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Found 13 papers, 5 papers with code
Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning
We provide several examples from SciML involving noisy data and \textit{epistemic uncertainty} to illustrate the potential advantages of our approach.
Efficient first-order algorithms for large-scale, non-smooth maximum entropy models with application to wildfire science
State-of-the-art algorithms for Maxent models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical Maxent models lack.
Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning
This connection allows us to reinterpret incremental updates to learned models as the evolution of an associated HJ PDE and optimal control problem in time, where all of the previous information is intrinsically encoded in the solution to the HJ PDE.
Leveraging Multi-time 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.
SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems
Solving high-dimensional optimal control problems in real-time is an important but challenging problem, with applications to multi-agent path planning problems, which have drawn increased attention given the growing popularity of drones in recent years.
Efficient and robust high-dimensional sparse logistic regression via nonlinear primal-dual hybrid gradient algorithms
Since modern big data sets can contain hundreds of thousands to billions of predictor variables, variable selection methods depend on efficient and robust optimization algorithms to perform well.
Accelerated nonlinear primal-dual hybrid gradient methods with applications to supervised machine learning
To address this issue, we introduce accelerated nonlinear PDHG methods that achieve an optimal convergence rate with stepsize parameters that are simple and efficient to compute.
On Hamilton-Jacobi PDEs and image denoising models with certain non-additive noise
We show that the optimal values are ruled by some Hamilton-Jacobi PDEs, while the optimizers are characterized by the spatial gradient of the solution to the Hamilton-Jacobi PDEs.
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs
In this paper, we propose two abstract neural network architectures which are respectively used to compute the value function and the optimal control for certain class of high dimensional optimal control problems.
Connecting Hamilton--Jacobi partial differential equations with maximum a posteriori and posterior mean estimators for some non-convex priors
In [23, 26], connections between these optimization problems and (multi-time) Hamilton--Jacobi partial differential equations have been proposed under the convexity assumptions of both the data fidelity and regularization terms.
A Caputo fractional derivative-based algorithm for optimization
We propose three versions -- non-adaptive, adaptive terminal and adaptive order.
Optimal Trajectories of a UAV Base Station Using Hamilton-Jacobi Equations
We derive closed-form formulas for the optimal trajectory when the traffic intensity is quadratic (single-phase) using Hamilton-Jacobi equations.
Optimization and Control Networking and Internet Architecture
On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton--Jacobi partial differential equations
We propose novel connections between several neural network architectures and viscosity solutions of some Hamilton--Jacobi (HJ) partial differential equations (PDEs) whose Hamiltonian is convex and only depends on the spatial gradient of the solution.
Numerical Analysis Numerical Analysis
