arXiv:2511. 04309v3 Announce Type: replace-cross Abstract: We consider numerical resolution of principal-agent (PA) problems in continuous time.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.
The paper proves that the deep Galerkin method (DGM) converges when applied to Hamilton‑Jacobi‑Bellman equations derived from finite‑state mean field control problems. By showing that the DGM loss can be driven arbitrarily low under sufficient regularity of the value function, and that a vanishing loss forces uniform convergence of the neural network approximators to the true value function on the simplex, the authors establish both existence and convergence results for the DGM. Numerical experiments further illustrate the method’s ability to handle high‑dimensional HJB equations.
arXiv:2408. 11266v5 Announce Type: replace Abstract: Deep learning is now common across many scientific fields, including the study of partial differential equations.
arXiv:2607. 24726v1 Announce Type: new Abstract: The Deep Galerkin Method (DGM) and Physics Informed Neural Networks (PINNs) have become widely-used methods for solving partial differential equations (PDEs) in the rapidly growing field of scientific machine learning.
The paper explores neural network solvers for infinity and p‑Laplace problems, employing Physics‑Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets). It addresses computational challenges for large p values (2 to 1000) across 2D and 3D domains, showing advantages over traditional mesh‑based solvers, especially in three dimensions. The authors provide conditional convergence results for PINNs, a universal approximation theorem for DeepONet on the parametric p‑Poisson problem, and validate their methods with numerical experiments comparing performance to conventional approaches.
arXiv:2608. 06595v1 Announce Type: cross Abstract: Neural networks applied to sequential decision-making tasks typically rely on latent representations of environment states.
The paper proposes a deep learning framework that learns priors for inverse problems by exploiting the relationship between proximal operators and Hamilton–Jacobi partial differential equations. Unlike existing methods that require inverting the prior after training, this approach learns the prior directly, enabling efficient evaluation in a single forward pass. Numerical experiments demonstrate the method’s effectiveness in dimensions up to 64.