Learning with PDE conservation laws

October 15, 2019 — June 3, 2024

calculus
dynamical systems
geometry
Hilbert space
how do science
Lévy processes
machine learning
neural nets
PDEs
physics
regression
sciml
SDEs
signal processing
statistics
statmech
stochastic processes
surrogate
time series
uncertainty
Figure 1

Unlike PINNs which penalize deviation from conservation laws in the loss, we can impose symmetries in our neural net architecture itself.

TBD

1 References

Bloem-Reddy, and Teh. 2020. “Probabilistic Symmetries and Invariant Neural Networks.”
Di Giovanni, Rowbottom, Chamberlain, et al. 2022. “Graph Neural Networks as Gradient Flows.”
Mialon, Garrido, Lawrence, et al. 2024. “Self-Supervised Learning with Lie Symmetries for Partial Differential Equations.”
Pestourie, Mroueh, Rackauckas, et al. 2022. “Physics-Enhanced Deep Surrogates for PDEs.”
Rezende, Racanière, Higgins, et al. 2019. “Equivariant Hamiltonian Flows.” In Machine Learning and the Physical Sciences Workshop at the 33rd Conference on Neural Information Processing Systems (NeurIPS).
Ruhe, Gupta, de Keninck, et al. 2023. “Geometric Clifford Algebra Networks.” In arXiv Preprint arXiv:2302.06594.
Smets, Portegies, Bekkers, et al. 2023. “PDE-Based Group Equivariant Convolutional Neural Networks.” Journal of Mathematical Imaging and Vision.