# NOMADS: Non-Markovian Optimization-based Modeling for Approximate Dynamics with Spatially-homogeneous Memory

arXiv: https://arxiv.org/abs/2409.19978 · HTML: https://mlsanity.com/paper/2409.19978/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 18 references that are in the map.
- First posted on arXiv 30 Sep 2024.

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

- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [The Nearest Graph Laplacian in Frobenius Norm](https://mlsanity.com/paper/2404.03371/) (2024)

## Abstract (arXiv)

We propose a system identification method, Non-Markovian Optimization-based Modeling for Approximate Dynamics with Spatially-homogeneous memory (NOMADS), for identifying linear dynamical systems from a set of multi-dimensional time-series data obtained through multiple partially excited experiments. NOMADS formulates model identification as a convex optimization problem, in which the state-space coefficient matrices and a memory kernel are estimated jointly under physically motivated constraints using projected gradient descent. The proposed framework models memory effects through a spatially homogeneous kernel, enabling scalable identification of non-Markovian dynamics while keeping the number of free parameters moderate. This structure allows NOMADS to integrate information from multiple multi-dimensional time-series data even when no single experiment provides full excitation. In the Markovian setting, physical constraints can be incorporated to enforce conservation laws. Numerical experiments on synthetic data demonstrate that NOMADS achieves substantially improved generalization accuracy compared to existing DMD-based methods even for noisy train data, and reproduces energy conservation in the Markovian case.