Related papers: New Optimization Methods for Converging Perturbati…
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…
The nonperturbative linear delta expansion (LDE) method is applied to the critical O(N) phi^4 three-dimensional field theory which has been widely used to study the critical temperature of condensation of dilute weakly interacting…
The hadronic decay rate of the tau lepton serves as one of the most precise determinations of the QCD coupling alpha_s. The dominant theoretical source of uncertainty at present resides in the seeming disparity of two approaches to…
Recently-developed variational perturbation expansions converge exponentially fast for positive coupling constants. They do not, however, possess the correct left-hand cut in the complex coupling constant plane, implying a wrong large-order…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
We present in detail a new systematic method which can be used to automatically eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions at all orders. We show that all of the nonconformal \beta-dependent…
We present a new approach to determining the strong coupling $\alpha_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $\Lambda_{\mathrm{QCD}}$ and up to the Planck scale $\sim1.22\cdot10^{19}$\,GeV, with the…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
A variant of variationally optimized perturbation, incorporating renormalization group properties in a straightforward way, uniquely fixes the variational mass interpolation in terms of the anomalous mass dimension. It is used at three…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We study cutoff and lattice effects in the O(n) symmetric $\phi^4$ theory for a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions. In the large-N limit above $T_c$, we show that $\phi^4$ field theory at finite…
A unified approach to derive optimal finite differences is presented which combines three critical elements for numerical performance especially for multi-scale physical problems, namely, order of accuracy, spectral resolution and…
We study the Hamiltonian truncation for the two-dimensional $\lambda\phi^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms…
We study the optimized perturbation theory (OPT) at finite temperature, which is a self-consistent resummation method. Firstly, we generalize the idea of the OPT to optimize the coupling constant in lambda phi^4 theory, and give a proof of…
In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown…
Perturbative coefficients grow factorially with the order and one needs a prescription to truncate the series in order to obtain a finite result. A common prescription consists in dropping the smallest contribution at a given coupling and…
Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite…
We introduce suitable coordinate systems for pipes and their variants that allow us to transform partial differential equations (PDEs) on the pipe surfaces or in the solid pipes into computational domains with fixed limits/ranges. Such a…
We introduce a conceptual framework for numerically solving linear elliptic, parabolic, and hyperbolic PDEs on bounded, polytopal domains in euclidean spaces by deep neural networks. The PDEs are recast as minimization of a least-squares…