Spectral element methods for fractional differential equations, with applications in applied analysis and medical imaging

Lead Research Organisation: University College London
Department Name: Medical Physics and Biomedical Eng

Abstract

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Publications

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Stanziola A (2021) A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound in Journal of Computational Physics

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Stanziola A (2022) Transcranial ultrasound simulation with uncertainty estimation in arXiv

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Miscouridou M (2022) Classical and Learned MR to Pseudo-CT Mappings for Accurate Transcranial Ultrasound Simulation. in IEEE transactions on ultrasonics, ferroelectrics, and frequency control

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Stanziola, A (2022) A Learned Born Series for Highly-Scattering Media in arXiv

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Stanziola A (2023) A learned Born series for highly-scattering media in JASA Express Letters

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Stanziola A (2023) j-Wave: An open-source differentiable wave simulator in SoftwareX

 
Title j-Wave: Differentiable acoustic simulations in JAX 
Description j-Wave is a library of simulators for acoustic applications. Is heavily inspired by k-Wave (a big portion of j-Wave is a port of k-Wave in JAX), and its intended to be used as a collection of modular blocks that can be easily included into any machine learning pipeline. Following the philosophy of JAX, j-Wave is developed with the following principles in mind: to be differentiable, to be fast via jit compilation, easy to run on GPUs, easy to customize. 
Type Of Technology Software 
Year Produced 2022 
Open Source License? Yes  
Impact j-Wave was used in a recent modelling intercomparison, and to study uncertainty in transcranial ultrasound simulation. 
URL https://github.com/ucl-bug/jwave
 
Title jaxdf - JAX-based Discretization Framework 
Description jaxdf is a JAX-based package defining a coding framework for writing differentiable numerical simulators with arbitrary discretizations. The intended use is to build numerical models of physical systems, such as wave propagation, or the numerical solution of partial differential equations, that are easy to customize to the user's research needs. Such models are pure functions that can be included into arbitrary differentiable programs written in JAX: for example, they can be used as layers of neural networks, or to build a physics loss function. 
Type Of Technology Software 
Year Produced 2022 
Open Source License? Yes  
Impact jaxdf is being used by researchers interested in differentiable models, and forms the basis for the j-Wave acoustic simulation software. 
URL https://github.com/ucl-bug/jaxdf