
Deep learning of free boundary and Stefan problems
Free boundary problems appear naturally in numerous areas of mathematics...
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Bayesian differential programming for robust systems identification under uncertainty
This paper presents a machine learning framework for Bayesian systems id...
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Exact artificial boundary conditions of 1D semidiscretized peridynamics
The peridynamic theory reformulates the equations of continuum mechanics...
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Understanding and mitigating gradient pathologies in physicsinformed neural networks
The widespread use of neural networks across different scientific domain...
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Machine learning in cardiovascular flows modeling: Predicting pulse wave propagation from noninvasive clinical measurements using physicsinformed deep learning
Advances in computational science offer a principled pipeline for predic...
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Multifidelity classification using Gaussian processes: accelerating the prediction of largescale computational models
Machine learning techniques typically rely on large datasets to create a...
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A comparative study of physicsinformed neural network models for learning unknown dynamics and constitutive relations
We investigate the use of discrete and continuous versions of physicsin...
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PhysicsConstrained Deep Learning for Highdimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
Surrogate modeling and uncertainty quantification tasks for PDE systems ...
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Conditional deep surrogate models for stochastic, highdimensional, and multifidelity systems
We present a probabilistic deep learning methodology that enables the co...
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Physicsinformed deep generative models
We consider the application of deep generative models in propagating unc...
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Adversarial Uncertainty Quantification in PhysicsInformed Neural Networks
We present a deep learning framework for quantifying and propagating unc...
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Machine Learning of SpaceFractional Differential Equations
Datadriven discovery of "hidden physics"  i.e., machine learning of d...
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Multistep Neural Networks for Datadriven Discovery of Nonlinear Dynamical Systems
The process of transforming observed data into predictive mathematical m...
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Physics Informed Deep Learning (Part II): Datadriven Discovery of Nonlinear Partial Differential Equations
We introduce physics informed neural networks  neural networks that ar...
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Physics Informed Deep Learning (Part I): Datadriven Solutions of Nonlinear Partial Differential Equations
We introduce physics informed neural networks  neural networks that ar...
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Numerical Gaussian Processes for Timedependent and Nonlinear Partial Differential Equations
We introduce the concept of numerical Gaussian processes, which we defin...
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