| Learning constitutive relations from indirect observations using deep neural networks DZ Huang, K Xu, C Farhat, E Darve Journal of Computational Physics 416, 109491, 2020 | 148 | 2020 |
| Learning constitutive relations using symmetric positive definite neural networks K Xu, DZ Huang, E Darve Journal of Computational Physics 428, 110072, 2021 | 134 | 2021 |
| Physics constrained learning for data-driven inverse modeling from sparse observations K Xu, E Darve Journal of Computational Physics 453, 110938, 2022 | 66 | 2022 |
| A general approach to seismic inversion with automatic differentiation W Zhu, K Xu, E Darve, GC Beroza Computers & Geosciences 151, 104751, 2021 | 54 | 2021 |
| Integrating deep neural networks with full-waveform inversion: Reparameterization, regularization, and uncertainty quantification W Zhu, K Xu, E Darve, B Biondi, GC Beroza Geophysics 87 (1), R93-R109, 2022 | 51 | 2022 |
| The neural network approach to inverse problems in differential equations K Xu, E Darve arXiv preprint arXiv:1901.07758, 2019 | 48 | 2019 |
| Coupled time‐lapse full‐waveform inversion for subsurface flow problems using intrusive automatic differentiation D Li, K Xu, JM Harris, E Darve Water Resources Research 56 (8), e2019WR027032, 2020 | 45 | 2020 |
| Learning nonlinear constitutive laws using neural network models based on indirectly measurable data X Liu, F Tao, H Du, W Yu, K Xu Journal of Applied Mechanics 87 (8), 081003, 2020 | 39 | 2020 |
| Learning viscoelasticity models from indirect data using deep neural networks K Xu, AM Tartakovsky, J Burghardt, E Darve Computer Methods in Applied Mechanics and Engineering 387, 114124, 2021 | 38 | 2021 |
| ADCME: Learning spatially-varying physical fields using deep neural networks K Xu, E Darve arXiv preprint arXiv:2011.11955, 2020 | 37 | 2020 |
| Predictive modeling with learned constitutive laws from indirect observations DZ Huang, K Xu, C Farhat, E Darve arXiv preprint arXiv:1905.12530, 2019 | 24 | 2019 |
| Solving inverse problems in stochastic models using deep neural networks and adversarial training K Xu, E Darve Computer Methods in Applied Mechanics and Engineering 384, 113976, 2021 | 23 | 2021 |
| Inverse modeling of viscoelasticity materials using physics constrained learning K Xu, AM Tartakovsky, J Burghardt, E Darve arXiv preprint arXiv:2005.04384, 2020 | 22 | 2020 |
| Isogeometric collocation method for the fractional Laplacian in the 2D bounded domain K Xu, E Darve Computer Methods in Applied Mechanics and Engineering 364, 112936, 2020 | 16 | 2020 |
| Solving inverse problems in steady-state navier-stokes equations using deep neural networks T Fan, K Xu, J Pathak, E Darve arXiv preprint arXiv:2008.13074, 2020 | 15 | 2020 |
| Spectral method for the fractional Laplacian in 2D and 3D K Xu, E Darve arXiv preprint arXiv:1812.08325, 2018 | 11 | 2018 |
| Distributed machine learning for computational engineering using MPI K Xu, W Zhu, E Darve arXiv preprint arXiv:2011.01349, 2020 | 9 | 2020 |
| Time-lapse full waveform inversion for subsurface flow problems with intelligent automatic differentiation D Li, K Xu, JM Harris, E Darve arXiv preprint arXiv:1912.07552, 2019 | 9 | 2019 |
| Efficient Numerical Method for Models Driven by L\'evy Process via Hierarchical Matrices K Xu, E Darve arXiv preprint arXiv:1812.08324, 2018 | 8 | 2018 |
| Calibrating multivariate Lévy processes with neural networks K Xu, E Darve Mathematical and Scientific Machine Learning, 207-220, 2020 | 6 | 2020 |
