Physics-Aware Policy Learning

Updated 6 December 2025

Physics-aware policy learning is a paradigm that embeds physical models into reinforcement learning to enhance sample efficiency, interpretability, and safety.
It combines hybrid modeling, physics-informed architectures, and constraint-based losses to achieve robust generalization and sim-to-real transfer.
This approach is widely applied in robotics, autonomous navigation, and human-AI collaboration, outperforming traditional model-free methods.

Physics-aware policy learning is a paradigm within reinforcement learning and optimal control that explicitly incorporates knowledge of physical laws, structures, or constraints into the learning and deployment of control policies. This approach leverages analytic physics models, structural priors, or physics-informed architectures to achieve data-efficient, robust, and interpretable policy learning—especially in domains where real data is scarce or direct rollout is impractical due to safety, cost, or complexity considerations. The foundational insight is that encoding the physics of the environment within the learning algorithm or policy representation can dramatically improve sample efficiency, generalization, and real-world transfer, while mitigating model-bias and "unphysical" behaviors.

1. Foundational Concepts and Motivations

The fundamental motivation for physics-aware policy learning arises from the challenges of sample inefficiency and model bias in standard (usually model-free) reinforcement learning, especially for systems governed by complex dynamics or stringent physical constraints. Standard approaches either ignore physical knowledge—leading to poor data efficiency and unsafe or unstable learned behaviors—or attempt to learn high-capacity black-box models, which can suffer from extrapolation errors when operating outside the training distribution. Physics-aware methods overcome this by integrating prior knowledge of the system's governing equations, conservation laws, or structural properties directly into the modeling or policy-learning process, providing several advantages:

Sample efficiency: Leveraging known structure reduces the hypothesis space and thus the number of required real-world interactions (Ramesh et al., 2022, Westenbroek et al., 2023, Zhu et al., 2017).
Generalization and transferability: Physics priors facilitate zero-shot or few-shot transfer across tasks and domains (Sebastian et al., 2023, Du et al., 2019, Semage et al., 2021).
Interpretability and safety: Explicit encoding of physical principles yields controllers with guaranteed stability, constraint satisfaction, and physically plausible behaviors (Sebastian et al., 2023, Meng et al., 15 Feb 2024, Kim et al., 3 Aug 2025).

Physics-aware policy learning subsumes techniques ranging from physics-informed model-based RL and neural simulators to partial-differential-equation (PDE)-constrained learning, system identification with physics engines, operator-theoretic IRL, and hierarchical planners with physics priors.

2. Model-Based Methods Leveraging Physics Structure

Physics-aware policy learning often builds upon model-based reinforcement learning (MBRL) frameworks, explicitly fusing first-principles models with data-driven corrections or embedding physical structure directly in the model architecture. Typical strategies include:

Hybrid modeling: Combining an analytic or physics-based model (e.g. ODEs for rigid-body motion) with a data-driven residual model, regularizing the learning so the residual is small (Asri et al., 2 Jul 2024). The fused model $\hat{\mathcal T}_\theta(s,a) = F^p_{\theta_p}(s,a) + F^r_{\theta_r}(s,a)$ is trained on real trajectory data with a loss function penalizing large deviations from the physics prior.
Physics-informed architectures: Using Lagrangian or Hamiltonian neural networks, which encode symmetries, conservation laws, or passivity directly in the model (Ramesh et al., 2022). By parameterizing mass matrices, potential energies, and generalized forces, these networks reproduce the algebraic and energetic structure of true mechanical systems.
Physics-respecting loss functions: Penalizing violations of physical laws (e.g. energy conservation) or enforcing PDE residuals arising from the system's governing equations (Ramesh et al., 2022, Kim et al., 3 Aug 2025, Meng et al., 15 Feb 2024).

Physics-aware MBRL achieves significant gains in sample efficiency and trajectory fidelity, especially in highly sensitive or chaotic environments that amplify model errors, where black-box models typically diverge (Ramesh et al., 2022, Asri et al., 2 Jul 2024).

3. Physics-Informed Policy Iteration and PDE-Constrained RL

A major direction uses the physics of optimal control—often Hamilton-Jacobi-Bellman (HJB) equations—to structure the policy search. Recent advances exploit physics-informed neural networks (PINNs) to represent the value function and policy, training by minimizing the residual of the corresponding PDE:

PINN-based policy iteration (PINN-PI): Iteratively approximates the value function by a neural network $V_\theta(x,t)$ , enforcing satisfaction of the HJB or related PDE either exactly (via linear least squares) or approximately (via collocation loss minimization) (Meng et al., 15 Feb 2024, Kim et al., 3 Aug 2025). The policy is updated by minimizing the cost-to-go according to the current value gradient, often in closed form for affine-control systems.
Error control and convergence: By linking the PDE residual norm to the $L^2$ error in the value function and policy, explicit convergence guarantees and error bounds are derived, distinguishing physics-based learning from standard rollout-based methods (Kim et al., 3 Aug 2025, Kim et al., 3 Aug 2025).
Extensions to stochastic and high-dimensional control: Modern PINN-PI schemes are demonstrated to scale to 10-dimensional LQR and nonlinear systems (e.g., pendulum, cartpole) with accuracy and stability not attainable by off-the-shelf RL (Meng et al., 15 Feb 2024, Kim et al., 3 Aug 2025).

