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We present a novel structure-preserving semi-implicit finite volume method on vertex-based staggered meshes for the compatible discretization of first order systems of time-dependent partial differential equations (PDEs). The method…
Combining discrete and continuous data is an important capability for generative models. We present Discrete Flow Models (DFMs), a new flow-based model of discrete data that provides the missing link in enabling flow-based generative models…
Anatomy is undergoing a renaissance driven by availability of large digital data sets generated by light microscopy. A central computational task is to map individual data volumes to standardized templates. This is accomplished by…
Navier-Stokes equations are significant partial differential equations that describe the motion of fluids such as liquids and air. Due to the importance of Navier-Stokes equations, the development on efficient numerical schemes is important…
Physics-Informed Neural Networks (PINN) has evolved into a powerful tool for solving partial differential equations, which has been applied to various fields such as energy, environment, en-gineering, etc. When utilizing PINN to solve…
We demonstrate a practical differentiable programming approach for acoustic inverse problems through two applications: admittance estimation and shape optimization for resonance damping. First, we show that JAX-FEM's automatic…
Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the strong mutual…
A primary challenge in using neural networks to approximate nonlinear dynamical systems governed by partial differential equations (PDEs) lies in recasting these systems into a tractable representation particularly when the dynamics are…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…
High-precision scientific simulation faces a long-standing trade-off between computational efficiency and physical fidelity. To address this challenge, we propose NeuralOGCM, an ocean modeling framework that fuses differentiable programming…
Accurate 3D aortic construction is crucial for clinical diagnosis, preoperative planning, and computational fluid dynamics (CFD) simulations, as it enables the estimation of critical hemodynamic parameters such as blood flow velocity,…
Mesh reconstruction of the cardiac anatomy from medical images is useful for shape and motion measurements and biophysics simulations to facilitate the assessment of cardiac function and health. However, 3D medical images are often acquired…
Computational Fluid Dynamics (CFD) is an important approach for analyzing flow phenomena and predicting engineering-relevant quantities. The governing physics is formulated as partial differential equations(PDEs) and solved numerically on…
A fully coupled implicit finite-volume algorithm for incompressible viscoelastic interfacial flows is proposed, whereby the viscoelasticity of the flow is described by an upper-convected Maxwell constitutive model, including limited…
Sequential robot manipulation tasks require finding collision-free trajectories that satisfy geometric constraints across multiple object interactions in potentially high-dimensional configuration spaces. Solving these problems in real-time…
We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz…
Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. The central challenge is to simulate turbulent flows in complex geometries, a compute-power intensive task due to the large…
Convexity is a fundamental geometric prior that underlies many natural and man-made structures, yet remains challenging to impose effectively in end-to-end trainable segmentation networks. We revisit convexity from a functional perspective…
High-fidelity simulation has become essential to the design and control of soft robots, where large geometric deformations and complex contact interactions challenge conventional modeling tools. Recent advances in the field demand…
The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions.…