Scriber Labs develops educational and research-oriented computational models for exploring how structure and dynmaics can be recovered from data.
- Interpretiblity
- Clarity (physics first, data second)
- Parsimony
- Scalability
- Computationally efficient
- Practicality (optional for low-fidelity projects and apps/widgets)
- scientific value
- educational
- Sing-develepor feasibility
🪀 Project 1: lf-pinn-harmonic-oscillator
Physics residual minimization does got guarantee physical inveriants unless sampling resolves the solution spectrum. This is a manifestation of spectral bias.
Residual minimization approximates the operator constraint, but conservation emerges from the generator s tructure. If the generator isnt structurally preserved (via sampling or architecture), invariants drift even under converged optimization.
- This connects spectral bias in neural nets to...
- Nyquist sampling theory
- Hamiltonian structure
- Conservation Laws
- PINN failure modes
@article{basir2022pinnfailures,
author = {Basir, Soroush and Senocak, Inanc},
title = {Critical Investigation of Failure Modes in Physics-Informed Neural Networks},
booktitle = {AIAA SCITECH 2022 Forum},
year = {2022},
doi = {10.2514/6.2022-2353}
}
@book{brunton2022datadriven,
author = {Brunton, Steven L. and Kutz, J. Nathan},
title = {Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control},
publisher = {Cambridge University Press},
year = {2022},
edition = {2}
}
@incollection{hestenes1993hamiltonian,
author = {Hestenes, David},
title = {Hamiltonian Mechanics with Geometric Calculus},
booktitle = {Clifford Algebras and Their Applications in Mathematical Physics},
pages = {203--214},
publisher = {Springer},
year = {1993},
doi = {10.1007/978-94-011-1719-7_25}
}
@article{kutzbrunton2022parsimony,
author = {Kutz, J. Nathan and Brunton, Steven L.},
title = {Parsimony as the ultimate regularizer for physics-informed machine learning},
journal = {Nonlinear Dynamics},
volume = {107},
number = {3},
pages = {1801--1817},
year = {2022},
doi = {10.1007/s11071-021-07118-3}
}
@article{raissi2019pinns,
author = {Raissi, Maziar and Perdikaris, Paris and Karniadakis, George Em},
title = {Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
journal = {Journal of Computational Physics},
volume = {378},
pages = {686--707},
year = {2019},
doi = {10.1016/j.jcp.2018.10.045}
}