Graph neural networks
Inverse problems
Model-based deep learning
Numerics-informed neural networks
Parareal time integrators based AI
Reduced order models
Y. Pan, Q. Wang, L. Zhang. "Identification of nonconcave aggregation production functions in spatial Solow models with technology diffusion", to appear on SIAM J. Appl. Math.
Celaya, Kirk, Fuentes, Riviere. ''Solutions to elliptic and parabolic problems via finite difference based unsupervised small linear convolutional neural networs'', Computers and Mathematics with Applications, 174, 31-42, 2024, doi
J. R. Cangelosi and M. Heinkenschloss, Sensitivity of ODE Solutions with Respect to Component Functions in the Dynamics, SIAM J. Numer. Anal., 2025, Vol. 65, No. 5, pp. 2094-2118
K. Ren, L. Zhang. A model-consistent data-driven computational strategy for PDE joint inversion problems, J. Comput. Phys., 2025, Vol. 539, 114232
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Li, Verma, Efimov, Kumar, Segarra. "GLANCE: graph-based learnable digital twin for communication networks", arXiv:2408.09040, 2024.
A. Celaya, Y. Wang, D. Fuentes, B. Riviere. "Learning Solutions to Elliptic PDEs via Local Mass Conservation Minimization", SIAM Journal on Scientific Computing, to appear, 2026, arXiv:2502.08783, 2025.
W. Ding, K. Ren, L. Zhang. "Coupling deep learning with full waveform inversion", submitted, 2025.
A. Celaya, D. Fuentes, B. Riviere. "An adaptive collocation point strategy for physics informed neural networks via the QR discrete empirical interpolation method", arXiv:2501.07700, 2025.
L. Liu, L. Zhang, A. Gelb. Neural entropy-stable conservative flux for neural networks for learning hyperbolic conservation laws, submitted, https://arxiv.org/abs/2507.01795
J. R. Cangelosi and M. Heinkenschloss, Sensitivity-Driven Adaptive Surrogate Modeling for Simulation and Optimization of Dynamical Systems, submitted, 2025, https://doi.org/10.48550/arXiv.2509.04651.
J. R. Cangelosi and M. Heinkenschloss, Sensitivity of Optimal Control Solutions and Quantities of Interest with Respect to Component Functions, submitted, 2025, https://doi.org/10.48550/arXiv.2506.10804.
D. S. Grundvig and M. Heinkenschloss, A Generalized l1-Merit Function SQP Method Using Function Approximations with Tunable Accuracy, submitted, 2025, https://doi.org/10.48550/arXiv.2507.06199.