no code implementations • 19 Nov 2023 • Zongren Zou, Xuhui Meng, George Em Karniadakis
As a result, UQ for noisy inputs becomes a crucial factor for reliable and trustworthy deployment of these models in applications involving physical knowledge.
no code implementations • 16 Oct 2023 • Zongren Zou, Xuhui Meng, George Em Karniadakis
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.
no code implementations • 26 Apr 2023 • Kamaljyoti Nath, Xuhui Meng, Daniel J Smith, George Em Karniadakis
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.
no code implementations • 30 Mar 2023 • Minglei Lu, Ali Mohammadi, Zhaoxu Meng, Xuhui Meng, Gang Li, Zhen Li
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%.
1 code implementation • 25 Aug 2022 • Zongren Zou, Xuhui Meng, Apostolos F Psaros, George Em Karniadakis
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.
no code implementations • 12 May 2022 • Kevin Linka, Amelie Schafer, Xuhui Meng, Zongren Zou, George Em Karniadakis, Ellen Kuhl
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.
1 code implementation • 19 Jan 2022 • Apostolos F Psaros, Xuhui Meng, Zongren Zou, Ling Guo, George Em Karniadakis
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.
2 code implementations • 1 Nov 2021 • Jeremy Yu, Lu Lu, Xuhui Meng, George Em Karniadakis
We tested gPINNs extensively and demonstrated the effectiveness of gPINNs in both forward and inverse PDE problems.
no code implementations • 8 Jun 2021 • Xuhui Meng, Liu Yang, Zhiping Mao, Jose del Aguila Ferrandis, George Em Karniadakis
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.
no code implementations • 19 Dec 2020 • Xuhui Meng, Hessam Babaee, George Em Karniadakis
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).
no code implementations • 13 Mar 2020 • Liu Yang, Xuhui Meng, George Em. Karniadakis
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.
no code implementations • 23 Sep 2019 • Xuhui Meng, Zhen Li, Dongkun Zhang, George Em. Karniadakis
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.
6 code implementations • 10 Jul 2019 • Lu Lu, Xuhui Meng, Zhiping Mao, George E. Karniadakis
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.
2 code implementations • 26 Feb 2019 • Xuhui Meng, George Em. Karniadakis
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