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The complex Langevin (CL) method shows great promise in enabling the calculation of observables for theories with complex actions. Nevertheless, real-time quantum field theories have remained largely unsolved due to the particular severity…
For approximately solving linear ill-posed problems in Hilbert spaces, we investigate the regularization properties of the aggregation method and the RatCG method. These recent algorithms use previously calculated solutions of Tikhonov…
We show that numerical quasi-one-dimensional renormalization group allows accurate study of weakly coupled chains with modest computational effort. We perform a systematic comparison with exact diagonalization results in two and three-leg…
System stabilization via policy gradient (PG) methods has drawn increasing attention in both control and machine learning communities. In this paper, we study their convergence and sample complexity for stabilizing linear time-invariant…
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…
A method is proposed to handle the sign problem in the simulation of systems having indefinite or complex-valued measures. In general, this new approach, which is based on renormalisation blocking, is shown to yield statistical errors…
This paper is concerned with the regularization of large-scale discrete inverse problems by means of inexact Krylov methods. Specifically, we derive two new inexact Krylov methods that can be efficiently applied to unregularized or…
We present a novel strategy aimed at restoring correct convergence in complex Langevin simulations. The central idea is to incorporate system-specific prior knowledge into the simulations, in order to circumvent the NP-hard sign problem. In…
We investigate the so-called ``Kaluza-Klein regularisation'' procedure in supersymmetric extensions of the standard model with additional compact dimensions and Scherk-Schwarz mechanism for supersymmetry breaking. This procedure uses a…
A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…
Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…
Consider reconstructing a signal $x$ by minimizing a weighted sum of a convex differentiable negative log-likelihood (NLL) (data-fidelity) term and a convex regularization term that imposes a convex-set constraint on $x$ and enforces its…
Regularization is a critical technique for ensuring well-posedness in solving inverse problems with incomplete measurement data. Traditionally, the regularization term is designed based on prior knowledge of the unknown signal's…
Two new hybrid algorithms are proposed for large-scale linear discrete ill-posed problems in general-form regularization. They are both based on Krylov subspace inner-outer iterative algorithms. At each iteration, they need to solve a…
In this article we combine the projective Landweber method, recently proposed by the authors, with Kaczmarz's method for solving systems of non-linear ill-posed equations. The underlying assumption used in this work is the tangential cone…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulnerable to small or even imperceptible input perturbations, so…
In this work, we propose Regularization-by-Equivariance (REV), a novel structure-adaptive regularization scheme for solving imaging inverse problems under incomplete measurements. This regularization scheme utilizes the equivariant…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
Lattice radial quantization was proposed in a recent paper by Brower, Fleming and Neuberger[1] as a nonperturbative method especially suited to numerically solve Euclidean conformal field theories. The lessons learned from the lattice…