Research
Preprints
Hardware Acceleration for HPS Algorithms in Two and Three Dimensions
Owen Melia, Daniel Fortunato, Jeremy Hoskins, and Rebecca Willett. Available on arXiv, March 2025.
Abstract
We provide a flexible, open-source framework for hardware acceleration, namely massively-parallel execution on general-purpose graphics processing units (GPUs), applied to the hierarchical Poincaré--Steklov (HPS) family of algorithms for building fast direct solvers for linear elliptic partial differential equations. To take full advantage of the power of hardware acceleration, we propose two variants of HPS algorithms to improve performance on two- and three-dimensional problems. In the two-dimensional setting, we introduce a novel recomputation strategy that minimizes costly data transfers to and from the GPU; in three dimensions, we modify and extend the adaptive discretization technique of [Geldermans & Gillman 2019] to greatly reduce peak memory usage. We provide an open-source implementation of these methods written in JAX, a high-level accelerated linear algebra package, which allows for the first integration of a high-order fast direct solver with automatic differentiation tools. We conclude with extensive numerical examples showing our methods are fast and accurate on two- and three-dimensional problems.
Journal Articles
Multi-Frequency Progressive Refinement for Learned Inverse Scattering
Owen Melia, Olivia Tsang, Vasileios Charisopoulos, Yuehaw Khoo, Jeremy Hoskins, and Rebecca Willett. Journal of Computational Physics, April 2025.
Abstract
Interpreting scattered acoustic and electromagnetic wave patterns is a computational task that enables remote imaging in a number of important applications, including medical imaging, geophysical exploration, sonar and radar detection, and nondestructive testing of materials. However, accurately and stably recovering an inhomogeneous medium from far-field scattered wave measurements is a computationally difficult problem, due to the nonlinear and non-local nature of the forward scattering process. We design a neural network, called Multi-Frequency Inverse Scattering Network (MFISNet), and a training method to approximate the inverse map from far-field scattered wave measurements at multiple frequencies. We consider three variants of MFISNet, with the strongest performing variant inspired by the recursive linearization method -- a commonly used technique for stably inverting scattered wavefield data -- that progressively refines the estimate with higher frequency content.
Journal version, arXiv, GitHub, Dataset
Rotation-Invariant Random Features Provide a Strong Baseline for Machine Learning on 3D Point Clouds
Owen Melia, Eric Jonas, and Rebecca Willett. Transactions on Machine Learning Research, July 2023.
Abstract
Rotational invariance is a popular inductive bias used by many fields in machine learning, such as computer vision and machine learning for quantum chemistry. Rotation-invariant machine learning methods set the state of the art for many tasks, including molecular property prediction and 3D shape classification. These methods generally either rely on task-specific rotation-invariant features, or they use general-purpose deep neural networks which are complicated to design and train. However, it is unclear whether the success of these methods is primarily due to the rotation invariance or the deep neural networks. To address this question, we suggest a simple and general-purpose method for learning rotation-invariant functions of three-dimensional point cloud data using a random features approach. Specifically, we extend the random features method of [Rahimi & Recht 2007] by deriving a version that is invariant to three-dimensional rotations and showing that it is fast to evaluate on point cloud data. We show through experiments that our method matches or outperforms the performance of general-purpose rotation-invariant neural networks on standard molecular property prediction benchmark datasets QM7 and QM9. We also show that our method is general-purpose and provides a rotation-invariant baseline on the ModelNet40 shape classification task. Finally, we show that our method has an order of magnitude smaller prediction latency than competing kernel methods.
Journal version, arXiv, GitHub
PhenomeXcan: Mapping the genome to the phenome through the transcriptome
Milton Pividori, Padma S. Rajagopal, Alvaro Barbeira, Yanyu Liang, Owen Melia, Lisa Bastarache, YoSon Park, GTEx Consortium, Xiaoquan Wen, and Hae K. Im. Science: Advances, September 2023.
Blurb
We develop statistical methods and user interfaces to allow for high-throughput analysis of genotype, phenotype, and transcription data. Our website phenomexcan.org provides user-friendly access to this data.
Fine-mapping and QTL tissue-sharing information improves the reliability of causal gene identification
Alvaro N. Barbeira, Owen J. Melia, Yanyu Liang, Rodrigo Bonazzola, Gao Wang, Heather E. Wheeler, François Aguet, Kristin G. Ardlie, Xiaoquan Wen, and Hae K. Im. Genetic Epidemiology, September 2023.
Blurb
We study and develop methods for two different problems, finding causal genetic variants of tissue-specific gene expression traits and predicting tissue-specific gene expression traits from genetic variant data. We show that the best-performing prediction models do not lead to more reliable causal discovery.