann-Whitney U tests were used to determine group differences in PVS outcomes. RESULTS: In total, 223 healthy SOF combat Soldiers (age = 33.1±4.3yrs) were included for analysis and 123 (55.16%) reported mTBI history. Soldiers with mTBI history had greater PVS number (z = 2.506, P = 0.013) and PVS volume (z = 2.419, P = 0.016). CONCLUSIONS: We found mTBI history is associated with increased PVS burden in SOF combat Soldiers that are clinically recovered from mTBI. This may indicate ongoing physiological post-mTBI changes that could lead to impaired waste clearance via the glymphatic system. Future studies should determine how sleep influences PVS burden following mTBI exposure and if PVS number and volume are meaningful neurobiological outcomes for neurodegenerative disease risk. Funded by US Special Operations Command

An Efficient Encoder-Decoder CNN for Brain Tumor Segmentation in MRI Images

An improved Encoder-Decoder Convolutional Neural Network (CNN) architecture is proposed for segmenting brain tumors in Magnetic Resonance Imaging (MRI). It consists of three encoding and decoding blocks. In the first encoding block, each input slice is convolved separately with two different filters and processed into upcoming encoding and decoding blocks for extracting the hierarchy of tumoral features. These are classified using softmax and compared with ground truth for evaluating performance. Experimental results were evaluated based on training and validation images in BRATS-2012, BRATS-2013 and BRATS-2018 datasets, which achieved 46.7%, 30.4% and 5.7% higher dice scores, respectively, compared to the existing segmentation methods.

A heteroencoder architecture for prediction of failure locations in porous metals using variational inference

In this work we employ an encoder–decoder convolutional neural network to predict the failure locations of porous metal tension specimens based only on their initial porosities. The process we model is complex, with a progression from initial void nucleation, to saturation, and ultimately failure. The objective of predicting failure locations presents an extreme case of class imbalance since most of the material in the specimens does not fail. In response to this challenge, we develop and demonstrate the effectiveness of data- and loss-based regularization methods. Since there is considerable sensitivity of the failure location to the particular configuration of voids, we also use variational inference to provide uncertainties for the neural network predictions. We connect the deterministic and Bayesian convolutional neural network formulations to explain how variational inference regularizes the training and predictions. We demonstrate that the resulting predicted variances are effective in ranking the locations that are most likely to fail in any given specimen.

A fully-convolutional residual encoder-decoder neural network to localize breast cancer on histopathology images

Cancer detection in its early stages may allow patients to receive the proper treatment and save lives along with recovering the routine lifestyles. Breast cancer is of the top leading causes of mortality among women all around the globe. A source to find these cancerous nuclei is through analyzing histopathology images. These images, however, are very complex and large. Thus, locating the cancerous nuclei in them is very challenging. Hence, if an expert fails to diagnose their patients via these images, the situation may be exacerbated. Therefore, this study aims to introduce a method to mask as many cancer nuclei on histopathology images as possible with a high visual aesthetic to make them distinguishable by experts easily. A tailored residual fully convolutional encoder-decoder neural network based on end-to-end learning is proposed to issue the matter. The proposed method is evaluated quantitatively and qualitatively on ER + BCa H&E-stained dataset. The average detection accuracy achieved by the method is 98.61%, which is much better than that of competitors.

Sub-Second Prediction of the Heatmap of Powder-Beds in Additive Manufacturing Using Deep Encoder–Decoder Convolutional Neural Networks

Abstract Physical modeling of the transient temperature during the Selective Laser Sintering (SLS) Additive Manufacturing (AM) process is essential for the characterization of the quality and structural integrity of the final products. The conventional numerical models used to simulate the thermal field of Additively Manufactured structures (AM structures) are time-consuming and could not be directly used to develop a real-time simulation or a process control system. This paper presents a deep learning encoder–decoder Convolutional Neural Network (CNN) model to predict the thermal field of AM structures. For deep learning training purposes, a time-consuming physics-based simulation was used to create a dataset including thousands of two-dimensional (2D) position-time representations of the laser head with different process parameters and their corresponding heatmap of AM structures. The deep learning model developed based on this dataset is capable of sub-second prediction of the heatmap being more than 41,000 times faster than the physics-based model. The resulting sub-second computational time of the developed deep learning model allows real-time process simulation as well as provides a basis for developing a process control system for the AM process in the future.

Deep learning-based precision agriculture through weed recognition in sugar beet fields

Weeds are among the major factors adversely affecting crop yield. Therefore, weed control with minimal environmental damage is a global concern. Traditional weed control methods are not cost-effective. Hence, precision agriculture proposes variable flow herbicide technology through regional weed management to distinguish weed and crop. In the present study, we employed the U-Net architecture, as a deep encoder-decoder convolutional neural network (CNN) for pixel-wise semantic segmentation of sugar beet, weed, and soil. We trained the U-Net architecture with ResNet50 as the encoder block using 1385 RGB images collected under different conditions and various heights. We utilized the combination of the dice and focal losses as a custom linear loss function to overcome imbalanced data and small area segmentation challenges. The structure of the dataset for the training process and using the custom loss function led to a model with the accuracy and intersection over union (IoU) score of 0.9606 and 0.8423, respectively. The results showed that using the image dataset with proper distribution and custom loss function can improve segmentation accuracy, especially in small regions. Furthermore, in an autonomous weed control robot, CNN-based automatic weed detection can be integrated into selective herbicide applications.

