# Symplectic Inductive Bias for Data-Driven Target Reachability in Hamiltonian Systems

arXiv: https://arxiv.org/abs/2604.17213 · HTML: https://mlsanity.com/paper/2604.17213/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 19 Apr 2026.

## Builds on (most cited first, 16 of 16)

- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Learning Stability Certificates from Data](https://mlsanity.com/paper/2008.05952/) (2020)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectories](https://mlsanity.com/paper/2009.00739/) (2020)
- [Data-Driven Model Predictive Control with Stability and Robustness Guarantees](https://mlsanity.com/paper/1906.04679/) (2019)
- [A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis](https://mlsanity.com/paper/2112.05745/) (2021)
- [On the sample complexity of stabilizing linear dynamical systems from data](https://mlsanity.com/paper/2203.00474/) (2022)
- [On the Sample Complexity of Stabilizing LTI Systems on a Single Trajectory](https://mlsanity.com/paper/2202.07187/) (2022)
- [Data-driven stabilization of nonlinear polynomial systems with noisy data](https://mlsanity.com/paper/2011.07833/) (2020)
- [Learning Stabilizing Policies via an Unstable Subspace Representation](https://mlsanity.com/paper/2505.01348/) (2025)
- [Data-Driven Control of Nonlinear Systems: Beyond Polynomial Dynamics](https://mlsanity.com/paper/2011.11355/) (2020)
- [A Versatile Framework for Data-Driven Control of Nonlinear Systems](https://mlsanity.com/paper/2405.10064/) (2024)
- [Safety-Critical Control via Recurrent Tracking Functions](https://mlsanity.com/paper/2510.01147/) (2025)
- [Recurrent Control Barrier Functions: A Path Towards Nonparametric Safety Verification](https://mlsanity.com/paper/2510.02127/) (2025)
- [Data-driven Practical Stabilization of Nonlinear Systems via Chain Policies: Sample Complexity and Incremental Learning](https://mlsanity.com/paper/2510.03982/) (2025)

## Abstract (arXiv)

Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for stabilization and optimal control. For general nonlinear dynamics, by contrast, guarantees often rely on smoothness assumptions (e.g., Lipschitz continuity) which, when combined with covering arguments, can lead to data requirements that grow exponentially with the ambient dimension. In this paper we argue that data-efficient nonlinear control demands exploiting inductive bias embedded in nature itself, namely, structure imposed by physical laws. Focusing on Hamiltonian systems, we leverage symplectic geometry and intrinsic recurrence on energy level sets to solve target reachability problems. Our approach combines the recurrence property with a recently proposed class of policies, called chain policies, which composes locally certified trajectory segments extracted from demonstrations to achieve target reachability. We provide sufficient conditions for reachability under this construction and show that the resulting data requirements depend on explicit geometric and recurrence properties of the Hamiltonian rather than the state dimension.