Related papers: Parallel algorithms for SAT in application to inve…

We propose a software architecture where SAT solvers act as a shared network resource for distributed business applications. There can be multiple parallel SAT solvers running either on dedicated hardware (a multi-processor system or a…

We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…

The present paper studies so-called deep image prior (DIP) techniques in the context of ill-posed inverse problems. DIP networks have been recently introduced for applications in image processing; also first experimental results for…

When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…

Inspired by the developments in quantum computing, building domain-specific classical hardware to solve computationally hard problems has received increasing attention. Here, by introducing systematic sparsification techniques, we…

In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…

Several types of simultaneous approximation term (SAT) for diffusion problems discretized with diagonal-norm multidimensional summation-by-parts (SBP) operators are analyzed based on a common framework. Conditions under which the SBP-SAT…

This paper proposes a method to estimate the total time required to solve SAT in distributed environments via partitioning approach. It is based on the observation that for some simple forms of problem partitioning one can use the Monte…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving…

Over the past few years, self-attention is shining in the field of deep learning, especially in the domain of natural language processing(NLP). Its impressive effectiveness, along with ubiquitous implementations, have aroused our interest…

This paper describes diff-SAT, an Answer Set and SAT solver which combines regular solving with the capability to use probabilistic clauses, facts and rules, and to sample an optimal world-view (multiset of satisfying Boolean variable…

Parametric linear programming is central in polyhedral computations and in certain control applications.We propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…

A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…

Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be…

Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…

Usage of multiprocessor and multicore computers implies parallel programming. Tools for preparing parallel programs include parallel languages and libraries as well as parallelizing compilers and convertors that can perform automatic…

There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to…

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…