# Neural Control Barrier Functions from Physics Informed Neural Networks

arXiv: https://arxiv.org/abs/2504.11045 · HTML: https://mlsanity.com/paper/2504.11045/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 15 Apr 2025.

## Builds on (most cited first, 22 of 22)

- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Safe Control Under Input Limits with Neural Control Barrier Functions](https://mlsanity.com/paper/2211.11056/) (2022)
- [Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification](https://mlsanity.com/paper/2312.09131/) (2023)
- [Exact Verification of ReLU Neural Control Barrier Functions](https://mlsanity.com/paper/2310.09360/) (2023)
- [A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems](https://mlsanity.com/paper/2502.11057/) (2025)
- [Learning a Formally Verified Control Barrier Function in Stochastic Environment](https://mlsanity.com/paper/2403.19332/) (2024)
- [Control Barrier Functions in Dynamic UAVs for Kinematic Obstacle Avoidance: A Collision Cone Approach](https://mlsanity.com/paper/2303.15871/) (2023)
- [Towards Learning and Verifying Maximal Neural Lyapunov Functions](https://mlsanity.com/paper/2304.07215/) (2023)
- [Exact Imposition of Safety Boundary Conditions in Neural Reachable Tubes](https://mlsanity.com/paper/2404.00814/) (2024)
- [Semi-Supervised Safe Visuomotor Policy Synthesis using Barrier Certificates](https://mlsanity.com/paper/2409.12616/) (2024)
- [Learning a Better Control Barrier Function](https://mlsanity.com/paper/2205.05429/) (2022)
- [Compositions of Multiple Control Barrier Functions Under Input Constraints](https://mlsanity.com/paper/2210.01354/) (2022)
- [Formally Verified Physics-Informed Neural Control Lyapunov Functions](https://mlsanity.com/paper/2409.20528/) (2024)
- [CP-NCBF: A Conformal Prediction-based Approach to Synthesize Verified Neural Control Barrier Functions](https://mlsanity.com/paper/2503.17395/) (2025)
- [Safe Legged Locomotion using Collision Cone Control Barrier Functions (C3BFs)](https://mlsanity.com/paper/2309.01898/) (2023)
- [Converse Barrier Functions via Lyapunov Functions](https://mlsanity.com/paper/2007.11086/) (2020)
- [Multiple Control Barrier Functions: An Application to Reactive Obstacle Avoidance for a Multi-steering Tractor-trailer System](https://mlsanity.com/paper/2209.05156/) (2022)

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

- [Safe Reinforcement Learning with Receding-Horizon Safety Critic and Differentiable Action Shields](https://mlsanity.com/paper/2610.20255/) (2026)

## Abstract (arXiv)

As autonomous systems become increasingly prevalent in daily life, ensuring their safety is paramount. Control Barrier Functions (CBFs) have emerged as an effective tool for guaranteeing safety; however, manually designing them for specific applications remains a significant challenge. With the advent of deep learning techniques, recent research has explored synthesizing CBFs using neural networks-commonly referred to as neural CBFs. This paper introduces a novel class of neural CBFs that leverages a physics-inspired neural network framework by incorporating Zubov's Partial Differential Equation (PDE) within the context of safety. This approach provides a scalable methodology for synthesizing neural CBFs applicable to high-dimensional systems. Furthermore, by utilizing reciprocal CBFs instead of zeroing CBFs, the proposed framework allows for the specification of flexible, user-defined safe regions. To validate the effectiveness of the approach, we present case studies on three different systems: an inverted pendulum, autonomous ground navigation, and aerial navigation in obstacle-laden environments.