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Found 11 papers, 3 papers with code
Leveraging viscous Hamilton-Jacobi PDEs for uncertainty quantification in scientific machine learning
We provide several examples from SciML involving noisy data and \textit{epistemic uncertainty} to illustrate the potential advantages of our approach.
Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators
As a result, UQ for noisy inputs becomes a crucial factor for reliable and trustworthy deployment of these models in applications involving physical knowledge.
Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning
This connection allows us to reinterpret incremental updates to learned models as the evolution of an associated HJ PDE and optimal control problem in time, where all of the previous information is intrinsically encoded in the solution to the HJ PDE.
Correcting model misspecification in physics-informed neural networks (PINNs)
Despite the effectiveness of PINNs for discovering governing equations, the physical models encoded in PINNs may be misspecified in complex systems as some of the physical processes may not be fully understood, leading to the poor accuracy of PINN predictions.
Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression
Specifically, we integrate physics informed neural networks (PINNs) and symbolic regression to discover a reaction-diffusion type partial differential equation for tau protein misfolding and spreading.
A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimes
Quantifying biomechanical properties of the human vasculature could deepen our understanding of cardiovascular diseases.
Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences.
L-HYDRA: Multi-Head Physics-Informed Neural Networks
We introduce multi-head neural networks (MH-NNs) to physics-informed machine learning, which is a type of neural networks (NNs) with all nonlinear hidden layers as the body and multiple linear output layers as multi-head.
NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators
In this paper, we present an open-source Python library (https://github. com/Crunch-UQ4MI), termed NeuralUQ and accompanied by an educational tutorial, for employing UQ methods for SciML in a convenient and structured manner.
Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systems
Our study reveals the inherent advantages and disadvantages of Neural Networks, Bayesian Inference, and a combination of both and provides valuable guidelines for model selection.
Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods.
