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The recent emergence of deep learning has led to a great deal of work on designing supervised deep semantic segmentation algorithms. As in many tasks sufficient pixel-level labels are very difficult to obtain, we propose a method which…
The large computing and memory cost of deep neural networks (DNNs) often precludes their use in resource-constrained devices. Quantizing the parameters and operations to lower bit-precision offers substantial memory and energy savings for…
A general adaptive approach rooted in stratified sampling (SS) is proposed for sample-based uncertainty quantification (UQ). To motivate its use in this context the space-filling, orthogonality, and projective properties of SS are compared…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
The Iterative Quasi-Monte Carlo (iQMC) method is a recently developed hybrid method for neutron transport simulations. iQMC replaces standard quadrature techniques used in deterministic linear solvers with Quasi-Monte Carlo simulation for…
We analyze the convergence of higher order Quasi-Monte Carlo (QMC) quadratures of solution-functionals to countably-parametric, nonlinear operator equations with distributed uncertain parameters taking values in a separable Banach space $X$…
Quantum Layout Synthesis (QLS) plays a crucial role in optimizing quantum circuit execution on physical quantum devices. As we enter the era where quantum computers have hundreds of qubits, we are faced with scalability issues using optimal…
Recently, deep learning based methods have demonstrated promising results on the graph matching problem, by relying on the descriptive capability of deep features extracted on graph nodes. However, one main limitation with existing deep…
In this paper, we study the deep Ritz method for solving the linear elasticity equation from a numerical analysis perspective. A modified Ritz formulation using the $H^{1/2}(\Gamma_D)$ norm is introduced and analyzed for linear elasticity…
Deep Q-learning Network (DQN) is a successful way which combines reinforcement learning with deep neural networks and leads to a widespread application of reinforcement learning. One challenging problem when applying DQN or other…
We consider distributed optimization problems where networked nodes cooperatively minimize the sum of their locally known convex costs. A popular class of methods to solve these problems are the distributed gradient methods, which are…
Three sampling methods are compared for efficiency on a number of test problems of various complexity for which analytic quadratures are available. The methods compared are Monte Carlo with pseudo-random numbers, Latin Hypercube Sampling,…
Quantum circuit mapping is a critical process in quantum computing that involves adapting logical quantum circuits to adhere to hardware constraints, thereby generating physically executable quantum circuits. Current quantum circuit mapping…
We investigate the application of randomized quasi-Monte Carlo (RQMC) methods in random feature approximations for kernel-based learning. Compared to the classical Monte Carlo (MC) approach \citep{rahimi2007random}, RQMC improves the…
Generalized Method of Moments (GMM) estimators in their various forms, including the popular Maximum Likelihood (ML) estimator, are frequently applied for the evaluation of complex econometric models with not analytically computable moment…
We present an enriched formulation of the Least Squares (LSQ) regression method for Uncertainty Quantification (UQ) using generalised polynomial chaos (gPC). More specifically, we enrich the linear system with additional equations for the…
Quantization is a widely used technique to compress neural networks. Assigning uniform bit-widths across all layers can result in significant accuracy degradation at low precision and inefficiency at high precision. Mixed-precision…
A deep neural network (DNN) is utilized to study the mass of the pseudoscalar glueball in lattice QCD based on Monte Carlo simulations. To obtain an accurate and stable mass value, I constructed a new network. The results show that this DNN…
This paper establishes the almost sure convergence and asymptotic normality of levels and differenced quasi maximum-likelihood (QML) estimators of dynamic panel data models. The QML estimators are robust with respect to initial conditions,…
Reinforcement learning methods typically use Deep Neural Networks to approximate the value functions and policies underlying a Markov Decision Process. Unfortunately, DNN-based RL suffers from a lack of explainability of the resulting…