Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons

Weight uncertainty in neural network,

C. Blundell, J. Cornebise, K. Kavukcuoglu, D. Wierstra, · 2015

Cited alongside, same era.

Variational dropout and the local reparameterization trick,

D. P. Kingma, T. Salimans, M. Welling, · 2015

Cited alongside, same era.

Learning Structured Output Representation using Deep Conditional Generative Models,

K. Sohn, H. Lee, X. Yan, · 2015

Cited alongside, same era.

I. Goodfellow, Y. Bengio, A. Courville, Y. Bengio, Deep Learning, volume 1, MIT press Cambridge, 2016

2016

Cited alongside, same era.

Uncertainty in deep learning,

Y. Gal, · 2016

Cited alongside, same era.

Deep variational information bottleneck,

Original

A. A. Alemi, I. Fischer, J. V. Dillon, K. Murphy, · 2016

Cited alongside, same era.

Learnable Bernoulli Dropout for Bayesian Deep Learning,

S. Boluki, R. Ardywibowo, S. Z. Dadaneh, M. Zhou, X. Qian, · 2020

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Estimating model uncertainty of neural networks in sparse information form,

J. Lee, M. Humt, J. Feng, R. Triebel, · 2020

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Uncertainty in neural networks: Approximately Bayesian ensembling,

T. Pearce, F. Leibfried, A. Brintrup, · 2020

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Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions,

T. Pearce, R. Tsuchida, M. Zaki, A. Brintrup, A. Neely, · 2020

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Physics-informed machine learning,

G. E. Karniadakis, I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, L. Yang, · 2021

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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators,

L. Lu, P. Jin, G. Pang, Z. Zhang, G. E. Karniadakis, · 2021

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A physics-informed variational DeepONet for predicting the crack path in brittle materials,

Original

S. Goswami, M. Yin, Y. Yu, G. E. Karniadakis, · 2021

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Learning the solution operator of parametric partial differential equations with physics-informed DeepONets,

Original

S. Wang, H. Wang, P. Perdikaris, · 2021

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Error estimates for deeponets: A deep learning framework in infinite dimensions,

Original

S. Lanthaler, S. Mishra, G. E. Karniadakis, · 2021

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On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations,

J. Darbon, T. Meng, · 2021

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Hp-VPINNs: Variational physics-informed neural networks with domain decomposition,

E. Kharazmi, Z. Zhang, G. E. Karniadakis, · 2021

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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs,

S. Mishra, R. Molinaro, · 2021

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Multi-fidelity Bayesian neural networks: Algorithms and applications,

X. Meng, H. Babaee, G. E. Karniadakis, · 2021

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B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data,

L. Yang, X. Meng, G. E. Karniadakis, · 2021

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DeepXDE: A deep learning library for solving differential equations,

L. Lu, X. Meng, Z. Mao, G. E. Karniadakis, · 2021

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NVIDIA SimNet™: An AI-Accelerated Multi-Physics Simulation Framework,

O. Hennigh, S. Narasimhan, M. A. Nabian, A. Subramaniam, K. Tangsali, Z. Fang, M. Rietmann, W. Byeon, S. Choudhry, · 2021

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Uncertainty Quantification and Deep Ensembles,

R. Rahaman, A. H. Thiery, · 2021

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Natural Posterior Network: Deep Bayesian Predictive Uncertainty for Exponential Family Distributions,

Original

B. Charpentier, O. Borchert, D. Zügner, S. Geisler, S. Günnemann, · 2021

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Multivariate Deep Evidential Regression,

Original

N. Meinert, A. Lavin, · 2021

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A Survey on Evidential Deep Learning For Single-Pass Uncertainty Estimation,

Original

D. Ulmer, · 2021

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A Survey of Uncertainty in Deep Neural Networks,

Original

J. Gawlikowski, C. R. N. Tassi, M. Ali, J. Lee, M. Humt, J. Feng, A. Kruspe, R. Triebel, P. Jung, R. Roscher, · 2021

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Aleatoric and epistemic uncertainty in machine learning: An introduction to concepts and methods,

E. Hüllermeier, W. Waegeman, · 2021

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Uncertainty Baselines: Benchmarks for Uncertainty & Robustness in Deep Learning,

Original

Z. Nado, N. Band, M. Collier, J. Djolonga, M. W. Dusenberry, S. Farquhar, A. Filos, M. Havasi, R. Jenatton, G. Jerfel, · 2021

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A Survey on Epistemic (Model) Uncertainty in Supervised Learning: Recent Advances and Applications,

Original

X. Zhou, H. Liu, F. Pourpanah, T. Zengd, X. Wang, · 2021

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Bayesian neural networks for uncertainty quantification in data-driven materials modeling,

A. Olivier, M. D. Shields, L. Graham-Brady, · 2021

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GAN-Based Priors for Quantifying Uncertainty in Supervised Learning,

