Neural Operators for Bypassing Gain and Control Computations in PDE Backstepping [PDF]
IEEE Transactions on Automatic Control, 2023 We introduce a framework for eliminating the computation of controller gain functions in partial differential equation (PDE) control. We learn the nonlinear operator from the plant parameters to the control gains with a (deep) neural network.
L. Bhan, Yuanyuan Shi, M. Krstić
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Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics [PDF]
International Conference on Machine Learning, 2023 We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material ...
Pingchuan Ma +6 more
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B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data [PDF]
Journal of Computational Physics, 2020 We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations (PDEs) and noisy data.
Liu Yang, Xuhui Meng, G. Karniadakis
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Clifford Neural Layers for PDE Modeling [PDF]
International Conference on Learning Representations, 2022 Partial differential equations (PDEs) see widespread use in sciences and engineering to describe simulation of physical processes as scalar and vector fields interacting and coevolving over time.
Johannes Brandstetter +3 more
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Quick Review and Assessment of Thermal Stress Analyses for Exact and Assumed Temperature Distribution for Composite and Sandwich Laminates [PDF]
Mechanics of Advanced Composite Structures, 2023 A simple semi-analytical approach is used in the present studies to achieve a thermal response of composite and sandwich layered materials in stresses and displacements. Three-dimensional (3D) heat conduction formulation has been formulated as a boundary
Sandeep Pendhari +4 more
doaj +1 more source
Elliptic PDE learning is provably data-efficient [PDF]
Proceedings of the National Academy of Sciences of the United States of America, 2023 Partial differential equations (PDE) learning is an emerging field that combines physics and machine learning to recover unknown physical systems from experimental data.
N. Boullé +2 more
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Learning Neural PDE Solvers with Parameter-Guided Channel Attention [PDF]
International Conference on Machine Learning, 2023 Scientific Machine Learning (SciML) is concerned with the development of learned emulators of physical systems governed by partial differential equations (PDE).
M. Takamoto +2 more
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Prostate magnetic resonance imaging and the value of experience: An intrareader variability study
Asian Journal of Urology, 2023 Objective: To measure the intraobserver concordance of an experienced genitourinary radiologist reporting of multiparametric magnetic resonance imaging of the prostate (mpMRIp) scans over time.
Thomas Whish-Wilson +4 more
doaj +1 more source
Learning to Solve PDE-constrained Inverse Problems with Graph Networks [PDF]
International Conference on Machine Learning, 2022 Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems.
Qingqing Zhao +2 more
semanticscholar +1 more source
Regularity Theory for Elliptic PDE [PDF]
, 2022 This manuscript aims to provide a self-contained introduction to the regularity theory for elliptic PDE, focusing on the main ideas rather than proving all results in their greatest generality.
Xavier Fernández-Real, Xavier Ros-Oton
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