Related papers: Flow reconstruction by multiresolution optimizatio…

We propose to formulate MRI image reconstruction as an optimization problem and model the optimization trajectory as a dynamic process using ordinary differential equations (ODEs). We model the dynamics in ODE with a neural network and…

Mean Deviation (MD) is a critical metric for assessing visual field loss in ophthalmology. While previous work has focused solely on predicting MD from Optical Coherence Tomography (OCT), it is intuitive to assume that combining OCT with…

In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…

The recent emergence of diffusion models has significantly advanced the precision of learnable priors, presenting innovative avenues for addressing inverse problems. Since inverse problems inherently entail maximum a posteriori estimation,…

Deep learning methods for accelerated MRI achieve state-of-the-art results but largely ignore additional speedups possible with noncartesian sampling trajectories. To address this gap, we created a generative diffusion model-based…

This study employs physics-informed neural networks (PINNs) to reconstruct multiple flow fields in a transient natural convection system solely based on instantaneous temperature data at an arbitrary moment. Transient convection problems…

Direct optimization of interpolated features on multi-resolution voxel grids has emerged as a more efficient alternative to MLP-like modules. However, this approach is constrained by higher memory expenses and limited representation…

Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex…

This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…

Multiscale Proper Orthogonal Decomposition (mPOD) decomposes fluid flows into energy-optimal modes within prescribed frequency bands by combining Proper Orthogonal Decomposition with a multiresolution analysis (MRA). In its classical…

A novel interface reconstruction strategy for volume of fluid (VOF) methods is introduced that represents the liquid-gas interface as two planes that co-exist within a single computational cell. In comparison to the piecewise linear…

This paper proposes a new data assimilation method for recovering high fidelity turbulent flow field around airfoil at high Reynolds numbers based on experimental data, which is called Proper Orthogonal Decomposition Inversion…

Optimizing shapes and topology of physical devices is crucial for both scientific and technological advancements, given its wide-ranging implications across numerous industries and research areas. Innovations in shape and topology…

Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate…

This paper describes the numerical implementation in a high-performance computing environment of an open-source library for model order reduction in fluid dynamics. This library, called pyLOM, contains the algorithms of proper orthogonal…

In this paper, we present a dimension reduction method to reduce the dimension of parameter space and state space and efficiently solve inverse problems. To this end, proper orthogonal decomposition (POD) and radial basis function (RBF) are…

A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing…

A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…

The fully implicit method is the most commonly used approach to solve black-oil problems in reservoir simulation. The method requires repeated linearization of large nonlinear systems and produces ill-condi\-tioned linear systems. We…

This paper studies the problem of estimating origin-destination (OD) flows from link flows. As the number of link flows is typically much less than that of OD flows, the inverse problem is severely ill-posed and hence prior information is…