Adrian Celaya

Adrian Celaya, Beatrice Riviere, David Fuentes

Within medical imaging segmentation, the Dice coefficient and Hausdorff-based metrics are standard measures of success for deep learning models. However, modern loss functions for medical image segmentation often only consider the Dice coefficient or similar region-based metrics during training. As a result, segmentation architectures trained over such loss functions run the risk of achieving high accuracy for the Dice coefficient but low accuracy for Hausdorff-based metrics. Low accuracy on Hausdorff-based metrics can be problematic for applications such as tumor segmentation, where such benchmarks are crucial. For example, high Dice scores accompanied by significant Hausdorff errors could indicate that the predictions fail to detect small tumors. We propose the Generalized Surface Loss function, a novel loss function to minimize Hausdorff-based metrics with more desirable numerical properties than current methods and with weighting terms for class imbalance. Our loss function outperforms other losses when tested on the LiTS and BraTS datasets using the state-of-the-art nnUNet architecture. These results suggest we can improve medical imaging segmentation accuracy with our novel loss function.

Adrian Celaya, Beatrice Riviere, David Fuentes

Accurate medical imaging segmentation is critical for precise and effective medical interventions. However, despite the success of convolutional neural networks (CNNs) in medical image segmentation, they still face challenges in handling fine-scale features and variations in image scales. These challenges are particularly evident in complex and challenging segmentation tasks, such as the BraTS multi-label brain tumor segmentation challenge. In this task, accurately segmenting the various tumor sub-components, which vary significantly in size and shape, remains a significant challenge, with even state-of-the-art methods producing substantial errors. Therefore, we propose two architectures, FMG-Net and W-Net, that incorporate the principles of geometric multigrid methods for solving linear systems of equations into CNNs to address these challenges. Our experiments on the BraTS 2020 dataset demonstrate that both FMG-Net and W-Net outperform the widely used U-Net architecture regarding tumor subcomponent segmentation accuracy and training efficiency. These findings highlight the potential of incorporating the principles of multigrid methods into CNNs to improve the accuracy and efficiency of medical imaging segmentation.

Adrian Celaya, Bertrand Denel, Yen Sun et al.

We introduce three algorithms that invert simulated gravity data to 3D subsurface rock/flow properties. The first algorithm is a data-driven, deep learning-based approach, the second mixes a deep learning approach with physical modeling into a single workflow, and the third considers the time dependence of surface gravity monitoring. The target application of these proposed algorithms is the prediction of subsurface CO$_2$ plumes as a complementary tool for monitoring CO$_2$ sequestration deployments. Each proposed algorithm outperforms traditional inversion methods and produces high-resolution, 3D subsurface reconstructions in near real-time. Our proposed methods achieve Dice scores of up to 0.8 for predicted plume geometry and near perfect data misfit in terms of $μ$Gals. These results indicate that combining 4D surface gravity monitoring with deep learning techniques represents a low-cost, rapid, and non-intrusive method for monitoring CO$_2$ storage sites.

Adrian Celaya, Evan Lim, Rachel Glenn et al.

Medical imaging segmentation is a highly active area of research, with deep learning-based methods achieving state-of-the-art results in several benchmarks. However, the lack of standardized tools for training, testing, and evaluating new methods makes the comparison of methods difficult. To address this, we introduce the Medical Imaging Segmentation Toolkit (MIST), a simple, modular, and end-to-end medical imaging segmentation framework designed to facilitate consistent training, testing, and evaluation of deep learning-based medical imaging segmentation methods. MIST standardizes data analysis, preprocessing, and evaluation pipelines, accommodating multiple architectures and loss functions. This standardization ensures reproducible and fair comparisons across different methods. We detail MIST's data format requirements, pipelines, and auxiliary features and demonstrate its efficacy using the BraTS Adult Glioma Post-Treatment Challenge dataset. Our results highlight MIST's ability to produce accurate segmentation masks and its scalability across multiple GPUs, showcasing its potential as a powerful tool for future medical imaging research and development.

Adrian Celaya, Mauricio Araya-Polo

We introduce a fully 3D, deep learning-based approach for the joint inversion of time-lapse surface gravity and seismic data for reconstructing subsurface density and velocity models. The target application of this proposed inversion approach is the prediction of subsurface CO2 plumes as a complementary tool for monitoring CO2 sequestration deployments. Our joint inversion technique outperforms deep learning-based gravity-only and seismic-only inversion models, achieving improved density and velocity reconstruction, accurate segmentation, and higher R-squared coefficients. These results indicate that deep learning-based joint inversion is an effective tool for CO$_2$ storage monitoring. Future work will focus on validating our approach with larger datasets, simulations with other geological storage sites, and ultimately field data.

