# Neural Operators for Multi-Task Control and Adaptation Source: [Neural Operators for Multi-Task Control and Adaptation]() Collection index: [llms.txt]() Data updated: 2026-04-08T05:00:04.658Z Authors: David Sewell, Xingjian Li, Stepan Tretiakov, Krishna Kumar, David Fridovich-Keil Published: 2026-04-03T20:45:32.000Z ## Abstract Neural operator methods have emerged as powerful tools for learning mappings between infinite-dimensional function spaces, yet their potential in optimal control remains largely unexplored. We focus on multi-task control problems, whose solution is a mapping from task description (e.g., cost or dynamics functions) to optimal control law (e.g., feedback policy). We approximate these solution operators using a permutation-invariant neural operator architecture. Across a range of parametric optimal control environments and a locomotion benchmark, a single operator trained via behavioral cloning accurately approximates the solution operator and generalizes to unseen tasks, out-of-distribution settings, and varying amounts of task observations. We further show that the branch-trunk structure of our neural operator architecture enables efficient and flexible adaptation to new tasks. We develop structured adaptation strategies ranging from lightweight updates to full-network fine-tuning, achieving strong performance across different data and compute settings. Finally, we introduce meta-trained operator variants that optimize the initialization for few-shot adaptation. These methods enable rapid task adaptation with limited data and consistently outperform a popular meta-learning baseline. Together, our results demonstrate that neural operators provide a unified and efficient framework for multi-task control and adaptation. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Behavioral Cloning on P2P-Dyn.](): Behavioral Cloning; P2P-Dyn.; Relative L2 Error: 0.081. - [Behavioral Cloning on P2P Small](): Behavioral Cloning; P2P Small; Relative L2 Error: 0.077. - [Behavioral Cloning on P2P-Cost](): Behavioral Cloning; P2P-Cost; Relative L2 Error: 6.9. - [Behavioral Cloning on Planar Quadrotor](): Behavioral Cloning; Planar Quadrotor; Relative L2 Error: 0.066. - [Behavioral Cloning on Obstacle](): Behavioral Cloning; obstacle; Relative L2 Error: 0.285. ## Original sources and implementation [Original paper]() [PDF]()