EMPIRIC: Experiment-Driven Learning of Residual World Models for Robot Planning

Yichao Liang; Amber Li; Dat Nguyen; Emily Bunnapradist; Michelangelo Naim; Sreela Kodali; Matteo Merler; Bowen Li

cs.ROSep 28, 2026

EMPIRIC: Experiment-Driven Learning of Residual World Models for Robot Planning

Authors: Yichao Liang, Amber Li, Dat Nguyen, Emily Bunnapradist, Michelangelo Naim, Sreela Kodali, Matteo Merler, Bowen Li, +8 more

Organizations: Basis Research Institute · University of Cambridge · Carnegie Mellon University · Harvard University · Fondazione Bruno Kessler · Massachusetts Institute of Technology · The Alan Turing Institute · Princeton University · Cornell University

Abstract

A robot should be able to learn through experiments how unfamiliar objects behave and interact, then plan with that knowledge. It need not start from scratch: physics engines supply knowledge of motion and contact, but can omit entire mechanisms, such as glue curing, water heating, or wind. We present EMPIRIC, an agent that learns a residual world model: a physics engine extended with code for the missing mechanisms. The learned programs can introduce new forces, constraints, and hidden state, and Bayesian inference estimates their parameters and states from noisy observations. The resulting model lets the agent predict the outcomes of actions, choose informative experiments, and revise its hypotheses when predictions fail. Across five simulated domains, EMPIRIC learns interpretable, reusable models, and solves more tasks with fewer environment interactions than all three baselines. On a physical robot, it learns wind forces and domino masses to solve a manipulation task. Website and code: https://yichao-liang.github.io/empiric

Figures & tables

Figure 1: Learning missing physics as code. Top: in Bridge, lifting one block of a glued pair also lifts its partner, which a base simulator without glue does not predict; the agent writes the glue into a simulator program, infers its parameters, and plans with it. The lift images and code are illustrative. Bottom: initial and final scenes from successful EMPIRIC test episodes in five simulated domains and on a real robot; each domain has mechanisms or parameters that the agent must learn.

Figure 2: Learning and planning during a continual run. In this Bridge example, the agent learns how glue bonds touching blocks after an unknown cure time. The loop is schematic: steps may repeat or occur in a different order.

Figure 3: Results with noisy observations across five domains. Top: percentage of the five runs with every training and test task solved. Bottom: percentage of runs solved within each environment-step budget; each curve steps up at a solved run’s total steps and ends at the agent’s rate above.

Figure 4: Recorded EMPIRIC runs from exploring to solving. Each row shows one run in time order, from the agent’s first experiments to solving the test task. The purple bar marks where the agent writes its simulator program $P$ and infers $\theta$ ; dashed frames show what the agent’s world model predicts for a plan. Top: in Bridge, the goal is to glue blocks into a bridge across two supports; the agent’s experiments show how glue bonds. Middle: in Balloons, the goal is to release balloons so that the box settles in a target height band; the agent’s experiments show that lift fades with height. Bottom: on the real robot, the test goal is to land the green domino in the pink patch; the fan cannot move the green domino, so the agent stands the gray one upwind to knock it in.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Domain	Position	Orientation	Scalar
Domino	10	0.04	0
Bridge	5	0.02	0
Balloons	10	0.02	0
Boil	12.5	0.05	0.07
Fan	5	0.02	0

Appendix

Table 1: Observation-noise scales in the simulated domains. Position is in millimeters, orientation in radians, and scalar readings in their feature units.

Figure 5: Recorded EMPIRIC runs in Domino, Boil, and Fan. As in Figure 4 , each row goes from experiments through learning (purple bar) and checks in the agent’s learned model (dashed frames) to the solved test task; in Domino, the agent adds no mechanism and fits only $\theta$ . Domino: the agent fits friction 0.50 to the training cascade, up from the base simulator’s 0.10; in the model, a domino struck side-on falls with the blow, and two blue dominoes turn the chain through $90^{\circ}$ in every rollout before the test chain is built. Boil: water from the tap lands in front of the drawn spout, and a jug placed on the puddle fills at a rate the agent measures; the model predicts that overlapping filling and boiling brings both jugs to a boil without a spill, as happens in the test episode. Fan: a fan burst rolls the ball 0.9 m, but in the model the ball stalls on a lip that noisy platform heights created, which the agent removes; the agent’s push, brake and blow plan then lands the ball on the pad in the model, and in the test episode the ball stops 6 mm from the predicted spot.

Parameter	Prior range	Fitted mean $\pm$ SD
Green mass (kg)	$[0.03,0.40]$	$0.299\pm 0.060$
Gray mass (kg)	$[0.03,0.40]$	$0.160\pm 0.073$
Friction coefficient	$[0.15,0.90]$	$0.617\pm 0.148$
Wind force $F_{0}$ (N)	$[0.05,1.50]$	$0.403\pm 0.141$
Decay time (s)	$[0.10,6.00]$	$3.278\pm 1.460$

Appendix

Table 2: Parameter belief after the two exploratory experiments. Priors are uniform over the stated ranges. Values are weighted means and standard deviations of the 80 kept samples. The agent chose the priors of the wind force and decay time, which its wind program introduces.

Figure 7: Exploratory experiments. From left to right: the green block before and after fan activation, followed by the gray block before and after activation. The green block remains upright; the gray block falls into the original target region.

Figure 8: Test setup and activation. From left to right: the relocated target, the green block placed first, the gray block placed upwind of it, and the robot holding the fan button.

Figure 9: Cascade and task completion. From left to right: the gray block topples toward the green block, reaches it, the green block falls, and the green block rests flat in the relocated target region.

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Open paper AskPDF arXiv

World models, which are predictive representations of how environments evolve under actions, have become a central component of robot learning. They support policy learning, planning, simulation, evaluation, data generation, and have advanced rapidly with the rise of foundation models and large-scale video generation. However, the literature remains fragmented across architectures, functional roles, and embodied application domains. To address this gap, we present a comprehensive review of world models from a robot-learning perspective. We examine how world models are coupled with robot policies, how they serve as learned simulators for reinforcement learning and evaluation, and how robotic video world models have progressed from imagination-based generation to controllable, structured, and foundation-scale formulations. We further connect these ideas to navigation and autonomous driving, and summarize representative datasets, benchmarks, and evaluation protocols. Overall, this survey systematically reviews the rapidly growing literature on world models for robot learning, clarifies key paradigms and applications, and highlights major challenges and future directions for predictive modeling in embodied agents. To facilitate continued access to newly emerging works, benchmarks, and resources, we will maintain and regularly update the accompanying GitHub repository alongside this survey.

Abstract

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