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We present fVDB, a novel GPU-optimized framework for deep learning on large-scale 3D data. fVDB provides a complete set of differentiable primitives to build deep learning architectures for common tasks in 3D learning such as convolution,…
We prove convergence of discrete duality finite volume (DDFV) schemes on distorted meshes for a class of simplified macroscopic bidomain models of the electrical activity in the heart. Both time-implicit and linearised time-implicit schemes…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core…
Unstructured meshes are among the most versatile approaches for capturing non-canonical geometries in fluid dynamics simulations. Despite this, most high-fidelity first-principles phase-change models are developed and applied on structured…
The precise segmentation of intracranial aneurysms and their parent vessels (IA-Vessel) is a critical step for hemodynamic analyses, which mainly depends on computational fluid dynamics (CFD). However, current segmentation methods…
Fast, accurate, and generalizable simulations are a key enabler of modern advances in robot design and control. However, existing simulation frameworks in robotics either model rigid environments and mechanisms only, or if they include…
Efficient deployment of Deep Neural Networks (DNNs), such as Large Language Models (LLMs), on tensor accelerators is essential for maximizing computational efficiency in modern AI systems. However, achieving this is challenging due to the…
Stripe patterns are ubiquitous in nature and everyday life. While the synthesis of these patterns has been thoroughly studied in the literature, their potential to control the mechanics of structured materials remains largely unexplored. In…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
Computational Fluid Dynamics (CFD) serves as a powerful tool for simulating fluid flow across diverse industries. High-resolution CFD simulations offer valuable insights into fluid behavior and flow patterns, aiding in optimizing design…
We introduce JAX FDM, a differentiable solver to design mechanically efficient shapes for 3D structures conditioned on target architectural, fabrication and structural properties. Examples of such structures are domes, cable nets and…
In this paper, we develop a multiscale finite element method for solving flows in fractured media. Our approach is based on Generalized Multiscale Finite Element Method (GMsFEM), where we represent the fracture effects on a coarse grid via…
Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain…
We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic…
Shock dynamics and nonlinear wave propagation are fundamental to computational fluid dynamics (CFD) and high-speed flow modeling. In this study, we developed explicit and implicit finite-difference solvers for the one-dimensional Burgers…
Consider a learning algorithm, which involves an internal call to an optimization routine such as a generalized eigenvalue problem, a cone programming problem or even sorting. Integrating such a method as a layer(s) within a trainable deep…
We propose a computational framework for vascular fluid-structure interaction (FSI), focusing on biomechanical modeling, geometric modeling, and solver technology. The biomechanical model is constructed based on the unified continuum…
Accurate segmentation of organs and lesions in medical images is essential for clinical applications including diagnosis, prognosis, and treatment planning. While Vision Transformers (ViTs) have shown impressive segmentation performance,…
This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries in the finite volume approach. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by…