arXiv subjects

Shoaib Goraya

Publications and source records attributed to Shoaib Goraya.

3 recordsLinked to original sources

arXiv2026

CardioComposer: Leveraging Differentiable Geometry for Compositional Control of Anatomical Diffusion Models

Generative models of 3D cardiovascular anatomy can synthesize informative structures for clinical research and medical device evaluation, but face a trade-off between geometric controllability and realism. We propose CardioComposer: a programmable, inference-time framework for generating multi-class anatomical label maps from interpretable ellipsoidal primitives. These primitives represent geometric attributes such as the size, shape, and position of discrete substructures. We specifically develop differentiable measurement functions based on voxel-wise geometric moments, enabling loss-based gradient guidance during diffusion model sampling. We demonstrate that these losses can constrain individual geometric attributes in a disentangled manner and provide compositional control over multiple substructures. Finally, we show that our method is compatible with a broad range of anatomical systems containing non-convex substructures, spanning cardiac, vascular, and skeletal organs. We release our code at https://github.com/kkadry/CardioComposer.

eess.IV↗

arXiv2025

Anatomica: Localized Control over Geometric and Topological Properties for Anatomical Diffusion Models

We present Anatomica: an inference-time framework for generating multi-class anatomical voxel maps with localized geo-topological control. During generation, we use cuboidal control domains of varying dimensionality, location, and shape to slice out relevant substructures. These local substructures are used to compute differentiable penalty functions that steer the sample towards target constraints. We control geometric features such as size, shape, and position through voxel-wise moments, while topological features such as connected components, loops, and voids are enforced through persistent homology. Lastly, we implement Anatomica for latent diffusion models, where neural field decoders partially extract substructures, enabling the efficient control of anatomical properties. Anatomica applies flexibly across diverse anatomical systems, composing constraints to control complex structures over arbitrary dimensions and coordinate systems, thereby enabling the rational design of synthetic datasets for virtual trials or machine learning workflows.

cs.LG↗

arXiv2022

Error Estimates and Physics Informed Augmentation of Neural Networks for Thermally Coupled Incompressible Navier Stokes Equations

Physics Informed Neural Networks (PINNs) are shown to be a promising method for the approximation of Partial Differential Equations (PDEs). PINNs approximate the PDE solution by minimizing physics-based loss functions over a given domain. Despite substantial progress in the application of PINNs to a range of problem classes, investigation of error estimation and convergence properties of PINNs, which is important for establishing the rationale behind their good empirical performance, has been lacking. This paper presents convergence analysis and error estimates of PINNs for a multi-physics problem of thermally coupled incompressible Navier-Stokes equations. Through a model problem of Beltrami flow it is shown that a small training error implies a small generalization error. Posteriori convergence rates of total error with respect to the training residual and collocation points are presented. This is of practical significance in determining appropriate number of training parameters and training residual thresholds to get good PINNs prediction of thermally coupled steady state laminar flows. These convergence rates are then generalized to different spatial geometries as well as to different flow parameters that lie in the laminar regime. A pressure stabilization term in the form of pressure Poisson equation is added to the PDE residuals for PINNs. This physics informed augmentation is shown to improve accuracy of the pressure field by an order of magnitude as compared to the case without augmentation. Results from PINNs are compared to the ones obtained from stabilized finite element method and good properties of PINNs are highlighted.

math.NA↗