Related papers: Variational Quantum Crank-Nicolson and Method of L…

A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference…

In this article, we study Bayesian inverse problems with multi-layered Gaussian priors. We first describe the conditionally Gaussian layers in terms of a system of stochastic partial differential equations. We build the computational…

Variational inequalities can in general support distinct solutions. In this paper we study an algorithm for computing distinct solutions of a variational inequality, without varying the initial guess supplied to the solver. The central idea…

Value functions are central to Dynamic Programming and Reinforcement Learning but their exact estimation suffers from the curse of dimensionality, challenging the development of practical value-function (VF) estimation algorithms. Several…

In this work, two novel classes of structure-preserving spectral Galerkin methods are proposed which based on the Crank-Nicolson scheme and the exponential scalar auxiliary variable method respectively, for solving the coupled fractional…

We propose a variational autoencoder (VAE) approach for parameter estimation in nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs) using longitudinal data from multiple subjects. In moderate dimensions,…

Learning representations for solutions of constrained optimization problems (COPs) with unknown cost functions is challenging, as models like (Variational) Autoencoders struggle to enforce constraints when decoding structured outputs. We…

As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the…

We propose a geometric approach for the numerical integration of singular initial value problems for (systems of) quasi-linear differential equations. It transforms the original problem into the problem of computing the unstable manifold at…

Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…

Sampling of sharp posteriors in high dimensions is a challenging problem, especially when gradients of the likelihood are unavailable. In low to moderate dimensions, affine-invariant methods, a class of ensemble-based gradient-free methods,…

In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…

Slow kinetic processes of molecular systems can be analyzed by computing dominant eigenpairs of the Koopman operator or its generator. In this context, the Variational Approach to Markov Processes (VAMP) provides a rigorous way of…

A method for carrying out semiclassical initial value representation calculations using first-principles molecular dynamics (FP-SC-IVR) is presented. This method can extract the full vibrational power spectrum of carbon dioxide from a…

We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are…

This paper presents a numerical method based on the variational quantum algorithm to solve potential and Stokes flow problems. In this method, the governing equations for potential and Stokes flows can be respectively written in the form of…

This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite…

Despite advances in deep probabilistic models, learning discrete latent representations remains challenging. This work introduces a novel method to improve inference in discrete Variational Autoencoders by reframing the inference problem…

Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE)…

We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…