Feature engineering with regularity structures

DOI10.1007/s10915-023-02401-4zbMath1527.60084arXiv2108.05879OpenAlexW3187934771MaRDI QIDQ6184277

Hendrik Weber, Ilya Chevyrev, Andris Gerasimovičs

Publication date: 5 January 2024

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.05879

zbMATH Keywords

supervised learningpartial differential equationsregressionregularity structurespath signatures

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Regularity structures (60L30)

Cites Work

• Unnamed Item
• The signature of a rough path: uniqueness
• A theory of regularity structures
• Regression modeling strategies. With applications to linear models, logistic regression, and survival analysis
• Characteristic functions of measures on geometric rough paths
• Parameter estimation for rough differential equations
• Uniqueness for the signature of a path of bounded variation and the reduced path group
• Differential equations driven by rough signals
• Algebraic renormalisation of regularity structures
• DGM: a deep learning algorithm for solving partial differential equations
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• An Introduction to Computational Stochastic PDEs
• Dynamic mode decomposition of numerical and experimental data
• Integration of Paths--A Faithful Representation of Paths by Noncommutative Formal Power Series
• Machine Learning for Fluid Mechanics
• Spectral analysis of nonlinear flows
• Kernels for sequentially ordered data
• Solving high-dimensional partial differential equations using deep learning
• An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions
• Numerical Method for Model-free Pricing of Exotic Derivatives in Discrete Time Using Rough Path Signatures
• Optimal Execution with Rough Path Signatures
• Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
• Deep Nitsche Method: Deep Ritz Method with Essential Boundary Conditions
• Stochastic Equations in Infinite Dimensions
• Learning data-driven discretizations for partial differential equations
• Reynolds averaged turbulence modelling using deep neural networks with embedded invariance

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