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We present an analysis of the Feynman path centroid density that provides new insight into the correspondence between the path integral and the Schr\"odinger formulations of statistical mechanics. The path centroid density is a central…
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
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…
This article deals with error estimates for the finite element approximation of variational normal derivatives and, as a consequence, error estimates for the finite element approximation of Dirichlet boundary control problems with energy…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step…
Particle theorists typically use expectation values to study the quantum back-reaction on inflation, whereas many cosmologists stress the stochastic nature of the process. While expectation values certainly give misleading results for some…
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting…
We give a pedagogical review of the application of field theoretic and path integral methods to calculate moments of the probability density function of stochastic differential equations perturbatively.
Equilibrium properties in statistical physics are obtained by computing averages with respect to Boltzmann-Gibbs measures, sampled in practice using ergodic dynamics such as the Langevin dynamics. Some quantities however cannot be computed…
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious…
The dramatically growing availability of observational data is being witnessed in various domains of science and technology, which facilitates the study of causal inference. However, estimating treatment effects from observational data is…
In this work, weakly corrected explicit, semi-implicit and implicit Milstein approximations are presented for the solution of nonlinear stochastic differential equations. The solution trajectories provided by the Milstein schemes are…
We address the problem of estimating the expected shortfall risk of a financial loss using a finite number of i.i.d. data. It is well known that the classical plug-in estimator suffers from poor statistical performance when faced with…
Effective harmonic methods allow for calculating temperature dependent phonon frequencies by incorporating the anharmonic contributions into an effective harmonic Hamiltonian. The systematic errors arising from such an approximation are…
Equilibrium measures are special invariant measures of chaotic dynamical systems and iterated function systems, commonly studied as salient examples of fractal measures. While useful analytic expressions are rare, computational exploration…
The self-consistent harmonic approximation is an effective harmonic theory to calculate the free energy of systems with strongly anharmonic atomic vibrations, and its stochastic implementation has proved to be an efficient method to study,…
So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov regularization for the solution of inverse problems for…
Rare trajectories of stochastic systems are important to understand -- because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their…
We propose a method for efficient simulations in extended ensembles, useful, e.g., for the study of problems with complex energy landscapes and for free energy calculations. The main difficulty in such simulations is the estimation of the a…