Additionally, some variants—such as "HJBPPO"—embed the continuous-time HJB equation as a regularizer in policy optimization architectures like PPO, yielding more stable value functions and improved high-dimensional performance (Mukherjee et al., 2023).

4. Physics-Guided System Identification, Sim2Real, and Meta-Learning

Physics-aware identification and rapid adaptation address the reality gap in sim-to-real transfer and environments with unknown or changing dynamics:

Bayesian identification with physics engines: Maintaining a posterior over latent system parameters (e.g. friction, mass) by matching simulator rollouts to real trajectories and selecting information-rich physical experiments via entropy search (Zhu et al., 2017).
Action grouping and partial grounding: Using intuitive or task-informed action classes (e.g. collision- or friction-sensitive moves) to efficiently probe and estimate only the most task-relevant latent factors, then fitting the simulator accordingly—yielding significantly lower sample complexity for sim-to-real transfer (Semage et al., 2021).
Implicit system identification: Embedding a brief physical probe (e.g. a high-acceleration trial) and observation into the policy's input, where the policy network implicitly encodes unknown physical parameters via supervised or RL-based end-to-end learning (Wang et al., 8 Feb 2025).

For manipulation and navigation, these strategies yield robust, efficient policy adaptation across unmodeled variation in environment physics, with strong generalization to real hardware (Zhu et al., 2017, Wang et al., 8 Feb 2025, Semage et al., 2021).

5. Embedding Physics in Multi-Agent and Distributed Control

Physics-aware policy learning extends naturally to multi-agent and distributed robot systems:

Port-Hamiltonian policy representations: Encoding energy-conserving and dissipative inter-agent interactions by parameterizing the system in port-Hamiltonian form. Learned policies ensure passivity and scalability, with block-sparse or self-attention mechanisms used for locality and permutation invariance (Sebastian et al., 2023).
Graph-structured message passing: Utilizing self-attention to aggregate information from local neighbors within a communication graph, producing scalable, distributed policies for large multi-robot teams (Sebastian et al., 2023).
Hierarchical planning: Solving global navigation via physics-constrained neural fields (e.g., Eikonal PDE) as local planners and maintaining sparse global graphs for long-horizon connectivity; physics priors (e.g., arrival-time fields) prevent spectral bias and catastrophic forgetting in modular RL systems (Chen et al., 1 Oct 2025).

Empirical results demonstrate robust scalability, zero-shot sim-to-real transfer, and superior per-robot reward compared to black-box or purely graph-based baselines (Sebastian et al., 2023, Chen et al., 1 Oct 2025).

6. Physics-Aware Policy Learning Beyond Dynamics: IRL and Human-AI Collaboration

Recent developments extend physics-aware methodologies to inverse reinforcement learning (IRL), safe RL, and human-in-the-loop systems:

Physics-constrained IRL: Leveraging analytical connections (e.g., Fokker-Planck equations) between MDPs and statistical physics to simultaneously infer transition and reward given observed agent densities. The inferred policy automatically inherits transport/diffusion structure (Huang et al., 2023).
Physics-enhanced RL with Human Feedback: Integrating physics-based policies (e.g., traffic-flow models) with human interventions in autonomous driving, ensuring that the learned policy is always at least as safe as the interpretable physics-based baseline (Huang et al., 1 Sep 2024).
Physical derivatives as a learning primitive: Instead of modeling the entire environment, direct estimation of trajectory sensitivities (policy parameter $\rightarrow$ state displacement) through empirical perturbation and regression allows locally data-efficient policy gradient computation on real systems (Mehrjou et al., 2022).

These approaches blend statistical learning, optimal control theory, and physical modeling to produce interpretable, safe, and robust outcomes in both single- and multi-agent settings.

7. Empirical Benchmarks, Limitations, and Open Directions

Comprehensive benchmarks across simulated and real-world domains validate the effectiveness of physics-aware policy learning:

Benchmarks: Standard robot manipulation (pushing, assembly), locomotion (cartpole, acrobot, LQR), large-scale navigation, soft-rigid manipulation, and stochastic control (Zhu et al., 2017, Ramesh et al., 2022, Meng et al., 15 Feb 2024, Chen et al., 1 Oct 2025, Wang et al., 8 Feb 2025).
Key results: Sample efficiency gains (5–10× relative to model-free RL), robust sim-to-real transfer, guaranteed or certified stability, and strong asymptotic performance under chaotic or underactuated dynamics (Ramesh et al., 2022, Asri et al., 2 Jul 2024, Kim et al., 3 Aug 2025, Sebastian et al., 2023).
Limitations: Scalability to very high dimensions may be hampered by PDE inference and density estimation bottlenecks (Huang et al., 2023, Meng et al., 15 Feb 2024). Physical consistency must be architecturally enforced or regularized; otherwise, unmodeled non-smooth phenomena (contacts, collisions) or stochasticity can still degrade performance (Ramesh et al., 2022, Meng et al., 15 Feb 2024).
Future challenges: Joint identification and control under partial observability, scalable formal verification, efficient handling of hybrid and switched dynamics, and learning "physical operators" for rapid generalization across tasks (Meng et al., 15 Feb 2024, Kim et al., 3 Aug 2025).

Physics-aware policy learning thus represents a comprehensive, theoretically grounded approach for integrating scientific modeling, data-driven learning, and optimal control, yielding a new generation of sample-efficient, robust, and interpretable policies for complex real-world systems across robotics, autonomous driving, and multi-agent domains.