Related papers: An algorithm for the optimization of finite elemen…
We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
In the following paper we present a new type of optimization algorithms adapted for neural network training. These algorithms are based upon sequential operator splitting technique for some associated dynamical systems. Furthermore, we…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
We motivate the use of quantum algorithms in particle physics and provide a brief overview of the most recent applications at high-energy colliders. In particular, we discuss in detail how a quantum approach reduces the complexity of jet…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
In this work, we propose a novel optimization model termed "sum-of-minimum" optimization. This model seeks to minimize the sum or average of $N$ objective functions over $k$ parameters, where each objective takes the minimum value of a…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Conventional rule learning algorithms aim at finding a set of simple rules, where each rule covers as many examples as possible. In this paper, we argue that the rules found in this way may not be the optimal explanations for each of the…
Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
This paper is devoted to GPU kernel optimization and performance analysis of three tensor-product operators arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving…
One of the most severe bottlenecks to reach high-precision predictions in QFT is the calculation of multiloop multileg Feynman integrals. Several new strategies have been proposed in the last years, allowing impressive results with deep…
Our research deals with the optimization version of the set partition problem, where the objective is to minimize the absolute difference between the sums of the two disjoint partitions. Although this problem is known to be NP-hard and…
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
The circuit-theoretic origins of maximal monotonicity are revisited using modern optimization algorithms for maximal monotone operators. We present an algorithm for computing the periodic behavior of an interconnection of maximal monotone…
Creating high performance implementations of deep learning primitives on CPUs is a challenging task. Multiple considerations including multi-level cache hierarchy, and wide SIMD units of CPU platforms influence the choice of program…