# Data-driven parameterization of the generalized Langevin equation

arXiv: https://arxiv.org/abs/1606.02596 · HTML: https://mlsanity.com/paper/1606.02596/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2016.

## Built on by (most cited first, 14 of 14)

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- [Coarse-graining conformational dynamics with multi-dimensional generalized Langevin equation: how, when, and why](https://mlsanity.com/paper/2405.12356/) (2024)
- [On the generalization ability of coarse-grained molecular dynamics models for non-equilibrium processes](https://mlsanity.com/paper/2409.11519/) (2024)
- [Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels](https://mlsanity.com/paper/2512.10256/) (2025)
- [Can Transformers overcome the lack of data in the simulation of history-dependent flows?](https://mlsanity.com/paper/2512.16305/) (2025)
- [Machine learning kinetics from molecular dynamics data](https://mlsanity.com/paper/2609.17736/) (2026)
- [Memory-Conditioned Diffusion Model for Generalized Langevin Dynamics](https://mlsanity.com/paper/2609.28371/) (2026)

## Abstract (arXiv)

We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. We show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory. We demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method.