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Found 7 papers, 1 papers with code
Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation
To improve training efficiency and to enable control of the approximation error, the network mimics an adaptive finite element method (AFEM).
Generative Modelling with Tensor Train approximations of Hamilton--Jacobi--Bellman equations
Sampling from probability densities is a common challenge in fields such as Uncertainty Quantification (UQ) and Generative Modelling (GM).
Functional SDE approximation inspired by a deep operator network architecture
A novel approach to approximate solutions of Stochastic Differential Equations (SDEs) by Deep Neural Networks is derived and analysed.
Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures
We sample from a given target distribution by constructing a neural network which maps samples from a simple reference, e. g. the standard normal distribution, to samples from the target.
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 numerical solution of high-dimensional parametric PDEs.
A neural multilevel method for high-dimensional parametric PDEs
In scientific machine learning, neural networks recently have become a popular tool for learning the solutions of differential equations.
Uncertainty Quantification
Vocal Bursts Intensity Prediction
Pricing high-dimensional Bermudan options with hierarchical tensor formats
An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented.
