Related papers: Deep Stochastic Mechanics
We prove spatiotemporal algebraically decaying estimates for the density of the solutions of the linearly damped nonlinear Schr\"odinger equation with localized driving, when supplemented with vanishing boundary conditions. Their derivation…
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…
We review an explicit approach to obtaining numerical solutions of the Schr\"odinger equation that is conceptionally straightforward and capable of significant accuracy and efficiency. The method and its efficacy are illustrated with…
Optimization and uncertainty quantification have been playing an increasingly important role in computational hemodynamics. However, existing methods based on principled modeling and classic numerical techniques have faced significant…
Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the…
This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…
We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control…
In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schr\"odinger bridges). We advocate stochastic control as a finite time and low variance alternative to popular…
Accurate numerical solutions for the Schr\"odinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining…
The Loewner equation, in its stochastic incarnation introduced by Schramm, is an insightful method for the description of critical random curves and interfaces in two-dimensional statistical mechanics. Two features are crucial, namely…
In order to inherit numerically the ergodicity of the damped stochastic nonlinear Schr\"odinger equation with additive noise, we propose a fully discrete scheme, whose spatial direction is based on spectral Galerkin method and temporal…
Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…
We discuss the time evolution of the wave function which is solution of a stochastic Schroedinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and…
Stochastic generators are essential to produce synthetic realizations that preserve target statistical properties. We propose GenFormer, a stochastic generator for spatio-temporal multivariate stochastic processes. It is constructed using a…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…
Robust control design for quantum systems is a challenging and key task for practical technology. In this work, we apply neural networks to learn the control problem for the semiclassical Schr\"odinger equation, where the control variable…
We give an example of a mathematical model describing quantum mechanical processes interacting with medium. As a model, we consider the process of heat scattering of a wave function defined on the phase space. We consider the case when the…
We consider the Schr\"odinger bridge problem which, given ensemble measurements of the initial and final configurations of a stochastic dynamical system and some prior knowledge on the dynamics, aims to reconstruct the "most likely"…
We consider an open model possessing a Markovian quantum stochastic limit and derive the limit stochastic Schrodinger equations for the wave function conditioned on indirect observations using only the von Neumann projection postulate. We…