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Found 14 papers, 5 papers with code
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.
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.
Physics-informed neural networks for predicting gas flow dynamics and unknown parameters in diesel engines
In other words, the mean value model uses both the PINN model and the DNNs to represent the engine's states, with the PINN providing a physics-based understanding of the engine's overall dynamics and the DNNs offering a more engine-specific and adaptive representation of the empirical formulae.
Deep neural operator for learning transient response of interpenetrating phase composites subject to dynamic loading
After an offline training, the DNO model can act as surrogate of physics-based FEA to predict the transient mechanical response in terms of reaction force and stress distribution of the IPCs to various strain loads in one second at an accuracy of 98%.
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.
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
We tested gPINNs extensively and demonstrated the effectiveness of gPINNs in both forward and inverse PDE problems.
Learning Functional Priors and Posteriors from Data and Physics
In summary, the proposed method is capable of learning flexible functional priors, and can be extended to big data problems using stochastic HMC or normalizing flows since the latent space is generally characterized as low dimensional.
Multi-fidelity Bayesian Neural Networks: Algorithms and Applications
We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs).
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while the Hamiltonian Monte Carlo (HMC) or the variational inference (VI) could serve as an estimator of the posterior.
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs
Consequently, compared to the original PINN approach, the proposed PPINN approach may achieve a significant speedup for long-time integration of PDEs, assuming that the CG solver is fast and can provide reasonable predictions of the solution, hence aiding the PPINN solution to converge in just a few iterations.
DeepXDE: A deep learning library for solving differential equations
We also present a Python library for PINNs, DeepXDE, which is designed to serve both as an education tool to be used in the classroom as well as a research tool for solving problems in computational science and engineering.
A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
It is comprised of three NNs, with the first NN trained using the low-fidelity data and coupled to two high-fidelity NNs, one with activation functions and another one without, in order to discover and exploit nonlinear and linear correlations, respectively, between the low-fidelity and the high-fidelity data.
Computational Physics
