How Should Robots Learn from Physical Laws? Finding the Best Way to Embed Physics in Robot Learning

Kurzbeschreibung

Beschreibung WHY THIS THESIS? Foundation models have been used to learn language from internet-scale data. Robots don't have that luxury: real-world data are expensive, scarce, and safety-critical. However, robots do have one advantage: they obey physics. Newton's laws, symmetries, energy conservation, and kinematic constraints are a free source of knowledge that a learning algorithm can exploit. This idea is behind physics-informed robot learning, a fast-growing field. Our recent survey paper on embedding physics priors in robot learning (https://arxiv.org/abs/2609.22319) reviews more than 300 papers and classifies them into three routes for injecting physics into machine learning: - Physics-guided learning: physics shapes the inputs and data of machine learning models (physics-based features, symmetry-based data augmentation). - Physics-encoded learning: physics is built into the architecture of machine learning models. - Physics-informed learning: physics enters the loss function (e.g., PINN-style residuals of the equations of motion). The open question is surprisingly fundamental: given the same physical knowledge, which of the three routes should you use, and is it worth combining them? Less than 4% of existing works combine routes, and no study has compared them fairly. Your thesis will provide some of the first answers. ------ THE CORE IDEA You will take pieces of physical knowledge and inject them into a learning model through all three routes, then compare the routes and their combinations. Take left/right steering symmetry of a vehicle as an example: steering left mirrors steering right. This physical prior can be embedded in three ways: - Physics-guided: mirror the training data, for free data augmentation. - Physics-encoded: build the architecture of the neural network or learning model so that its output is odd in the steering input, by construction. - Physics-informed: add a loss term that penalizes asymmetric predictions, even on unlabeled states. By keeping the physics fixed and changing only where it enters the learning pipeline, you can answer: - Which route is most data-efficient when only minutes (or seconds) of data are available? - Which route generalizes best to unseen conditions (new speeds, tires, payloads)? - What happens when the physics prior is slightly wrong? Which route breaks, and which degrades gracefully? - When do routes reinforce each other, and when are they redundant or even conflicting? ------ WHAT YOU WILL WORK ON The thesis is flexible and can be shaped around your interests. A possible path: 1. Get started (month 1). Learn the three routes and set up the software: nnodely, our open-source library for embedding physics priors into neural networks. 2. Build the comparison (months 2-3). Implement specific physical priors through each route, with black-box baselines (MLP, GRU, Transformer). 3. Run the experiments (months 3-5). Vary the amount of training data, the correctness of the prior, and the test conditions. Measure accuracy, long-horizon prediction, and physical consistency. 4. Distill the insights (months 5-6). Turn the results into practical guidelines: "if you have this much data and this good a model, use this route." Application domains (more than one choice is possible): - Simple mechanical systems: pendulums, double pendulums, and similar. Good to start with, because the physics is simple and the data are cheap to generate. - Vehicle dynamics: real driving data from our 1:10-scale autonomous RoboRacer, and from a full-scale autonomous race car. The task is learning how a car accelerates, brakes, and turns near its handling limits. - Robot dynamics: manipulators, legged robots. Types of machine learning models: - Neural networks (MLPs, recurrent networks, ...) - Custom-designed neural architectures that encode physics priors (model-structured neural networks) - Vision-Language-Action models (optional track): extend the study to large multimodal models that generate driving trajectories from images and language instructions. ------ WHAT YOU WILL GAIN - Hands-on experience at the intersection of machine learning, robotics, and dynamics, one of the most active research directions in robot learning. - Real data from real robots, from small-scale vehicles to a full-scale autonomous race car. - A research contribution that addresses an open question highlighted in the literature. Strong results are intended to become a scientific publication, co-authored with the team. - Close supervision in an international group working on autonomous vehicles, physics-informed learning, and differentiable control, with collaborators in other universities in Germany and Italy. - Open-source impact: your implementation can become part of the nnodely library. Voraussetzungen Required: - Good Python skills and basic experience with PyTorch / Keras / Tensorflow / learning frameworks. - Curiosity about how machine learning can benefit from physics, and a structured, experimental mindset. Nice to have: - Background in vehicle dynamics, robot dynamics, or control.