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Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems
Two of the main challenges in optimal control are solving problems with state-dependent running costs and develo** efficient numerical solvers that...
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Decomposition of Convex High Dimensional Aggregative Stochastic Control Problems
We consider the framework of convex high dimensional stochastic control problems, in which the controls are aggregated in the cost function. As first...
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Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems
Numerical methods for the optimal feedback control of high-dimensional dynamical systems typically suffer from the curse of dimensionality. In the...
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VI-DGP: A Variational Inference Method with Deep Generative Prior for Solving High-Dimensional Inverse Problems
Solving high-dimensional Bayesian inverse problems (BIPs) with the variational inference (VI) method is promising but still challenging. The main...
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Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton–Jacobi PDEs
Solving high-dimensional optimal control problems and corresponding Hamilton–Jacobi PDEs are important but challenging problems in control...
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Application of the Godunov Scheme to Solve Three-Dimensional Problems of High-Speed Interactions of Elastoplastic Bodies
AbstractA 3D technique for modeling the high-speed shock-wave interaction of solid deformable bodies with large displacements and deformations in...
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One-Dimensional Variational Problems
This chapter is devoted to one of the most classical classes of variational problems, the one-dimensional case.
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A posteriori error analysis and adaptivity for high-dimensional elliptic and parabolic boundary value problems
We derive a posteriori error estimates for the (stopped) weak Euler method to discretize SDE systems which emerge from the probabilistic...
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Fast Algorithm for Solving Some Three-Dimensional Inverse Problems of Magnetometry
AbstractTypical three-dimensional inverse problems of magnetic prospecting are considered: determination of the vector density of magnetic dipoles in...
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Two-Dimensional Riemann Problems: Transonic Shock Waves and Free Boundary Problems
We are concerned with global solutions of multidimensional (M-D) Riemann problems for nonlinear hyperbolic systems of conservation laws, focusing on...
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High-Dimensional FFT
In this chapter, we discuss methods for the approximation of d-variate functions in high-dimension...
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Split S-ROCK Methods for High-Dimensional Stochastic Differential Equations
We propose explicit stochastic Runge–Kutta (RK) methods for high-dimensional Itô stochastic differential equations. By providing a linear error...
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High-Dimensional Dependent Randomness
The methodology outlined in Chap. 4 will need to be extended in many directions, and most of what is...
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The Calculus of Variations for One-dimensional Problems
The goal of this chapter is to study one-dimensional variational problems where one tries to minimize an integral functionalIntegral functional of...
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High-dimensional approximation with kernel-based multilevel methods on sparse grids
Moderately high-dimensional approximation problems can successfully be solved by combining univariate approximation processes using an intelligent...
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Sparse Spectral Methods for Solving High-Dimensional and Multiscale Elliptic PDEs
In his monograph Chebyshev and Fourier Spectral Methods , John Boyd claimed that, regarding Fourier spectral methods for solving differential...
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A deep learning method for pricing high-dimensional American-style options via state-space partition
This paper proposes a deep learning approach for solving optimal stop** problems and high-dimensional American-style options pricing problems....
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Two-Dimensional Dynamic Problems of the Theory of Elasticity Reduced to Singular Integral Equations with Immobile Singularities
We consider two-dimensional dynamic problems of the theory of elasticity, which can be reduced to singular integral or integrodifferential equations...
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Testing high-dimensional covariance structures using double-normalized observations
In this paper, we focus on the test for high-dimensional covariance structures using double-normalized observations for an elliptical population. By...
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Discretization and index-robust error analysis for constrained high-index saddle dynamics on the high-dimensional sphere
We develop and analyze numerical discretization to the constrained high-index saddle dynamics, the dynamics searching for the high-index saddle...