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In sharp contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems. In this paper we establish the feasible interpolation technique for all resolution-based QBF systems, whether modelling…
This study presents an advanced sharp-interface immersed boundary method (IBM) integrated with the blastFOAM library on the OpenFOAM platform for high-speed compressible flow simulations. The developed solver extends the existing IBM…
Optimization problems, particularly NP-Hard Combinatorial Optimization problems, are some of the hardest computing problems with no known polynomial time algorithm existing. Recently there has been interest in using dedicated hardware to…
Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding…
Motivated by the fact that the gradient-based optimization algorithms can be studied from the perspective of limiting ordinary differential equations (ODEs), here we derive an ODE representation of the accelerated triple momentum (TM)…
It is needed to solve generalized eigenvalue problems (GEP) in many applications, such as the numerical simulation of vibration analysis, quantum mechanics, electronic structure, etc. The subspace iteration is a kind of widely used…
We propose a new framework for black-box convex optimization which is well-suited for situations where gradient computations are expensive. We derive a new method for this framework which leverages several concepts from convex optimization,…
Reinforcement learning (RL) in episodic, factored Markov decision processes (FMDPs) is studied. We propose an algorithm called FMDP-BF, which leverages the factorization structure of FMDP. The regret of FMDP-BF is shown to be exponentially…
Various hardware accelerators have been developed for energy-efficient and real-time inference of neural networks on edge devices. However, most training is done on high-performance GPUs or servers, and the huge memory and computing costs…
We introduce new optimized first-order methods for smooth unconstrained convex minimization. Drori and Teboulle recently described a numerical method for computing the $N$-iteration optimal step coefficients in a class of first-order…
We introduce efficient solutions to optimize the cost of tree-like tensor network state method calculations when an expensive GPU-accelerated hardware is utilized. By supporting a main powerful compute node with additional auxiliary, but…
Recent advances in flow-based generative modelling have provided scalable methods for computing the Schr\"odinger Bridge (SB) between distributions, a dynamic form of entropy-regularised Optimal Transport (OT) for the quadratic cost. The…
This paper advances the computational efficiency of Deep Hedging frameworks through the novel integration of Kronecker-Factored Approximate Curvature (K-FAC) optimization. While recent literature has established Deep Hedging as a…
This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…
NVIDIA researchers have pioneered an explicit method, position-based dynamics (PBD), for simulating systems with contact forces, gaining widespread use in computer graphics and animation. While the method yields visually compelling…
In this paper, we propose first-order feasible methods for difference-of-convex (DC) programs with smooth inequality and simple geometric constraints. Our strategy for maintaining feasibility of the iterates is based on a "retraction" idea…
Inspired by the row and column action methods for solving large-scale linear systems, in this work, we explore the use of frontal slices for solving tensor linear systems. In particular, this paper presents a novel approach for using…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
This paper studies second-order methods for nonconvex-strongly-convex bilevel optimization. We propose a novel fully second-order bilevel approximation method (FSBA) that achieves an iteration complexity of…
Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of…