Software

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