Publications & Codes 

Software & Codes

NOEM — Neural-operator element method: the finite element method accelerated by reusable, pre-trained neural operators. Examples include heat transfer, Darcy flow, and multiscale problems. Apache-2.0. Nature Computational Science 6, 417–429 (2026)

tLaSDI — Thermodynamics-informed latent space dynamics identification: reduced-order models that satisfy the first and second laws of thermodynamics by construction. Examples include Couette flow, gas containers, and Burgers’ equation. MIT license, LLNL-CODE-867909. Also registered as a US Department of Energy software release. Computer Methods in Applied Mechanics and Engineering 429, 117144 (2024)

pGFINN-tLaSDI — Parametric extension of tLaSDI. Examples include the 1D Burgers and 1D/1V Vlasov–Poisson equations. Transactions on Machine Learning Research (2026)

GFINNs — Reference implementation of GENERIC formalism informed neural networks on the gas-container benchmark. Philosophical Transactions of the Royal Society A 380, 20210207 (2022)

libROM — Lawrence Livermore National Laboratory’s data-driven reduced-order modeling library, the hyper-reduction ecosystem in which the S-OPT algorithm was developed. SIAM Journal on Scientific Computing 46(4), B474–B501 (2024)

Journal Articles

2026

25. J. S. R. Park, A. H. Hashim, S. W. Cheung, Y. Choi, Y. Shin. WGFINNs: Weak formulation-based GENERIC formalism informed neural networks. Computer Methods in Applied Mechanics and Engineering 461: 119213 (2026). arXiv

24. W. Ouyang, Y. Shin, S.-W. Liu, L. Lu. NOEM: Efficient and scalable finite element method enabled by reusable neural operators. Nature Computational Science 6(4), 417–429 (2026). journal · arXiv · code

23. X. He, Y. Shin, A. Gruber, S. Jung, K. Lee, Y. Choi. Thermodynamically consistent latent dynamics identification for parametric systems. Transactions on Machine Learning Research (2026). OpenReview · arXiv · code

2024

22. J. T. Lauzon, S. W. Cheung, Y. Shin, Y. Choi, D. M. Copeland, K. Huynh. S-OPT: A points selection algorithm for hyper-reduction in reduced order models. SIAM Journal on Scientific Computing 46(4), B474–B501 (2024). DOI · arXiv · code

21. J. S. R. Park, S. W. Cheung, Y. Choi, Y. Shin. tLaSDI: Thermodynamics-informed latent space dynamics identification. Computer Methods in Applied Mechanics and Engineering 429: 117144 (2024). arXiv · code

20. S. Lee, Y. Shin. On the training and generalization of deep operator networks. SIAM Journal on Scientific Computing 46(4), C273–C296 (2024). arXiv

2023

19. Y. Shin, Z. Zhang, G. E. Karniadakis. Error estimates of residual minimization using neural networks for linear PDEs. Journal of Machine Learning for Modeling and Computing 4(4), 73–101 (2023). arXiv

18. Y. Shin, J. Darbon, G. E. Karniadakis. Accelerating gradient descent and Adam via fractional gradients. Neural Networks 161, 185–201 (2023). arXiv

2022

17. B. Deng, Y. Shin, L. Lu, Z. Zhang, G. E. Karniadakis. Approximation rates of DeepONets for learning operators arising from advection–diffusion equations. Neural Networks 153, 411–426 (2022). arXiv

16. M. Ainsworth, Y. Shin. Active Neuron Least Squares: A training method for multivariate rectified neural networks. SIAM Journal on Scientific Computing 44(4), A2253–A2275 (2022).

