mlsanityData to 14 Oct 2026

DeepReach: A Deep Learning Approach to High-Dimensional Reachability

arXiv 2011.02082 ↗First posted 4 Nov 2020cs.RO cs.AI cs.LGcited by 91

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Abstract (arXiv)

Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical control systems. Its advantages include compatibility with general nonlinear system dynamics, formal treatment of bounded disturbances, and the ability to deal with state and input constraints. However, it involves solving a PDE, whose computational and memory complexity scales exponentially with respect to the number of state variables, limiting its direct use to small-scale systems. We propose DeepReach, a method that leverages new developments in sinusoidal networks to develop a neural PDE solver for high-dimensional reachability problems. The computational requirements of DeepReach do not scale directly with the state dimension, but rather with the complexity of the underlying reachable tube. DeepReach achieves comparable results to the state-of-the-art reachability methods, does not require any explicit supervision for the PDE solution, can easily handle external disturbances, adversarial inputs, and system constraints, and also provides a safety controller for the system. We demonstrate DeepReach on a 9D multi-vehicle collision problem, and a 10D narrow passage problem, motivated by autonomous driving applications.

Key facts. Cited by 91 papers in the map (data through 14 Oct 2026). First posted on arXiv 4 Nov 2020.

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Citing papers per year: 2021: 5; 2022: 10; 2023: 9; 2024: 20; 2025: 26; 2026: 21.

91 papers.

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  1. 2023The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systemscited by 88
  2. 2024Agile But Safe: Learning Collision-Free High-Speed Legged Locomotioncited by 73
  3. 2022Reachability Constrained Reinforcement Learningcited by 59
  4. 2021Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learningcited by 49
  5. 2025Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysiscited by 45
  6. 2023Iterative Reachability Estimation for Safe Reinforcement Learningcited by 37
  7. 2025Uncertainty-aware Latent Safety Filters for Avoiding Out-of-Distribution Failurescited by 33
  8. 2022ISAACS: Iterative Soft Adversarial Actor-Critic for Safetycited by 28
  9. 2021Fast PDE-constrained optimization via self-supervised operator learningcited by 25
  10. 2023Verification of Neural Reachable Tubes via Scenario Optimization and Conformal Predictioncited by 23
  11. 2024Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imaginationcited by 16
  12. 2021Neural Network Verification in Controlcited by 14
38 more
  1. 2024SAFE-GIL: SAFEty Guided Imitation Learning for Robotic Systemscited by 14
  2. 2023Tensor-Compressed Back-Propagation-Free Training for (Physics-Informed) Neural Networkscited by 12
  3. 2024Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanescited by 12
  4. 2025A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systemscited by 12
  5. 2021Learning Density Distribution of Reachable States for Autonomous Systemscited by 11
  6. 2022Generating Formal Safety Assurances for High-Dimensional Reachabilitycited by 11
  7. 2023Deception Game: Closing the Safety-Learning Loop in Interactive Robot Autonomycited by 10
  8. 2025Preemptive Detection and Steering of LLM Misalignment via Latent Reachabilitycited by 10
  9. 2022SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problemscited by 9
  10. 2024One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environmentscited by 9
  11. 2025How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraintscited by 9
  12. 2024Neural Network Approaches for Parameterized Optimal Controlcited by 8
  13. 2022TT-PINN: A Tensor-Compressed Neural PDE Solver for Edge Computingcited by 7
  14. 2024Human-AI Safety: A Descendant of Generative AI and Control Systems Safetycited by 7
  15. 2024MAGICS: Adversarial RL with Minimax Actors Guided by Implicit Critic Stackelberg for Convergent Neural Synthesis of Robot Safetycited by 7
  16. 2025AnySafe: Adapting Latent Safety Filters at Runtime via Safety Constraint Parameterization in the Latent Spacecited by 7
  17. 2026Safe Large-Scale Robust Nonlinear MPC in Milliseconds via Reachability-Constrained System Level Synthesis on the GPUcited by 7
  18. 2022Infinite-Horizon Reach-Avoid Zero-Sum Games via Deep Reinforcement Learningcited by 6
  19. 2025Goal Reaching with Eikonal-Constrained Hierarchical Quasimetric Reinforcement Learningcited by 6
  20. 2021Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEscited by 5
  21. 2022Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Modelscited by 5
  22. 2022Approximating Discontinuous Nash Equilibrial Values of Two-Player General-Sum Differential Gamescited by 5
  23. 2022Discovering Closed-Loop Failures of Vision-Based Controllers via Reachability Analysiscited by 5
  24. 2023Bridging Dimensions: Confident Reachability for High-Dimensional Controllerscited by 5
  25. 2023Detecting and Mitigating System-Level Anomalies of Vision-Based Controllerscited by 4
  26. 2023Real-Time FJ/MAC PDE Solvers via Tensorized, Back-Propagation-Free Optical PINN Trainingcited by 4
  27. 2024Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuationcited by 4
  28. 2025Statistically Assuring Safety of Control Systems using Ensembles of Safety Filters and Conformal Predictioncited by 4
  29. 2023Value Approximation for Two-Player General-Sum Differential Games with State Constraintscited by 3
  30. 2024Pontryagin Neural Operator for Solving Parametric General-Sum Differential Gamescited by 3
  31. 2024Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environmentscited by 3
  32. 2025Ultra Memory-Efficient On-FPGA Training of Transformers via Tensor-Compressed Optimizationcited by 3
  33. 2025Your Learned Constraint is Secretly a Backward Reachable Tubecited by 3
  34. 2025Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functionscited by 3
  35. 2025Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environmentscited by 3
  36. 2025Provably Optimal Reinforcement Learning under Safety Filteringcited by 3
  37. 2025Back to Base: Towards Hands-Off Learning via Safe Resets with Reach-Avoid Safety Filterscited by 2
  38. 2025Scalable Back-Propagation-Free Training of Optical Physics-Informed Neural Networkscited by 2

50 most cited of 91 All 91 (JSON)