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Found 10 papers, 6 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.
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.
In-Context Operator Learning with Data Prompts for Differential Equation Problems
This paper introduces a new neural-network-based approach, namely In-Context Operator Networks (ICON), to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight update.
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.
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.
Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates
We propose a simple but effective modification of the discriminators, namely measure-conditional discriminators, as a plug-and-play module for different GANs.
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
