CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929428226899968 |
|---|---|
| author | Berman, Jules Peherstorfer, Benjamin |
| author_facet | Berman, Jules Peherstorfer, Benjamin |
| contents | This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the evolution of solution fields at new physics parameters and new initial conditions. The adaptation can be either purely data-driven or via an equation-driven variational approach that provides Galerkin-optimal approximations. Because CoLoRA approximates solution fields locally in time, the rank of the weights can be kept small, which means that only few training trajectories are required offline so that CoLoRA is well suited for data-scarce regimes. Predictions with CoLoRA are orders of magnitude faster than with classical methods and their accuracy and parameter efficiency is higher compared to other neural network approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations Berman, Jules Peherstorfer, Benjamin Machine Learning Numerical Analysis This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the evolution of solution fields at new physics parameters and new initial conditions. The adaptation can be either purely data-driven or via an equation-driven variational approach that provides Galerkin-optimal approximations. Because CoLoRA approximates solution fields locally in time, the rank of the weights can be kept small, which means that only few training trajectories are required offline so that CoLoRA is well suited for data-scarce regimes. Predictions with CoLoRA are orders of magnitude faster than with classical methods and their accuracy and parameter efficiency is higher compared to other neural network approaches. |
| title | CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2402.14646 |