15. Z. Zhang, Y. Shin, G. E. Karniadakis. GFINNs: GENERIC formalism informed neural networks for deterministic and stochastic dynamical systems. Philosophical Transactions of the Royal Society A 380: 20210207 (2022). arXiv · code

14. Y. Shin. Effects of depth, width, and initialization: A convergence analysis of layer-wise training for deep linear neural networks. Analysis and Applications 20(1), 73–119 (2022). arXiv

13. A. D. Jagtap, Y. Shin, K. Kawaguchi, G. E. Karniadakis. Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions. Neurocomputing 468, 165–180 (2022). arXiv

2021

12. M. Ainsworth, Y. Shin. Plateau phenomenon in gradient descent training of ReLU networks: Explanation, quantification, and avoidance. SIAM Journal on Scientific Computing 43(5), A3438–A3468 (2021). arXiv

11. J. Hou, Y. Shin, D. Xiu. Identification of corrupted data via k-means clustering for function approximation. CSIAM Transactions on Applied Mathematics 2, 81–107 (2021).

2020

10. Y. Shin, J. Darbon, G. E. Karniadakis. On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs. Communications in Computational Physics 28, 2042–2074 (2020). Among the journal’s most downloaded and viewed articles. arXiv

9. L. Lu, Y. Shin, Y. Su, G. E. Karniadakis. Dying ReLU and initialization: Theory and numerical examples. Communications in Computational Physics 28, 1671–1706 (2020). arXiv

8. Y. Shin, G. E. Karniadakis. Trainability of ReLU networks and data-dependent initialization. Journal of Machine Learning for Modeling and Computing 1(1), 39–74 (2020). arXiv

2016 – 2018

7. Y. Shin, K. Wu, D. Xiu. Sequential function approximation using randomized samples. Journal of Computational Physics 371, 363–381 (2018).

6. K. Wu, Y. Shin, D. Xiu. A randomized tensor quadrature method for high dimensional polynomial approximation. SIAM Journal on Scientific Computing 39(5), A1811–A1833 (2017).

5. Y. Shin, D. Xiu. A randomized algorithm for multivariate function approximation. SIAM Journal on Scientific Computing 39(3), A983–A1002 (2017).

4. L. Yan, Y. Shin, D. Xiu. Sparse approximation using ℓ1–ℓ2 minimization and its applications to stochastic collocation. SIAM Journal on Scientific Computing 39(1), A229–A254 (2017).

3. Y. Shin, D. Xiu. Correcting data corruption errors for multivariate function approximation. SIAM Journal on Scientific Computing 38(4), A2492–A2511 (2016).

2. Y. Shin, D. Xiu. On a near optimal sampling strategy for least squares polynomial regression. Journal of Computational Physics 326, 931–946 (2016).

1. Y. Shin, D. Xiu. Nonadaptive quasi-optimal points selection for least squares linear regression. SIAM Journal on Scientific Computing 38(1), A385–A411 (2016).

Review Articles & Book Chapters

Y. Shin, Z. Zhang, G. E. Karniadakis. Theoretical foundations of physics-informed neural networks and deep neural operators: A brief review. Handbook of Numerical Analysis 25, 293–358 (2024).

C. Bonneville, X. He, A. Tran, J. S. R. Park, W. Fries, D. A. Messenger, S. W. Cheung, Y. Shin, D. M. Bortz, D. Ghosh, J.-S. Chen, J. L. Belof, Y. Choi. A comprehensive review of latent space dynamics identification algorithms for intrusive and non-intrusive reduced-order modeling (2024). arXiv

Preprints

K. Chawla, S. Lee, Y. Shin. A parallel and adaptive mesh-free method for discontinuous coefficient fields in heterogeneous porous media (2026). arXiv

S. Park, Y. Shin, J. Choo. Deep operator network for surrogate modeling of poroelasticity with random permeability fields. Under revision, Journal of Computational Physics. arXiv

M. Ainsworth, Y. Shin. σ-ANLS: An effective training method for neural networks with smooth activation. Under revision, SIAM Journal on Scientific Computing.

K. Shukla, Y. Shin. Randomized forward mode of automatic differentiation for optimization algorithms. Under review, Journal of Scientific Computing. arXiv

Software Releases

S. W. Cheung, J. S. R. Park, Y. Choi, Y. Shin. Thermodynamics-informed latent space dynamics identification. US Department of Energy Software, 246 (2024). LLNL-CODE-867909.