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math.OC2019
Overcoming the curse of dimensionality for some Hamilton--Jacobi partial differential equations via neural network architectures
Jerome Darbon, Gabriel P. Langlois, Tingwei Meng
We propose new and original mathematical connections between Hamilton-Jacobi (HJ) partial differential equations (PDEs) with initial data and neural network architectures. Specific…
math.OC2019
On Decomposition Models in Imaging Sciences and Multi-time Hamilton-Jacobi Partial Differential Equations
Jérôme Darbon, Tingwei Meng
This paper provides new theoretical connections between multi-time Hamilton-Jacobi partial differential equations and variational image decomposition models in imaging sciences. We…