Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning

arXiv:2311.07790v2 Announce Type: replace
Abstract: We address two major challenges in scientific machine learning (SciML): interpretability and computational efficiency. We increase the interpretability of certain learning processes by establishing a new theoretical connection between optimization problems arising from SciML and a generalized Hopf formula, which represents the viscosity solution to a Hamilton-Jacobi partial differential equation (HJ PDE) with time-dependent Hamiltonian. Namely, we show that when we solve certain regularized learning problems with integral-type losses, we actually solve an optimal control …

abstract arxiv challenges computational continual cs.lg efficiency generalized hamilton interpretability machine machine learning major math.oc optimization processes scientific solution type