Inthispaper,wepropose a tractable algorithm that estimates the probabilistic aggregation map from the system'strajectory.

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propose a tractable algorithm that estimates the probabilistic aggregation map from the system's trajectory. We adopt a soft-aggregation model, where each meta-state has a signature raw state, called an anchor state.

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states

We thank three reviewers for the constructive comments. In what follows we make a few clarifications and itemized responses. We are the first to bring the perspective of NMF/topic modeling to Markov state aggregation. We hope our work would inspire future work and more efficient methods may be developed. Making this idea work, both in theory and in applications, requires substantial efforts and nontrivial analysis.

Imitation learning (IL) has proven effective across a wide range of manipulation tasks. However, IL policies often struggle when faced with out-of-distribution observations; for instance, when the target object is in a previously unseen position or occluded by other objects. In these cases, extensive demonstrations are needed for current IL methods to reach robust and generalizable behaviors. But when humans are faced with these sorts of atypical initial states, we often rearrange the environment for more favorable task execution. For example, a person might rotate a coffee cup so that it is easier to grasp the handle, or push a box out of the way so they can directly grasp their target object. In this work we seek to equip robot learners with the same capability: enabling robots to prepare the environment before executing their given policy. We propose ReSET, an algorithm that takes initial states -- which are outside the policy's distribution -- and autonomously modifies object poses so that the restructured scene is similar to training data. Theoretically, we show that this two step process (rearranging the environment before rolling out the given policy) reduces the generalization gap. Practically, our ReSET algorithm combines action-agnostic human videos with task-agnostic teleoperation data to i) decide when to modify the scene, ii) predict what simplifying actions a human would take, and iii) map those predictions into robot action primitives. Comparisons with diffusion policies, VLAs, and other baselines show that using ReSET to prepare the environment enables more robust task execution with equal amounts of total training data. See videos at our project website: https://reset2025paper.github.io/

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propose a tractable algorithm that estimates the probabilistic aggregation map from the system's trajectory. We adopt a soft-aggregation model, where each meta-state has a signature raw state, called an anchor state.

Modern techniques for physical simulations rely on numerical schemes and meshrefinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power. Data-driven methods based on large-scale machine learning promise high adaptivity by integrating long-range dependencies more directly and efficiently. In this work, we focus on fluid dynamics and address the shortcomings of a large part of the literature, which are based on fixed support for computations and predictions in the form of regular or irregular grids. We propose a novel setup to perform predictions in a continuous spatial and temporal domain while being trained on sparse observations. We formulate the task as a double observation problem and propose a solution with two interlinked dynamical systems defined on, respectively, the sparse positions and the continuous domain, which allows to forecast and interpolate a solution from the initial condition. Our practical implementation involves recurrent GNNs and a spatio-temporal attention observer capable of interpolating the solution at arbitrary locations. Our model not only generalizes to new initial conditions (as standard auto-regressive models do) but also performs evaluation at arbitrary space and time locations. We evaluate on three standard datasets in fluid dynamics and compare to strong baselines, which are outperformed both in classical settings and in the extended new task requiring continuous predictions. The Lavoisier conservation principle states that changes in physical quantities in closed regions must be attributed to either input, output, or source terms. By applying this rule at an infinitesimal scale, we retrieve partial differential equations (PDEs) governing the evolution of a large majority of physics scenarios. Consequently, the development of efficient solvers is crucial in various domains involving physical phenomena. Therefore, there is a need for faster and more versatile simulation tools that are reliable and efficient, and data-driven methods offer a promising opportunity. Large-scale machine learning offers a natural solution to this problem. In this paper, we address data-driven solvers for physics, but with additional requirements on the behavior of the simulator: R1.

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propose a tractable algorithm that estimates the probabilistic aggregation map from the system's trajectory. We adopt a soft-aggregation model, where each meta-state has a signature raw state, called an anchor state. This model includes several common state aggregation models as special cases.

State aggregation is a model reduction method rooted in control theory and reinforcement learning. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. In this paper, we study the unsupervised estimation of unknown state aggregation structures based on Markov trajectories. We formulate the state aggregation of Markov processes into a nonnegative factorization model, where left and right factor matrices correspond to aggregation and disaggregation distributions respectively. By leveraging techniques developed in the context of topic modeling, we propose an efficient polynomial-time algorithm for computing the estimated state aggregation model. Under some "anchor state" assumption, we show that one can reliably recover the state aggregation structure from sample transitions with high probability. Sharp divergence error bounds are proved for the estimated aggregation and disaggregation distributions, and experiments with Manhattan traffic data are provided.