# Multi-Preconditioned LBFGS for Training Finite-Basis PINNs

arXiv: https://arxiv.org/abs/2601.08709 · HTML: https://mlsanity.com/paper/2601.08709/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 19 references that are in the map.
- First posted on arXiv 13 Jan 2026.

## Builds on (most cited first, 5 of 5)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://mlsanity.com/paper/2107.07871/) (2021)
- [Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies](https://mlsanity.com/paper/2306.17648/) (2023)
- [Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications](https://mlsanity.com/paper/2406.10997/) (2024)
- [Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization](https://mlsanity.com/paper/2507.11513/) (2025)

## Built on by (most cited first, 2 of 2)

- [Two-level domain-decomposition AdaGrad method for scalable training of graph neural networks](https://mlsanity.com/paper/2608.22575/) (2026)
- [An overview of machine learning-enhanced iterative methods for systems of linear and nonlinear equations](https://mlsanity.com/paper/2610.07211/) (2026)

## Abstract (arXiv)

A multi-preconditioned LBFGS (MP-LBFGS) algorithm is introduced for training finite-basis physics-informed neural networks (FBPINNs). The algorithm is motivated by the nonlinear additive Schwarz method and exploits the domain-decomposition-inspired additive architecture of FBPINNs, in which local neural networks are defined on subdomains, thereby localizing the network representation. Parallel, subdomain-local quasi-Newton corrections are then constructed on the corresponding local parts of the architecture. A key feature is a novel nonlinear multi-preconditioning mechanism, in which subdomain corrections are optimally combined through the solution of a low-dimensional subspace minimization problem. Numerical experiments indicate that MP-LBFGS can improve convergence speed, as well as model accuracy over standard LBFGS while incurring lower communication overhead.