Active learning in materials science with emphasis on adaptive sampling using uncertainties for targeted design

T Lookman, PV Balachandran, D Xue… - npj Computational …, 2019 - nature.com
One of the main challenges in materials discovery is efficiently exploring the vast search
space for targeted properties as approaches that rely on trial-and-error are impractical. We …

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

J Zhang - Wiley Interdisciplinary Reviews: Computational …, 2021 - Wiley Online Library
Uncertainty quantification (UQ) includes the characterization, integration, and propagation of
uncertainties that result from stochastic variations and a lack of knowledge or data in the …

fPINNs: Fractional physics-informed neural networks

G Pang, L Lu, GE Karniadakis - SIAM Journal on Scientific Computing, 2019 - SIAM
Physics-informed neural networks (PINNs), introduced in M. Raissi, P. Perdikaris, and G.
Karniadakis, J. Comput. Phys., 378 (2019), pp. 686--707, are effective in solving integer …

nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications

G Pang, M D'Elia, M Parks, GE Karniadakis - Journal of Computational …, 2020 - Elsevier
Physics-informed neural networks (PINNs) are effective in solving inverse problems based
on differential and integro-differential equations with sparse, noisy, unstructured, and multi …

Identifiability and predictability of integer-and fractional-order epidemiological models using physics-informed neural networks

E Kharazmi, M Cai, X Zheng, Z Zhang, G Lin… - Nature Computational …, 2021 - nature.com
We analyze a plurality of epidemiological models through the lens of physics-informed
neural networks (PINNs) that enable us to identify time-dependent parameters and data …

Applying Bayesian optimization with Gaussian process regression to computational fluid dynamics problems

Y Morita, S Rezaeiravesh, N Tabatabaei… - Journal of …, 2022 - Elsevier
Bayesian optimization (BO) based on Gaussian process regression (GPR) is applied to
different CFD (computational fluid dynamics) problems which can be of practical relevance …

Wellposedness and regularity of the variable-order time-fractional diffusion equations

H Wang, X Zheng - Journal of Mathematical Analysis and Applications, 2019 - Elsevier
It was proved that the solution to a time-fractional partial differential equation lacks regularity
at the initial time t= 0, which is often inconsistent with the physical problem being modeled …

Neural-net-induced Gaussian process regression for function approximation and PDE solution

G Pang, L Yang, GE Karniadakis - Journal of Computational Physics, 2019 - Elsevier
Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity
of deep neural networks (deep NNs) as well as the uncertainty quantification property of …

Fractional modeling in action: A survey of nonlocal models for subsurface transport, turbulent flows, and anomalous materials

JL Suzuki, M Gulian, M Zayernouri, M D'Elia - Journal of Peridynamics and …, 2023 - Springer
Modeling of phenomena such as anomalous transport via fractional-order differential
equations has been established as an effective alternative to partial differential equations …

Parameter estimation for unsteady MHD oscillatory free convective flow of generalized second grade fluid with Hall effects and thermal radiation effects

S Wang, H Zhang, X Jiang - International Journal of Heat and Mass …, 2024 - Elsevier
This work first establishes an unsteady magnetohydrodynamic (MHD) oscillatory free
convection flow model of the generalized second grade fluid with Hall heat and mass …