Embedding Physics Priors in Robot Learning: A Survey

Mattia Piccinini, Lucas Schulze, Alice Plebe, Matteo Saveriano, Thomas Beckers, Yuan Gao, Oleg Arenz, Baha Zarrouki, Dingrui Wang, Finn Rasmus Sch\"afer, Jan Peters, Johannes Betz, Gastone Pietro Rosati Papini · N/A · 2026

Summary

The rapid progress of artificial intelligence is reshaping robotics and accelerating the adoption of learning-based approaches.

Abstract Summary

The rapid progress of artificial intelligence is reshaping robotics and accelerating the adoption of learning-based approaches. While purely data-driven methods have achieved remarkable success in computer vision and natural language processing, robotics remains constrained by limited data, complex real-world interactions, and the need for reliable operation. These challenges have motivated the exploration of physics-embedded robot learning, which embeds physics priors into learning algorithms. By encoding the underlying physical laws and constraints, physics priors can complement limited data with robotics-specific inductive biases, potentially improving generalization, interpretability, and sample efficiency. However, the literature on physics-embedded robot learning remains fragmented across terminology, methodologies, and application domains, making it difficult to assess this growing body of work. This survey reviews physics-embedded robot learning across a broad range of physics priors, robotics applications, and machine learning models, from single-layer perceptrons to generative foundation models. We adopt a unified taxonomy that classifies existing approaches according to their physics embedding: physics-guided inputs, data, and representations; physics-encoded model architectures; and physics-informed training loss functions. Building on this taxonomy, we review methods for robot dynamics learning, trajectory planning, prediction, control, and estimation, together with the corresponding open-source software ecosystem. We identify key open challenges, and outline promising future research directions. Overall, we argue that physics priors provide a particularly relevant robotics-specific inductive bias, complementing rather than replacing data-driven learning, and paving the way toward more generalizable, data-efficient, and trustworthy robotic systems.

Key Points

The rapid progress of artificial intelligence is reshaping robotics and accelerating the adoption of learning-based approaches.
While purely data-driven methods have achieved remarkable success in computer vision and natural language processing, robotics remains constrained by limited data, complex real-world interactions, and the need for reliable operation.
These challenges have motivated the exploration of physics-embedded robot learning, which embeds physics priors into learning algorithms.
By encoding the underlying physical laws and constraints, physics priors can complement limited data with robotics-specific inductive biases, potentially improving generalization, interpretability, and sample efficiency.
However, the literature on physics-embedded robot learning remains fragmented across terminology, methodologies, and application domains, making it difficult to assess this growing body of work.

Physics-Guided, Physics-Encoded, and Physics-Informed Robot Learning: Overview and Organization

Does the method embed physics priors that express specific physical knowledge of a robotic system, rather than generic mathematical structure? Are any physics priors used to transform, enrich, curate, select, or correct the inputs, data, or representations provided to/by the learning model, either before training or as pre- or post-processing guidance at inference?

Physics-Guided Are any physics priors encoded in learning model architectures, remaining active during inference? Physics-Encoded Are any physics priors incorporated into the trainin...

Physics-Guided, Physics-Encoded, and Physics-Informed Robot Learning: Overview and Organization — Embedding Physics Priors in Robot Learning: A Survey — Figure 5 : Sub-categories of physics-encoded robot learning architectures (Sec. 3 ).

Physics-Encoded Architectures

A first approach to embedding physics priors in robot learning is to design model architectures that explicitly encode physical principles and constraints. This introduces inductive biases aligned with the underlying dynamics, with the potential to improve interpretability, generalization, and sample efficiency. Following Faroughi et al.

(2024) , we refer to physics-encoded NNs as models that “forcibly encode known physics into their core architecture”.

Physics-Informed Loss Functions

Physics-informed approaches provide a flexible and data-efficient framework for solving forward and inverse problems governed by differential equations, by embedding physical laws as soft constraints in the training loss functions. The combination of data-driven and physics-informed loss terms can improve generalization in data-scarce regions, and hence improve the physical consistency of the learned model.

Physics-Guided Inputs, Data, and Representations

Physics-guided learning exploits physics priors to transform, enrich, curate, select, or correct input features, training data, and learned representations.

Rather than modifying the model architecture or training objective, these methods embed physical knowledge into the inputs, data, or representations before training or as pre- or post-processing guidance at inference, while preserving the flexibility of standard ML models.

Software Tools

✓ denotes primary or native support, while $\sim$ denotes partial, indirect, or application-dependent support. Blank cells indicate functionalities that are not objectives of the framework.

In the Optimizers column, Wrapper indicates that the framework relies on optimization algorithms provided by its underlying backend or external libraries, whereas Custom indicates dedicated optimization procedures or training algorithms.

Open Research Questions and Challenges

Despite the rapid progress reviewed in this survey, embedding physics priors in robot learning methods remains an open research field. We organize the main open questions and challenges around the following themes. Challenge 1 – Generality versus Physics-based Inductive Bias: A fundamental trade-off exists between the flexibility of data-driven learning and the inductive bias introduced by physics priors.

The success of foundation models suggests that large-scale pre-training can yield remarkable generalization.

Future Research Directions

To address the open challenges outlined in Sec. 7 , we identify seven research directions that, in our view, represent the most promising paths toward complementing data-driven robot learning with physics priors.

Direction 1 – Combining Multiple Physics-Prior Routes: A promising future direction is the systematic combination of physics-guided inputs and data, physics-encoded architectures, and physics-informed loss functions within unified learning frameworks.

Sources and Demonstrations

Figures are reproduced from Piccinini et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.