Low-rank tensor methods for partial differential equations
M Bachmayr - Acta Numerica, 2023 - cambridge.org
Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …
functions. These concepts, which essentially amount to generalizations of classical …
An optimal control perspective on diffusion-based generative modeling
We establish a connection between stochastic optimal control and generative models based
on stochastic differential equations (SDEs), such as recently developed diffusion …
on stochastic differential equations (SDEs), such as recently developed diffusion …
Learning optimal feedback operators and their sparse polynomial approximations
K Kunisch, D Vásquez-Varas, D Walter - Journal of Machine Learning …, 2023 - jmlr.org
A learning based method for obtaining feedback laws for nonlinear optimal control problems
is proposed. The learning problem is posed such that the open loop value function is its …
is proposed. The learning problem is posed such that the open loop value function is its …
Data-driven tensor train gradient cross approximation for hamilton–jacobi–bellman equations
A gradient-enhanced functional tensor train cross approximation method for the resolution of
the Hamilton–Jacobi–Bellman (HJB) equations associated with optimal feedback control of …
the Hamilton–Jacobi–Bellman (HJB) equations associated with optimal feedback control of …
[HTML][HTML] Approximation of optimal control problems for the Navier-Stokes equation via multilinear HJB-POD
We consider the approximation of some optimal control problems for the Navier-Stokes
equation via a Dynamic Programming approach. These control problems arise in many …
equation via a Dynamic Programming approach. These control problems arise in many …
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems
T Ehring, B Haasdonk - Advances in Computational Mathematics, 2024 - Springer
Numerical methods for the optimal feedback control of high-dimensional dynamical systems
typically suffer from the curse of dimensionality. In the current presentation, we devise a …
typically suffer from the curse of dimensionality. In the current presentation, we devise a …
From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs
The numerical approximation of partial differential equations (PDEs) poses formidable
challenges in high dimensions since classical grid-based methods suffer from the so-called …
challenges in high dimensions since classical grid-based methods suffer from the so-called …
[HTML][HTML] Optimal polynomial feedback laws for finite horizon control problems
K Kunisch, D Vásquez-Varas - Computers & Mathematics with Applications, 2023 - Elsevier
A learning technique for finite horizon optimal control problems and its approximation based
on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is …
on polynomials is analyzed. It allows to circumvent, in part, the curse dimensionality which is …
Learning optimal feedback operators and their polynomial approximation
A learning based method for obtaining feedback laws for nonlinear optimal control problems
is proposed. The learning problem is posed such that the open loop value function is its …
is proposed. The learning problem is posed such that the open loop value function is its …
Dynamical low‐rank approximations of solutions to the Hamilton–Jacobi–Bellman equation
M Eigel, R Schneider, D Sommer - Numerical Linear Algebra …, 2023 - Wiley Online Library
We present a novel method to approximate optimal feedback laws for nonlinear optimal
control based on low‐rank tensor train (TT) decompositions. The approach is based on the …
control based on low‐rank tensor train (TT) decompositions. The approach is based on the …