D. V. Patel, A. A. Oberai, · 2021

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Solving inverse problems in stochastic models using deep neural networks and adversarial training,

K. Xu, E. Darve, · 2021

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Stochastic Physics-Informed Neural Networks (SPINN): A Moment-Matching Framework for Learning Hidden Physics within Stochastic Differential Equations,

Original

J. O’Leary, J. A. Paulson, A. Mesbah, · 2021

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Variational Inference Formulation for a Model-Free Simulation of a Dynamical System with Unknown Parameters by a Recurrent Neural Network,

K. Yeo, D. E. C. Grullon, F.-K. Sun, D. S. Boning, J. R. Kalagnanam, · 2021

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Robust Learning of Physics Informed Neural Networks,

Original

C. Bajaj, L. McLennan, T. Andeen, A. Roy, · 2021

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PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics,

Original

A. Daw, M. Maruf, A. Karpatne, · 2021

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Interval and fuzzy physics-informed neural networks for uncertain fields,

Original

J. N. Fuhg, I. Kalogeris, A. Fau, N. Bouklas, · 2021

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Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks,

Original

Y. Gao, M. K. Ng, · 2021

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Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs,

Original

G. Lin, C. Moya, Z. Zhang, · 2021

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Flow Field Tomography with Uncertainty Quantification using a Bayesian Physics-Informed Neural Network,

Original

J. P. Molnar, S. J. Grauer, · 2021

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Efficient uncertainty quantification for dynamic subsurface flow with surrogate by Theory-guided Neural Network,

N. Wang, H. Chang, D. Zhang, · 2021

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Inverse Design under Uncertainty using Conditional Normalizing Flows,

P. Tsilifis, S. Ghosh, · 2021

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Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models,

Original

L. Guo, H. Wu, T. Zhou, · 2021

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Meta-learning PINN loss functions,

Original

A. F. Psaros, K. Kawaguchi, G. E. Karniadakis, · 2021

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Uncertainty modelling in deep learning for safer neuroimage enhancement: Demonstration in diffusion MRI,

R. Tanno, D. E. Worrall, E. Kaden, A. Ghosh, F. Grussu, A. Bizzi, S. N. Sotiropoulos, A. Criminisi, D. C. Alexander, · 2021

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Learning Functional Priors and Posteriors from Data and Physics,

Original

X. Meng, L. Yang, Z. Mao, J. d. A. Ferrandis, G. E. Karniadakis, · 2021

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Output-weighted and relative entropy loss functions for deep learning precursors of extreme events,

Original

S. Rudy, T. Sapsis, · 2021

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Detecting unusual input to neural networks,

J. Martin, C. Elster, · 2021

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You Can’t Fool All the Models: Detect Adversarial Samples via Pruning Models,

R. Wang, Z. Chen, H. Dong, Q. Xuan, · 2021

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Laplace Redux–Effortless Bayesian Deep Learning,

Original

E. Daxberger, A. Kristiadi, A. Immer, R. Eschenhagen, M. Bauer, P. Hennig, · 2021

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A survey of deep active learning,

P. Ren, Y. Xiao, X. Chang, P.-Y. Huang, Z. Li, B. B. Gupta, X. Chen, X. Wang, · 2021

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A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification,

Original

A. N. Angelopoulos, S. Bates, · 2021

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Valid prediction intervals for regression problems (2021)

N. Dewolf, B. De Baets, W. Waegeman, · 2021

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Bayesian Neural Network Priors Revisited,

Original

V. Fortuin, A. Garriga-Alonso, F. Wenzel, G. Rätsch, R. Turner, M. van der Wilk, L. Aitchison, · 2021

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Deep Gaussian processes: A survey,

Original

K. Jakkala, · 2021

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Deep kernel processes,

L. Aitchison, A. Yang, S. W. Ober, · 2021

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Meta-Learning Divergences for Variational Inference,

R. Zhang, Y. Li, C. De Sa, S. Devlin, C. Zhang, · 2021

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Variational Laplace for Bayesian neural networks,

Original

A. Unlu, L. Aitchison, · 2021

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Scalable marginal likelihood estimation for model selection in deep learning,

Original

A. Immer, M. Bauer, V. Fortuin, G. Rätsch, M. E. Khan, · 2021

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Improving predictions of Bayesian neural nets via local linearization,

A. Immer, M. Korzepa, M. Bauer, · 2021

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Bayesian Deep Learning via Subnetwork Inference,

E. Daxberger, E. Nalisnick, J. U. Allingham, J. Antoran, J. M. Hernandez-Lobato, · 2021

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Predictive Complexity Priors,

E. Nalisnick, J. Gordon, J. M. Hernandez-Lobato, · 2021

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Priors in Bayesian Deep Learning: A Review,

Original

V. Fortuin, · 2021

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Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations,

A. D. Jagtap, G. E. Karniadakis, · 2041

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