PDE-Discovery:
Weak-PDE-LEARN
Stephany, R., Earls, C.J. (2024) “Weak-PDE-LEARN: A weak form based approach to discovering PDEs from noisy, limited data,” Journal of Computational Physics, Vol. 506, 112950 arXiv:2309.04699
PDE-LEARN
Stephany, R., Earls, C.J. (2024) “PDE-LEARN: Using deep learning to discover partial differential equations from noisy, limited data,” Neural Networks, Elsevier, Vol. 174, 106242, pp. 1-16 arXiv:2212.04971
PDE-READ
Stephany, R., Earls, C.J. (2022) “PDE-READ: Human-readable partial differential equation discovery using deep learning,” Neural Networks, Elsevier, Vol. 154, pp. 360-382 arXiv:2111.00998
Bayesian PDE discovery
Bonneville, C., Earls, C.J. (2022) “Bayesian deep learning for partial differential equation parameter discovery with sparse and noisy data,” Journal of Computational Physics, Elsevier, Vol. 16, 100115 arXiv:2108.04085
Green’s Function Discovery:
Greenlearning
Boullé, N., Earls, C.J., Townsend, A. (2022) “Data-driven discovery of Green’s functions with human-understandable deep learning,” Scientific Reports, Vol. 12, No. 4824, Springer Nature.
EmpiricalGreensFunctions
Praveen, H., Boullé, N., Earls, C.J. (2023) “Principled interpolation of Green’s functions learned from data,” Computer Methods in Applied Mechanics and Engineering, Elsevier, Vol. 409, 115971 arXiv:2211.06299
chebgreen
Praveen, H., Brown, J., Earls, C.J. (2025) “chebgreen: Learning and interpolating continuous empirical Green’s functions from data,” IN REVIEW. arXiv:2501.18715
Finite Element Analysis:
CU-BENs: 3D Nonlinear finite element structural modeling software: geometric and material nonlinear, static and transient dynamic, along with acoustic fluid-structure interaction
Download from GitHub repository
Simple CU-BEN installation guide and tutorial
“Theory manual (incomplete)” for CU-BEN: based on Cornell CEE7790 class notes
