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Found 5 papers, 1 papers with code
Ensemble-Based Annealed Importance Sampling
We discuss how the proposed algorithm can be implemented and derive a partial differential equation governing the evolution of the ensemble under the continuous time and mean-field limit.
When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimality
We demonstrate that this kind of quadrature rule can improve the Monte Carlo rate and achieve the minimax optimal rate under a sufficient smoothness assumption.
Physics-Informed Neural Operator for Learning Partial Differential Equations
Specifically, in PINO, we combine coarse-resolution training data with PDE constraints imposed at a higher resolution.
Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality
In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs).
Statistical Numerical PDE : Fast Rate, Neural Scaling Law and When it’s Optimal
In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs).
