Related papers: Bayesian Parameter Shift Rule in Variational Quant…

The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…

The variational quantum eigensolver is a hybrid algorithm composed of quantum state driving and classical parameter optimization, for finding the ground state of a given Hamiltonian. The natural gradient method is an optimization method…

The phase shift rules enable the estimation of the derivative of a quantum state with respect to phase parameters, providing valuable insights into the behavior and dynamics of quantum systems. This capability is essential in quantum…

This paper proposes a new gradient-based optimization approach for designing optimal feedback kernels for parabolic distributed parameter systems with boundary control. Unlike traditional kernel optimization methods for parabolic systems,…

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…

Gaussian processes (GPs) are Bayesian non-parametric models popular in a variety of applications due to their accuracy and native uncertainty quantification (UQ). Tuning GP hyperparameters is critical to ensure the validity of prediction…

Stochastic kinetic models are ubiquitous in physics, yet inferring their parameters from experimental data remains challenging. In deterministic models, parameter inference often relies on gradients, as they can be obtained efficiently…

Recent advances in quantum computing and their increased availability has led to a growing interest in possible applications. Among those is the solution of partial differential equations (PDEs) for, e.g., material or flow simulation.…

This paper considers mean square error (MSE) analysis for stochastic gradient sampling algorithms applied to underdamped Langevin dynamics under a global convexity assumption. A novel discrete Poisson equation framework is developed to…

We present a novel approach to accelerate stochastic gradient descent (SGD) by utilizing curvature information obtained from Hessian-vector products or finite differences of parameters and gradients, similar to the BFGS algorithm. Our…

The Adaptive Variational Quantum Eigensolver (ADAPT-VQE) is a promising approach for quantum algorithms in the Noisy Intermediate-Scale Quantum (NISQ) era, offering advantages over traditional VQE methods by reducing circuit depth and…

Variational algorithms are promising candidates to be implemented on near-term quantum computers. The variational quantum eigensolver (VQE) is a prominent example, where a parametrized trial state of the quantum mechanical wave function is…

We derive finite-particle rates for the regularized Stein variational gradient descent (R-SVGD) algorithm introduced by He et al. (2024) that corrects the constant-order bias of the SVGD by applying a resolvent-type preconditioner to the…

Gaussian processes provide probabilistic surrogates for various applications including classification, uncertainty quantification, and optimization. Using a gradient-enhanced covariance matrix can be beneficial since it provides a more…

Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…

Over the past decade, a number of algorithms for full-field elastic strain estimation from neutron and X-ray measurements have been published. Many of the recently published algorithms rely on modelling the unknown strain field as a…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation…

Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…

Consider the following distributed optimization scenario. A worker has access to training data that it uses to compute the gradients while a server decides when to stop iterative computation based on its target accuracy or delay…