Related papers: Sequential Refinement Solver using Space-Time Doma…
Accurate autoregressive prediction of 3D turbulent flows remains challenging for neural PDE solvers, as small errors in fine-scale structures can accumulate rapidly over rollout. In this paper, we propose FlowRefiner, a flow matching-based…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer…
This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP algorithm for solving nonlinear optimization…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Temporal convolutional networks (TCNs) are a commonly used architecture for temporal video segmentation. TCNs however, tend to suffer from over-segmentation errors and require additional refinement modules to ensure smoothness and temporal…
The sequential fully implicit (SFI) scheme was introduced (Jenny et al. 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and…
We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…
Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
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…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…
Sequential Bayesian inference over predictive functions is a natural framework for continual learning from streams of data. However, applying it to neural networks has proved challenging in practice. Addressing the drawbacks of existing…
Optimal power flow (OPF) is an important problem in the operation of electric power systems. Due to the OPF problem's non-convexity, there may exist multiple local optima. Certifiably obtaining the global solution is important for certain…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…