[HTML][HTML] Integrating machine learning with human knowledge
Machine learning has been heavily researched and widely used in many disciplines.
However, achieving high accuracy requires a large amount of data that is sometimes …
However, achieving high accuracy requires a large amount of data that is sometimes …
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning
In recent years, tremendous progress has been made on numerical algorithms for solving
partial differential equations (PDEs) in a very high dimension, using ideas from either …
partial differential equations (PDEs) in a very high dimension, using ideas from either …
Deep splitting method for parabolic PDEs
In this paper, we introduce a numerical method for nonlinear parabolic partial differential
equations (PDEs) that combines operator splitting with deep learning. It divides the PDE …
equations (PDEs) that combines operator splitting with deep learning. It divides the PDE …
Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard …
One of the most challenging problems in applied mathematics is the approximate solution of
nonlinear partial differential equations (PDEs) in high dimensions. Standard deterministic …
nonlinear partial differential equations (PDEs) in high dimensions. Standard deterministic …
Deep reinforcement learning for adaptive mesh refinement
Finite element discretizations of problems in computational physics often rely on adaptive
mesh refinement (AMR) to preferentially resolve regions containing important features …
mesh refinement (AMR) to preferentially resolve regions containing important features …
Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities
Partial differential equations (PDEs) are a fundamental tool in the modeling of many real-
world phenomena. In a number of such real-world phenomena the PDEs under …
world phenomena. In a number of such real-world phenomena the PDEs under …
Iterative value-aware model learning
A Farahmand - Advances in Neural Information Processing …, 2018 - proceedings.neurips.cc
This paper introduces a model-based reinforcement learning (MBRL) framework that
incorporates the underlying decision problem in learning the transition model of the …
incorporates the underlying decision problem in learning the transition model of the …
Space-time error estimates for deep neural network approximations for differential equations
Over the last few years deep artificial neural networks (ANNs) have very successfully been
used in numerical simulations for a wide variety of computational problems including …
used in numerical simulations for a wide variety of computational problems including …
Exploiting the flexibility inside park-level commercial buildings considering heat transfer time delay: A memory-augmented deep reinforcement learning approach
The energy consumed by commercial buildings for heating and cooling is significantly
increased. To better cope with the uncertainty introduced by the high penetration of …
increased. To better cope with the uncertainty introduced by the high penetration of …