Explainable machine learning for scientific insights and discoveries
Machine learning methods have been remarkably successful for a wide range of application
areas in the extraction of essential information from data. An exciting and relatively recent …
areas in the extraction of essential information from data. An exciting and relatively recent …
[HTML][HTML] Forecasting global climate drivers using Gaussian processes and convolutional autoencoders
Abstract Machine learning (ML) methods have become an important tool for modelling and
forecasting complex high-dimensional spatiotemporal datasets such as those found in …
forecasting complex high-dimensional spatiotemporal datasets such as those found in …
A theoretical analysis of deep neural networks and parametric PDEs
We derive upper bounds on the complexity of ReLU neural networks approximating the
solution maps of parametric partial differential equations. In particular, without any …
solution maps of parametric partial differential equations. In particular, without any …
Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space
Optimal control of diffusion processes is intimately connected to the problem of solving
certain Hamilton–Jacobi–Bellman equations. Building on recent machine learning inspired …
certain Hamilton–Jacobi–Bellman equations. Building on recent machine learning inspired …
Numerical solution of the parametric diffusion equation by deep neural networks
M Geist, P Petersen, M Raslan, R Schneider… - Journal of Scientific …, 2021 - Springer
We perform a comprehensive numerical study of the effect of approximation-theoretical
results for neural networks on practical learning problems in the context of numerical …
results for neural networks on practical learning problems in the context of numerical …
Numerically solving parametric families of high-dimensional Kolmogorov partial differential equations via deep learning
We present a deep learning algorithm for the numerical solution of parametric families of
high-dimensional linear Kolmogorov partial differential equations (PDEs). Our method is …
high-dimensional linear Kolmogorov partial differential equations (PDEs). Our method is …
Multilevel CNNs for Parametric PDEs
We combine concepts from multilevel solvers for partial differential equations (PDEs) with
neural network based deep learning and propose a new methodology for the efficient …
neural network based deep learning and propose a new methodology for the efficient …
Active importance sampling for variational objectives dominated by rare events: Consequences for optimization and generalization
GM Rotskoff, AR Mitchell… - … and Scientific Machine …, 2022 - proceedings.mlr.press
Deep neural networks, when optimized with sufficient data, provide accurate representations
of high-dimensional functions; in contrast, function approximation techniques that have …
of high-dimensional functions; in contrast, function approximation techniques that have …
Data-driven tensor train gradient cross approximation for hamilton–jacobi–bellman equations
A gradient-enhanced functional tensor train cross approximation method for the resolution of
the Hamilton–Jacobi–Bellman (HJB) equations associated with optimal feedback control of …
the Hamilton–Jacobi–Bellman (HJB) equations associated with optimal feedback control of …
Research on deep learning image processing technology of second-order partial differential equations
Q Wu - Neural Computing and Applications, 2023 - Springer
Image classification can effectively manage and organize images, laying a good foundation
for the work in multiple fields of image processing. With the rise of Internet technology and …
for the work in multiple fields of image processing. With the rise of Internet technology and …