Deep-Learning Based Adaptive Ultrasound Imaging From Sub-Nyquist Channel Data.

Traditional beamforming of medical ultrasound images relies on sampling rates significantly higher than the actual Nyquist rate of the received signals. This results in large amounts of data to store and process, imposing hardware and software challenges on the development of ultrasound machinery and algorithms, and impacting the resulting performance. In light of the capabilities demonstrated by deep learning methods over the past years across a variety of fields, including medical imaging, it is natural to consider their ability to recover high-quality ultrasound images from partial data. Here, we propose an approach for deep-learning-based reconstruction of B-mode images from temporally and spatially sub-sampled channel data. We begin by considering sub-Nyquist sampled data, time-aligned in the frequency domain and transformed back to the time domain. The data are further sampled spatially so that only a subset of the received signals is acquired. The partial data is used to train an encoder-decoder convolutional neural network (CNN), using as targets minimum-variance (MV) beamformed signals that were generated from the original, fully-sampled data. Our approach yields high-quality B-mode images, with up to two times higher resolution than previously proposed reconstruction approaches (NESTA) from compressed data as well as delay-and-sum (DAS) beamforming of the fully-sampled data. In terms of contrast-to- noise ratio (CNR), our results are comparable to MV beamforming of the fully-sampled data, and provide up to 2 dB higher CNR values than DAS and NESTA, thus enabling better and more efficient imaging than what is used in clinical practice today.

A selective kernel-based cycle-consistent generative adversarial network for unpaired low-dose CT denoising.

Low-dose computed tomography (LDCT) denoising is an indispensable procedure in the medical imaging field, which not only improves image quality, but can mitigate the potential hazard to patients caused by routine doses. Despite the improvement in performance of the cycle-consistent generative adversarial network (CycleGAN) due to the well-paired CT images shortage, there is still a need to further reduce image noise while retaining detailed features. Inspired by the residual encoder–decoder convolutional neural network (RED-CNN) and U-Net, we propose a novel unsupervised model using CycleGAN for LDCT imaging, which injects a two-sided network into selective kernel networks (SK-NET) to adaptively select features, and uses the patchGAN discriminator to generate CT images with more detail maintenance, aided by added perceptual loss. Based on patch-based training, the experimental results demonstrated that the proposed SKFCycleGAN outperforms competing methods in both a clinical dataset and the Mayo dataset. The main advantages of our method lie in noise suppression and edge preservation.

Mitigating transmit-B1 artifacts by predicting parallel transmission images with deep learning: A feasibility study using high-resolution whole-brain diffusion at 7 Tesla.

PurposeTo propose a novel deep learning (DL) approach to transmit‐B1 (B1 +)‐artifact mitigation without direct use of parallel transmission (pTx), by predicting pTx images from single‐channel transmission (sTx) images.MethodsA deep encoder–decoder convolutional neural network was constructed and trained to learn the mapping from sTx to pTx images. The feasibility was demonstrated using 7 T Human‐Connectome Project (HCP)‐style diffusion MRI. The training dataset comprised images acquired on 5 healthy subjects using commercial Nova RF coils. Relevant hyperparameters were tuned with a nested cross‐validation, and the generalization performance evaluated using a regular cross‐validation.ResultsOur DL method effectively improved the image quality for sTx images by restoring the signal dropout, with quality measures (including normalized root‐mean‐square error, peak SNR, and structural similarity index measure) improved in most brain regions. The improved image quality was translated into improved performances for diffusion tensor imaging analysis; our method improved accuracy for fractional anisotropy and mean diffusivity estimations, reduced the angular errors of principal eigenvectors, and improved the fiber orientation delineation relative to sTx images. Moreover, the final DL model trained on data of all 5 subjects was successfully used to predict pTx images for unseen new subjects (randomly selected from the 7 T HCP database), effectively recovering the signal dropout and improving color‐coded fractional anisotropy maps with largely reduced noise levels.ConclusionThe proposed DL method has potential to provide images with reduced B1+ artifacts in healthy subjects even when pTx resources are inaccessible on the user side.

Attention U-Net as a surrogate model for groundwater prediction

Numerical simulations of groundwater flow are used to analyze and predict the response of an aquifer system to its change in state by approximating the solution of the fundamental groundwater physical equations. The most used and classical methodologies, such as Finite Difference (FD) and Finite Element (FE) Methods, use iterative solvers which are associated with high computational cost. This study proposes a physics-based convolutional encoder-decoder neural network as a surrogate model to quickly calculate the response of the groundwater system. Holding strong promise in cross-domain mappings, encoder-decoder networks are applicable for learning complex input-output mappings of physical systems. This manuscript presents an Attention U-Net model that attempts to capture the fundamental input-output relations of the groundwater system and generates solutions of hydraulic head in the whole domain given a set of physical parameters and boundary conditions. The model accurately predicts the steady state response of a highly heterogeneous groundwater system given the locations and piezometric head of up to 3 wells as input. The network learns to pay attention only in the relevant parts of the domain and the generated hydraulic head field corresponds to the target samples in great detail. Even relative to coarse finite difference approximations the proposed model is shown to be significantly faster than a comparative state-of-the-art numerical solver, thus providing a base for further development of the presented networks as surrogate models for groundwater prediction.