# Information-theoretic receding-horizon active learning of nonlinear dynamical systems

arXiv: https://arxiv.org/abs/2609.36712 · HTML: https://mlsanity.com/paper/2609.36712/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 21 of 21)

- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [Prediction-Oriented Bayesian Active Learning](https://mlsanity.com/paper/2304.08151/) (2023)
- [Learning nonlinear dynamical systems from a single trajectory](https://mlsanity.com/paper/2004.14681/) (2020)
- [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024)
- [Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systems](https://mlsanity.com/paper/2002.08538/) (2020)
- [Out-of-Domain Generalization in Dynamical Systems Reconstruction](https://mlsanity.com/paper/2402.18377/) (2024)
- [Optimistic Active Exploration of Dynamical Systems](https://mlsanity.com/paper/2306.12371/) (2023)
- [Active Learning in Robotics: A Review of Control Principles](https://mlsanity.com/paper/2106.13697/) (2021)
- [Bayesian Sequential Optimal Experimental Design for Nonlinear Models Using Policy Gradient Reinforcement Learning](https://mlsanity.com/paper/2110.15335/) (2021)
- [Optimal Exploration for Model-Based RL in Nonlinear Systems](https://mlsanity.com/paper/2306.09210/) (2023)
- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)
- [Receding Horizon Curiosity](https://mlsanity.com/paper/1910.03620/) (2019)
- [Goal-Oriented Bayesian Optimal Experimental Design for Nonlinear Models using Markov Chain Monte Carlo](https://mlsanity.com/paper/2403.18072/) (2024)
- [Localized active learning of Gaussian process state space models](https://mlsanity.com/paper/2005.02191/) (2020)
- [Active Learning for Control-Oriented Identification of Nonlinear Systems](https://mlsanity.com/paper/2404.09030/) (2024)
- [FLEX: an Adaptive Exploration Algorithm for Nonlinear Systems](https://mlsanity.com/paper/2304.13426/) (2023)
- [A Receding Horizon Approach for Simultaneous Active Learning and Control using Gaussian Processes](https://mlsanity.com/paper/2101.10351/) (2021)
- [Space-Filling Input Design for Nonlinear State-Space Identification](https://mlsanity.com/paper/2405.18207/) (2024)
- [Adaptive Experiment Design for Nonlinear System Identification with Operational Constraints](https://mlsanity.com/paper/2502.20941/) (2025)

## Abstract (arXiv)

Accurately learning nonlinear dynamics from a finite-duration experiment requires the efficient collection of informative data. We address this challenge for stochastic controlled nonlinear dynamical systems whose state is observed along a single trajectory. Our goal is to reconstruct the unknown controlled state-increment map over a prescribed compact subset of state-input space. We construct a parametric estimator of the map using fixed nonlinear features, so that the model is nonlinear in the state and input, but linear in the unknown parameters. A Gaussian prior over the parameters yields recursive Bayesian posterior updates as data stream in, enabling online quantification of predictive uncertainty in the reconstructed dynamics over the target set. We formulate an optimal adaptive-design problem over an information state, using a prediction-oriented acquisition criterion based on the mean marginal mutual information between candidate future trajectories and the reconstructed dynamics over the target set. We then approximate the resulting adaptive-design problem by a non-myopic receding-horizon formulation, evaluate its remaining expectation using a scenario-based sample average, and solve the resulting deterministic program with the cross-entropy method, leveraging parallel candidate-scenario evaluations. Numerical experiments on a noisy multistable system demonstrate that the proposed adaptive information-seeking strategy reduces predictive uncertainty and reconstruction error more efficiently than common excitation baselines under comparable experimental constraints.