# Adaptive Nonlinear Vector Autoregression: Robust Forecasting for Noisy Chaotic Time Series

arXiv: https://arxiv.org/abs/2507.08738 · HTML: https://mlsanity.com/paper/2507.08738/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 56 references that are in the map.
- First posted on arXiv 11 Jul 2025.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Scalable and accurate deep learning for electronic health records](https://mlsanity.com/paper/1801.07860/) (2018)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [Learning to Diagnose with LSTM Recurrent Neural Networks](https://mlsanity.com/paper/1511.03677/) (2015)
- [Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model](https://mlsanity.com/paper/1803.04779/) (2018)
- [Reservoir Computing Universality With Stochastic Inputs](https://mlsanity.com/paper/1807.02621/) (2018)
- [Predicting Clinical Events by Combining Static and Dynamic Information Using Recurrent Neural Networks](https://mlsanity.com/paper/1602.02685/) (2016)
- [Infinite-dimensional next-generation reservoir computing](https://mlsanity.com/paper/2412.09800/) (2024)
- [Learning dynamical systems with hit-and-run random feature maps](https://mlsanity.com/paper/2501.06661/) (2025)
- [Revisiting the Necessity of Graph Learning and Common Graph Benchmarks](https://mlsanity.com/paper/2412.06173/) (2024)
- [Predicting Chaotic System Behavior using Machine Learning Techniques](https://mlsanity.com/paper/2408.05702/) (2024)

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

- [PCA-Enhanced Adaptive NVAR Framework for High-Resolution Sea Surface Temperature Forecasting in the East Sea](https://mlsanity.com/paper/2606.12141/) (2026)
- [CheMLFlow: An Open-Source Platform for Cheminformatics and Materials Informatics Applications](https://mlsanity.com/paper/2608.04942/) (2026)

## Abstract (arXiv)

Nonlinear vector autoregression (NVAR) and reservoir computing (RC) have shown promise in forecasting chaotic dynamical systems, such as the Lorenz-63 model and El Nino-Southern Oscillation. However, their reliance on fixed nonlinear transformations - polynomial expansions in NVAR or random feature maps in RC - limits their adaptability to high noise or complex real-world data. Furthermore, these methods also exhibit poor scalability in high-dimensional settings due to costly matrix inversion during optimization. We propose a data-adaptive NVAR model that combines delay-embedded linear inputs with features generated by a shallow, trainable multilayer perceptron (MLP). Unlike standard NVAR and RC models, the MLP and linear readout are jointly trained using gradient-based optimization, enabling the model to learn data-driven nonlinearities, while preserving a simple readout structure and improving scalability. Initial experiments across multiple chaotic systems, tested under noise-free and synthetically noisy conditions, showed that the adaptive model outperformed in predictive accuracy the standard NVAR, a leaky echo state network (ESN) - the most common RC model - and a hybrid ESN, thereby showing robust forecasting under noisy conditions.