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Herbert's Projects

graphgalerkin icon graphgalerkin

Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems

pde-surrogate icon pde-surrogate

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

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References on Optimal Control, Reinforcement Learning and Motion Planning

phygeonet icon phygeonet

PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parametric PDEs on Irregular Domain

picnnsr icon picnnsr

Super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels -- parametric forward SR and boundary inference

pinns icon pinns

PyTorch Implementation of Physics-informed Neural Networks

pinns-based-mpc icon pinns-based-mpc

We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs are not suited for control tasks in their original form since they are not designed to handle variable control actions or variable initial values. We thus present the idea of enhancing PINNs by adding control actions and initial conditions as additional network inputs. The high-dimensional input space is subsequently reduced via a sampling strategy and a zero-hold assumption. This strategy enables the controller design based on a PINN as an approximation of the underlying system dynamics. The additional benefit is that the sensitivities are easily computed via automatic differentiation, thus leading to efficient gradient-based algorithms. Finally, we present our results using our PINN-based MPC to solve a tracking problem for a complex mechanical system, a multi-link manipulator.

ppnn icon ppnn

Predicting parametric spatiotemporal dynamics by multi-resolution PDE structure-preserved deep learning

sga-pde icon sga-pde

Symbolic genetic algorithm for discovering open-form partial differential equations

sno icon sno

Spectral Neural Operator

udtl icon udtl

Source codes for the paper "Applications of Unsupervised Deep Transfer Learning to Intelligent Fault Diagnosis: A Survey and Comparative Study" published in TIM

uqpinns-tf2.0 icon uqpinns-tf2.0

TensorFlow 2.0 implementation of Yibo Yang, Paris Perdikaris’s adversarial Uncertainty Quantification in Physics Informed Neural Networks (UQPINNs).

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