相关论文: Analytical approximation schemes for solving exact…

A functional analytic approach to obtaining self-improving properties of solutions to linear non-local elliptic equations is presented. It yields conceptually simple and very short proofs of some previous results due to Kuusi-Mingione-Sire…

In this paper, we analyze convergence and supercloseness properties of a class of weak Galerkin (WG) finite element methods for solving second-order elliptic problems. It is shown that the WG solution is superclose to the Lagrange type…

Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…

Heterogeneous treatment effect (HTE) estimation from observational data poses significant challenges due to treatment selection bias. Existing methods address this bias by minimizing distribution discrepancies between treatment groups in…

A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…

Exact renormalization group techniques are applied to mass deformed N=4 supersymmetric Yang-Mills theory, viewed as a regularised N=2 model. The solution of the flow equation, in the local potential approximation, reproduces the one-loop…

In this work, we consider a non-standard preconditioning strategy for the numerical approximation of the classical elliptic equations with log-normal random coefficients. In \cite{Wan_model}, a Wick-type elliptic model was proposed by…

Reinforcement learning (RL) problems over general state and action spaces are notoriously challenging. In contrast to the tableau setting, one can not enumerate all the states and then iteratively update the policies for each state. This…

In this paper, we investigate a Local Discontinuous Galerkin (LDG) approximation for systems with balanced Orlicz-structure. We propose a new numerical flux, which yields optimal convergence rates for linear ansatz functions. In particular,…

This paper considers a convex composite optimization problem with affine constraints, which includes problems that take the form of minimizing a smooth convex objective function over the intersection of (simple) convex sets, or regularized…

We study the problem of likelihood maximization when the likelihood function is intractable but model simulations are readily available. We propose a sequential, gradient-based optimization method that directly models the Fisher score based…

In this article we propose a shooting algorithm for partially-affine optimal control problems, this is, systems in which the controls appear both linearly and nonlinearly in the dynamics. Since the shooting system generally has more…

Over the last several years, there has been a resurgence of interest in using non-perturbative approximation methods based on Wilson's continuous renormalization group. In this lecture, I review progress particularly in the past year,…

The study of the effective potential for non-renormalisable scalar SO(N) symmetric theories leads to recurrence relations for the coefficients of the leading logarithms. These relations can be transformed into generalised…

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…

We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension…

In this paper, we derive an asymptotic error expansion for the eigenvalue approximations by the lowest order Raviart-Thomas mixed finite element method for the general second order elliptic eigenvalue problems. Extrapolation based on such…

We extend the Deep Galerkin Method (DGM) introduced in Sirignano and Spiliopoulos (2018)} to solve a number of partial differential equations (PDEs) that arise in the context of optimal stochastic control and mean field games. First, we…

In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish novel (weighted) conditional stability estimates under very…

We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is…