Leveraging multitime Hamilton–Jacobi PDEs for certain scientific machine learning problems
Hamilton–Jacobi partial differential equations (HJ PDEs) have deep connections with a wide
range of fields, including optimal control, differential games, and imaging sciences. By …
range of fields, including optimal control, differential games, and imaging sciences. By …
Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning
We address two major challenges in scientific machine learning (SciML): interpretability and
computational efficiency. We increase the interpretability of certain learning processes by …
computational efficiency. We increase the interpretability of certain learning processes by …
Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning
Uncertainty quantification (UQ) in scientific machine learning (SciML) combines the powerful
predictive power of SciML with methods for quantifying the reliability of the learned models …
predictive power of SciML with methods for quantifying the reliability of the learned models …
Adaptive deep learning for high-dimensional Hamilton--Jacobi--Bellman equations
Computing optimal feedback controls for nonlinear systems generally requires solving
Hamilton--Jacobi--Bellman (HJB) equations, which are notoriously difficult when the state …
Hamilton--Jacobi--Bellman (HJB) equations, which are notoriously difficult when the state …
Primal-dual hybrid gradient algorithms for computing time-implicit Hamilton-Jacobi equations
Hamilton-Jacobi (HJ) partial differential equations (PDEs) have diverse applications
spanning physics, optimal control, game theory, and imaging sciences. This research …
spanning physics, optimal control, game theory, and imaging sciences. This research …
Weak form generalized hamiltonian learning
We present a method for learning generalized Hamiltonian decompositions of ordinary
differential equations given a set of noisy time series measurements. Our method …
differential equations given a set of noisy time series measurements. Our method …
Algorithms of data generation for deep learning and feedback design: A survey
Recent research reveals that deep learning is an effective way of solving high dimensional
Hamilton–Jacobi–Bellman equations. The resulting feedback control law in the form of a …
Hamilton–Jacobi–Bellman equations. The resulting feedback control law in the form of a …
Recursive regression with neural networks: Approximating the HJI PDE solution
Most machine learning applications using neural networks seek to approximate some
function g (x) by minimizing some cost criterion. In the simplest case, if one has access to …
function g (x) by minimizing some cost criterion. In the simplest case, if one has access to …
Constrained physical-statistics models for dynamical system identification and prediction
Modeling dynamical systems combining prior physical knowledge and machinelearning
(ML) is promising in scientific problems when the underlying processesare not fully …
(ML) is promising in scientific problems when the underlying processesare not fully …
A causality-free neural network method for high-dimensional Hamilton-Jacobi-Bellman equations
T Nakamura-Zimmerer, Q Gong… - 2020 American Control …, 2020 - ieeexplore.ieee.org
Computing optimal feedback controls for nonlinear systems generally requires solving
Hamilton-Jacobi-Bellman (HJB) equations, which, in high dimensions, are notoriously …
Hamilton-Jacobi-Bellman (HJB) equations, which, in high dimensions, are notoriously …