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The perturbation theory based on typicality introduced in Ref. [1] and further refined in Refs. [2, 3] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while relying only on a few parameters. Even…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…
We consider the inverse conductivity problem with discontinuous conductivities. We show in a rigorous way, by a convergence analysis, that one can construct a completely discrete minimization problem whose solution is a good approximation…
In this paper, we consider the 1D wave equation where the spatial domain is a bounded interval. Assuming the initial conditions to be known, we are here interested in identifying an unknown source term, while we take the Neumann derivative…
Linear time-domain simulations of acoustic oscillations are unstable in the stellar convection zone. To overcome this problem it is customary to compute the oscillations of a stabilized background stellar model. The stabilization, however,…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as…
We study an inverse source problem for the acoustic wave equation in a random waveguide. The goal is to estimate the source of waves from measurements of the acoustic pressure at a remote array of sensors. The waveguide effect is due to…
We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
We apply an extension of a new method of group classification to a family of nonlinear wave equations labelled by two arbitrary functions, each depending on its own argument. The results obtained confirm the efficiency of the proposed…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…
We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We use the non-perturbative renormalization group to clarify some features of perturbation theory in thermal field theory. For the specific case of the scalar field theory with O(N) symmetry, we solve the flow equations within the local…