Constructing high‐dimensional neural network potentials: a tutorial review
J Behler - International Journal of Quantum Chemistry, 2015 - Wiley Online Library
A lot of progress has been made in recent years in the development of atomistic potentials
using machine learning (ML) techniques. In contrast to most conventional potentials, which …
using machine learning (ML) techniques. In contrast to most conventional potentials, which …
Neural network potential-energy surfaces in chemistry: a tool for large-scale simulations
J Behler - Physical Chemistry Chemical Physics, 2011 - pubs.rsc.org
The accuracy of the results obtained in molecular dynamics or Monte Carlo simulations
crucially depends on a reliable description of the atomic interactions. A large variety of …
crucially depends on a reliable description of the atomic interactions. A large variety of …
When do extended physics-informed neural networks (XPINNs) improve generalization?
Physics-informed neural networks (PINNs) have become a popular choice for solving high-
dimensional partial differential equations (PDEs) due to their excellent approximation power …
dimensional partial differential equations (PDEs) due to their excellent approximation power …
Approximation theory of the MLP model in neural networks
A Pinkus - Acta numerica, 1999 - cambridge.org
In this survey we discuss various approximation-theoretic problems that arise in the
multilayer feedforward perceptron (MLP) model in neural networks. The MLP model is one of …
multilayer feedforward perceptron (MLP) model in neural networks. The MLP model is one of …
Mathematical modeling of interdependent infrastructure: An object-oriented approach for generalized network-system analysis
Risk and resilience analysis research has favored simpler models such as topological
connectivity and maximum flow algorithm to model infrastructure performance. However …
connectivity and maximum flow algorithm to model infrastructure performance. However …
[图书][B] Recurrent neural networks for prediction: learning algorithms, architectures and stability
DP Mandic, J Chambers - 2001 - dl.acm.org
From the Publisher: From mobile communications to robotics to space technology to medical
instrumentation, new technologies are demanding increasingly complex methods of digital …
instrumentation, new technologies are demanding increasingly complex methods of digital …
Approximation rates for neural networks with general activation functions
We prove some new results concerning the approximation rate of neural networks with
general activation functions. Our first result concerns the rate of approximation of a two layer …
general activation functions. Our first result concerns the rate of approximation of a two layer …
Extreme learning machine collocation for the numerical solution of elliptic PDEs with sharp gradients
We address a new numerical method based on machine learning and in particular based on
the concept of the so-called Extreme Learning Machines, to approximate the solution of …
the concept of the so-called Extreme Learning Machines, to approximate the solution of …
New approach to calculation of atmospheric model physics: Accurate and fast neural network emulation of longwave radiation in a climate model
VM Krasnopolsky, MS Fox-Rabinovitz… - Monthly Weather …, 2005 - journals.ametsoc.org
A new approach based on a synergetic combination of statistical/machine learning and
deterministic modeling within atmospheric models is presented. The approach uses neural …
deterministic modeling within atmospheric models is presented. The approach uses neural …
High-order approximation rates for shallow neural networks with cosine and ReLUk activation functions
We study the approximation properties of shallow neural networks with an activation function
which is a power of the rectified linear unit. Specifically, we consider the dependence of the …
which is a power of the rectified linear unit. Specifically, we consider the dependence of the …