# Learning Memory Kernels in Generalized Langevin Equations

arXiv: https://arxiv.org/abs/2402.11705 · HTML: https://mlsanity.com/paper/2402.11705/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 39 references that are in the map.
- First posted on arXiv 18 Feb 2024.

## Builds on (most cited first, 2 of 2)

- [Data-driven parameterization of the generalized Langevin equation](https://mlsanity.com/paper/1606.02596/) (2016)
- [Data adaptive RKHS Tikhonov regularization for learning kernels in operators](https://mlsanity.com/paper/2203.03791/) (2022)

## Built on by (most cited first, 3 of 3)

- [Identifiable learning of dissipative dynamics](https://mlsanity.com/paper/2510.24160/) (2025)
- [Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels](https://mlsanity.com/paper/2512.10256/) (2025)
- [Memory-Conditioned Diffusion Model for Generalized Langevin Dynamics](https://mlsanity.com/paper/2609.28371/) (2026)

## Abstract (arXiv)

We introduce a novel approach for learning memory kernels in Generalized Langevin Equations. This approach initially utilizes a regularized Prony method to estimate correlation functions from trajectory data, followed by regression over a Sobolev norm-based loss function with RKHS regularization. Our method guarantees improved performance within an exponentially weighted L^2 space, with the kernel estimation error controlled by the error in estimated correlation functions. We demonstrate the superiority of our estimator compared to other regression estimators that rely on L^2 loss functions and also an estimator derived from the inverse Laplace transform, using numerical examples that highlight its consistent advantage across various weight parameter selections. Additionally, we provide examples that include the application of force and drift terms in the equation.