# Domain Adaptive Safety Filters via Deep Operator Learning

arXiv: https://arxiv.org/abs/2410.14528 · HTML: https://mlsanity.com/paper/2410.14528/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 39 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman Equations](https://mlsanity.com/paper/1907.05317/) (2019)
- [Safe Control Under Input Limits with Neural Control Barrier Functions](https://mlsanity.com/paper/2211.11056/) (2022)
- [Adaptive Safety with Control Barrier Functions](https://mlsanity.com/paper/1910.00555/) (2019)
- [SABLAS: Learning Safe Control for Black-box Dynamical Systems](https://mlsanity.com/paper/2201.01918/) (2022)
- [Refining Control Barrier Functions through Hamilton-Jacobi Reachability](https://mlsanity.com/paper/2204.12507/) (2022)
- [Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments](https://mlsanity.com/paper/2201.01347/) (2022)
- [Composing Control Barrier Functions for Complex Safety Specifications](https://mlsanity.com/paper/2309.06647/) (2023)
- [Integral Control Barrier Functions for Dynamically Defined Control Laws](https://mlsanity.com/paper/2006.16936/) (2020)
- [Soft-Minimum and Soft-Maximum Barrier Functions for Safety with Actuation Constraints](https://mlsanity.com/paper/2305.10620/) (2023)
- [Compositions of Multiple Control Barrier Functions Under Input Constraints](https://mlsanity.com/paper/2210.01354/) (2022)
- [Data-Efficient Control Barrier Function Refinement](https://mlsanity.com/paper/2303.05973/) (2023)
- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [Safety-Critical Control with Input Delay in Dynamic Environment](https://mlsanity.com/paper/2112.08445/) (2021)
- [Soft-Minimum Barrier Functions for Safety-Critical Control Subject to Actuation Constraints](https://mlsanity.com/paper/2304.00693/) (2023)
- [Time-Varying Soft-Maximum Control Barrier Functions for Safety in an A Priori Unknown Environment](https://mlsanity.com/paper/2310.05261/) (2023)
- [Learning Feasibility Constraints for Control Barrier Functions](https://mlsanity.com/paper/2303.09403/) (2023)
- [Learning a Better Control Barrier Function Under Uncertain Dynamics](https://mlsanity.com/paper/2310.04795/) (2023)
- [Distributed Safe Navigation of Multi-Agent Systems using Control Barrier Function-Based Optimal Controllers](https://mlsanity.com/paper/2402.06195/) (2024)

## Built on by (most cited first, 1 of 1)

- [Safe PDE Boundary Control with Neural Operators](https://mlsanity.com/paper/2411.15643/) (2024)

## Abstract (arXiv)

Learning-based approaches for constructing Control Barrier Functions (CBFs) are increasingly being explored for safety-critical control systems. However, these methods typically require complete retraining when applied to unseen environments, limiting their adaptability. To address this, we propose a self-supervised deep operator learning framework that learns the mapping from environmental parameters to the corresponding CBF, rather than learning the CBF directly. Our approach leverages the residual of a parametric Partial Differential Equation (PDE), where the solution defines a parametric CBF approximating the maximal control invariant set. This framework accommodates complex safety constraints, higher relative degrees, and actuation limits. We demonstrate the effectiveness of the method through numerical experiments on navigation tasks involving dynamic obstacles.