Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons
From MaRDI portal
Publication:2681129
DOI10.1016/j.jcp.2022.111902OpenAlexW4315628777MaRDI QIDQ2681129
Zongren Zou, Apostolos F. Psaros, Xuhui Meng, Ling Guo, George Em. Karniadakis
Publication date: 10 February 2023
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2201.07766
stochastic partial differential equationsuncertainty quantificationBayesian frameworkphysics-informed neural networksscientific machine learningneural operator learning
Parametric inference (62Fxx) Artificial intelligence (68Txx) Probabilistic methods, stochastic differential equations (65Cxx)
Related Items
NeuralUQ, Constant Q-transform-based deep learning architecture for detection of obstructive sleep apnea, Discrete-time nonlinear feedback linearization via physics-informed machine learning, Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems, Reliable extrapolation of deep neural operators informed by physics or sparse observations, Conditional Karhunen-Loève regression model with basis adaptation for high-dimensional problems: uncertainty quantification and inverse modeling, Variational inference in neural functional prior using normalizing flows: application to differential equation and operator learning problems, Quality measures for the evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems, NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators, Physics-informed variational inference for uncertainty quantification of stochastic differential equations, Physics-informed learning under epistemic uncertainty with an application to system health modeling, Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression, Generalised likelihood profiles for models with intractable likelihoods
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Learning constitutive relations from indirect observations using deep neural networks
- Inconsistency of Bayesian inference for misspecified linear models, and a proposal for repairing it
- Deep learning: a Bayesian perspective
- Convergence of a stochastic approximation version of the EM algorithm
- Deep UQ: learning deep neural network surrogate models for high dimensional uncertainty quantification
- DGM: a deep learning algorithm for solving partial differential equations
- PPINN: parareal physics-informed neural network for time-dependent PDEs
- Efficient uncertainty quantification for dynamic subsurface flow with surrogate by theory-guided neural network
- \textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
- Aleatoric and epistemic uncertainty in machine learning: an introduction to concepts and methods
- Bayesian neural networks: an introduction and survey
- GINNs: graph-informed neural networks for multiscale physics
- On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton-Jacobi partial differential equations
- B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
- Multi-fidelity Bayesian neural networks: algorithms and applications
- Meta-learning PINN loss functions
- A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the small data regime
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems
- Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks
- Solving inverse problems in stochastic models using deep neural networks and adversarial training
- Bayesian neural networks for uncertainty quantification in data-driven materials modeling
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems
- Langevin diffusions and the Metropolis-adjusted Langevin algorithm
- Wasserstein generative adversarial uncertainty quantification in physics-informed neural networks
- Scalable uncertainty quantification for deep operator networks using randomized priors
- Probable networks and plausible predictions — a review of practical Bayesian methods for supervised neural networks
- Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
- Variational Inference Formulation for a Model-Free Simulation of a Dynamical System with Unknown Parameters by a Recurrent Neural Network
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- GAN-Based Priors for Quantifying Uncertainty in Supervised Learning
- Bayesian differential programming for robust systems identification under uncertainty
- Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
- On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
- An Introduction to Variational Autoencoders
- Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
- Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
- fPINNs: Fractional Physics-Informed Neural Networks
- Deep Learning: An Introduction for Applied Mathematicians
- Probabilistic Forecasts, Calibration and Sharpness
- Advanced Lectures on Machine Learning
- Stochastic Gradient Markov Chain Monte Carlo
- Multivariate Chebyshev Inequality With Estimated Mean and Variance