Adrian Celaya, Keegan Kirk, David Fuentes et al.

In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods like PINNs rely on auto differentiation and sampling collocation points, leading to a lack of interpretability and lower accuracy than traditional numerical methods. As a result, we propose a fully unsupervised approach, requiring no training data, to estimate finite difference solutions for PDEs directly via small linear convolutional neural networks. Our proposed approach uses substantially fewer parameters than similar finite difference-based approaches while also demonstrating comparable accuracy to the true solution for several selected elliptic and parabolic problems compared to the finite difference method.

Adrian Celaya, Tucker Netherton, Dawid Schellingerhout et al.

Medical image segmentation continues to advance rapidly, yet rigorous comparison between methods remains challenging due to a lack of standardized and customizable tooling. In this work, we present the current state of the Medical Imaging Segmentation Toolkit (MIST), with a particular focus on its flexible and modular postprocessing framework designed for the BraTS 2025 pre- and post-treatment glioma segmentation challenge. Since its debut in the 2024 BraTS adult glioma post-treatment segmentation challenge, MIST's postprocessing module has been significantly extended to support a wide range of transforms, including removal or replacement of small objects, extraction of the largest connected components, and morphological operations such as hole filling and closing. These transforms can be composed into user-defined strategies, enabling fine-grained control over the final segmentation output. We evaluate three such strategies - ranging from simple small-object removal to more complex, class-specific pipelines - and rank their performance using the BraTS ranking protocol. Our results highlight how MIST facilitates rapid experimentation and targeted refinement, ultimately producing high-quality segmentations for the BraTS 2025 challenge. MIST remains open source and extensible, supporting reproducible and scalable research in medical image segmentation.

Adrian Celaya, Yimo Wang, David Fuentes et al.

In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods, such as physics-informed neural networks, depend on automatic differentiation and the sampling of collocation points, which can result in a lack of interpretability and lower accuracy compared to traditional numerical methods. To address this issue, we propose two approaches for learning discontinuous Galerkin solutions to PDEs using small linear convolutional neural networks. Our first approach is supervised and depends on labeled data, while our second approach is unsupervised and does not rely on any training data. In both cases, our methods use substantially fewer parameters than similar numerics-based neural networks while also demonstrating comparable accuracy to the true and DG solutions for elliptic problems.

Adrian Celaya, David Fuentes, Beatrice Riviere

Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have improved PINN accuracy, the impact of collocation point sampling on their performance remains underexplored. Fixed sampling methods, such as uniform random sampling and equispaced grids, can fail to capture critical regions with high solution gradients, limiting their effectiveness for complex PDEs. Adaptive methods, inspired by adaptive mesh refinement from traditional numerical methods, address this by dynamically updating collocation points during training but may overlook residual dynamics between updates, potentially losing valuable information. To overcome this limitation, we propose two adaptive collocation point selection strategies utilizing the QR Discrete Empirical Interpolation Method (QR-DEIM), a reduced-order modeling technique for efficiently approximating nonlinear functions. Our results on benchmark PDEs demonstrate that our QR-DEIM-based approaches improve PINN accuracy compared to existing methods, offering a promising direction for adaptive collocation point strategies.

Rajarajeswari Muthusivarajan, Adrian Celaya, Joshua P. Yung et al.

Deep neural networks with multilevel connections process input data in complex ways to learn the information.A networks learning efficiency depends not only on the complex neural network architecture but also on the input training images.Medical image segmentation with deep neural networks for skull stripping or tumor segmentation from magnetic resonance images enables learning both global and local features of the images.Though medical images are collected in a controlled environment,there may be artifacts or equipment based variance that cause inherent bias in the input set.In this study, we investigated the correlation between the image quality metrics of MR images with the neural network segmentation accuracy.For that we have used the 3D DenseNet architecture and let the network trained on the same input but applying different methodologies to select the training data set based on the IQM values.The difference in the segmentation accuracy between models based on the random training inputs with IQM based training inputs shed light on the role of image quality metrics on segmentation accuracy.By running the image quality metrics to choose the training inputs,further we may tune the learning efficiency of the network and the segmentation accuracy.

Adrian Celaya, Jonas A. Actor, Rajarajeswari Muthusivarajan et al.

Medical imaging deep learning models are often large and complex, requiring specialized hardware to train and evaluate these models. To address such issues, we propose the PocketNet paradigm to reduce the size of deep learning models by throttling the growth of the number of channels in convolutional neural networks. We demonstrate that, for a range of segmentation and classification tasks, PocketNet architectures produce results comparable to that of conventional neural networks while reducing the number of parameters by multiple orders of magnitude, using up to 90% less GPU memory, and speeding up training times by up to 40%, thereby allowing such models to be trained and deployed in resource-constrained settings.