Related papers: Nonlinear Evolutionary PDE-Based Refinement of Opt…

We propose several variants of the primal-dual method due to Chambolle and Pock. Without requiring full strong convexity of the objective functions, our methods are accelerated on subspaces with strong convexity. This yields mixed rates,…

Simulation is a powerful tool to better understand physical systems, but generally requires computationally expensive numerical methods. Downstream applications of such simulations can become computationally infeasible if they require many…

This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…

With the advent of neuromorphic vision sensors such as event-based cameras, a paradigm shift is required for most computer vision algorithms. Among these algorithms, optical flow estimation is a prime candidate for this process considering…

A physics-informed neural network (PINN), which has been recently proposed by Raissi et al [J. Comp. Phys. 378, pp. 686-707 (2019)], is applied to the partial differential equation (PDE) of liquid film flows. The PDE considered is the time…

We present the method for computation of fluid flows that are characterized by the large degree of expansion/contraction and in which the fluid velocity is dominated by the bulk component associated with the expansion/contraction and/or…

Event cameras are novel bio-inspired sensors that offer advantages over traditional cameras (low latency, high dynamic range, low power, etc.). Optical flow estimation methods that work on packets of events trade off speed for accuracy,…

We study several iterative methods for fully coupled flow and reactive transport in porous media. The resulting mathematical model is a coupled, nonlinear evolution system. The flow model component builds on the Richards equation, modified…

Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity…

We develop a framework for non-asymptotic analysis of deterministic samplers used for diffusion generative modeling. Several recent works have analyzed stochastic samplers using tools like Girsanov's theorem and a chain rule variant of the…

We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

Optical flow is a fundamental technique for motion estimation, widely applied in video stabilization, interpolation, and object tracking. Traditional optical flow estimation methods rely on restrictive assumptions like brightness constancy…

Generative models, including diffusion and flow-based models, often exhibit systematic biases that degrade sample quality, particularly in high-dimensional settings. We revisit refinement methods and show that effective bias correction can…

In this work, we introduce a novel first-order nonlocal partial differential equation with saturated diffusion to describe the macroscopic behavior of traffic dynamics. We show how the proposed model is better in comparison with existing…

Few-step video generation has been significantly advanced by consistency distillation. However, the performance of consistency-distilled models often degrades as more sampling steps are allocated at test time, limiting their effectiveness…

This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node…

We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution…

Scene flow estimation, which aims to predict per-point 3D displacements of dynamic scenes, is a fundamental task in the computer vision field. However, previous works commonly suffer from unreliable correlation caused by locally constrained…

Optical flow estimation remains challenging due to untextured areas, motion boundaries, occlusions, and more. Thus, the estimated flow is not equally reliable across the image. To that end, post-hoc confidence measures have been introduced…

We propose to modify the common training protocols of optical flow, leading to sizable accuracy improvements without adding to the computational complexity of the training process. The improvement is based on observing the bias in sampling…