Correcting model misspecification in physics-informed neural networks (PINNs)

Journal of Computational Physics, Journal Year: 2024, Volume and Issue: 505, P. 112918 - 112918

Published: March 9, 2024

Language: Английский

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A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks

Computer Methods in Applied Mechanics and Engineering, Journal Year: 2024, Volume and Issue: 431, P. 117290 - 117290

Published: Aug. 19, 2024

Language: Английский

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From PINNs to PIKANs: recent advances in physics-informed machine learning

Machine learning for computational science and engineering, Journal Year: 2025, Volume and Issue: 1(1)

Published: March 11, 2025

Language: Английский

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Discovering a reaction–diffusion model for Alzheimer’s disease by combining PINNs with symbolic regression

Computer Methods in Applied Mechanics and Engineering, Journal Year: 2023, Volume and Issue: 419, P. 116647 - 116647

Published: Nov. 27, 2023

Language: Английский

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A Comprehensive and Fair Comparison between Mlp and Kan Representations for Differential Equations and Operator Networks

Published: Jan. 1, 2024

Language: Английский

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Leveraging Viscous Hamilton–Jacobi PDEs for Uncertainty Quantification in Scientific Machine Learning

SIAM/ASA Journal on Uncertainty Quantification, Journal Year: 2024, Volume and Issue: 12(4), P. 1165 - 1191

Published: Oct. 10, 2024

.Uncertainty quantification (UQ) in scientific machine learning (SciML) combines the powerful predictive power of SciML with methods for quantifying reliability learned models. However, two major challenges remain: limited interpretability and expensive training procedures. We provide a new interpretation UQ problems by establishing theoretical connection between some Bayesian inference arising viscous Hamilton–Jacobi partial differential equations (HJ PDEs). Namely, we show that posterior mean covariance can be recovered from spatial gradient Hessian solution to HJ PDE. As first exploration this connection, specialize linear models, Gaussian likelihoods, priors. In case, associated PDEs solved using Riccati ODEs, develop Riccati-based methodology provides computational advantages when continuously updating model predictions. Specifically, our approach efficiently add or remove data points set invariant order tune hyperparameters. Moreover, neither update requires retraining on access previously incorporated data. several examples involving noisy epistemic uncertainty illustrate potential approach. particular, approach's amenability streaming applications demonstrates its real-time inferences, which, turn, allows which predicted is used dynamically alter process.Keywordsmulti-time PDEsscientific learninguncertainty quantificationBayesian inferenceRiccati equationMSC codes35F2162F1565L9965N9968T0535B37

Language: Английский

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Uncertainty quantification for noisy inputs–outputs in physics-informed neural networks and neural operators

Computer Methods in Applied Mechanics and Engineering, Journal Year: 2024, Volume and Issue: 433, P. 117479 - 117479

Published: Oct. 31, 2024

Language: Английский

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Uncertainty Quantification for Noisy Inputs-Outputs in Physics-Informed Neural Networks and Neural Operators

Published: Jan. 1, 2024

Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly critical as neural networks (NNs) are being widely adopted addressing complex problems across various disciplines. Representative SciML models physics-informed (PINNs) and operators (NOs). While UQ has been investigated recent years, very few works have focused on the uncertainty caused by noisy inputs, such spatial-temporal coordinates PINNs input functions NOs. The presence of noise inputs can pose significantly more challenges compared to outputs models, primarily due inherent nonlinearity most algorithms. As a result, for crucial factor reliable trustworthy deployment these applications involving physical knowledge. To this end, we introduce Bayesian approach quantify arising from inputs-outputs We show that be seamlessly integrated into NOs, when they employed encode information. incorporate physics including terms via automatic differentiation, either loss function or likelihood, often take coordinate. Therefore, present method equips with capability address where observed coordinate is subject noise. On other hand, pretrained NOs also commonly equation-free surrogates solving differential equations inverse problems, which inputs. proposed enables them handle measurements both output UQ. series numerical examples demonstrate consequences ignoring effectiveness our learning.

Language: Английский

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Structure-Preserving Neural Networks in Data-Driven Rheological Models

SIAM Journal on Scientific Computing, Journal Year: 2025, Volume and Issue: 47(1), P. C182 - C206

Published: Feb. 20, 2025

Language: Английский

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Prediction of damage evolution in CMCs considering the real microstructures through a deep-learning scheme

Computer Methods in Applied Mechanics and Engineering, Journal Year: 2025, Volume and Issue: 439, P. 117923 - 117923

Published: March 11, 2025

Language: Английский

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