Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

HJRNO: Hamilton-Jacobi Reachability with Neural Operators

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A neural operator trained once can map an obstacle geometry directly to the safety region of an autonomous system, predicting unseen scenarios in milliseconds with relative L2 errors between 0.002 and 0.037.

desk verdict First neural-operator treatment of BRTs with genuinely fast inference, but the reduction of velocity and heading to constant hyperparameters means the reported errors may be for a surrogate 2D problem, not the true dynamics. read the letter →

arxiv 2504.19989 v2 pith:JMQFUXKJ submitted 2025-04-28 cs.RO

Yankai Li , Mo Chen This is my paper · ORCID
classification cs.RO
keywords Hamilton-JacobireachabilityneuraloperatorsFourierOperatorbackwardreachabletubesafetyanalysisautonomoussystemsvaluefunctiongeneralization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that the computationally expensive Hamilton-Jacobi-Isaacs (HJI) PDE solution behind backward reachable tubes (BRTs) can be replaced by a neural operator that maps the initial value function -- equivalently the obstacle geometry -- directly to the converged value function $V_\infty(x)$. Training once on randomly generated obstacle scenarios suffices to predict unseen scenarios with relative L2 errors between 0.002 and 0.037 and inference times near 0.001 to 0.005 seconds, orders of magnitude faster than traditional grid solvers. If true, this makes real-time safety analysis for autonomous systems practical: safety filters could be updated as the environment changes without re-solving the PDE. The main reduction treats non-spatial states such as velocity and heading as constant hyperparameters, which keeps the model two-dimensional.

What carries the argument

The central mechanism is the learned operator equation $s = \mathcal{M}_\theta(a)$, instantiated with two neural operator architectures: the Fourier Neural Operator, which performs global convolution in the spectral domain using the convolution theorem, and the Galerkin Transformer, which approximates the integral operator via self-attention. Both map the input function $a(x)=V(t=0,x,h)$ sampled on a uniform grid to the output $V_\infty(x,h)$ and are discretization-invariant, so the same model can be evaluated at new resolutions. The non-spatial state dimensions are folded into the input as constant functions $\tilde h(x)=h$, reducing the effective problem to two spatial coordinates and making the mapping tractable for FNO and TNO.

What would settle it

Take a Dubins car with a wide speed range and an obstacle whose clearance grows rapidly with speed (e.g., radius as an exponential of $v$, as in the velocity-dependent experiment), solve the full 4D HJI equation with a grid solver, and compare the predicted $V_\infty$ from the 2D-reduced HJRNO model to the full-state ground truth; if the relative L2 error is far above the reported 0.002-0.037 band, the central generalization claim fails for genuinely velocity-dependent dynamics.

Watch

Extended reading notes

Core claim

On its own terms, the discovery is that the operator $\mathcal{M}_\theta$ taking the initial value function $a(x)=V(t=0,x,h)$ to the converged value function $s(x)=V_\infty(x,h)$ is learnable by neural operators, specifically the Fourier Neural Operator and the Galerkin Transformer. With scalar system hyperparameters embedded as constant functions over the state domain, a single trained model generalizes across random obstacle shapes, multi-obstacle layouts, indoor environments, velocity-dependent obstacle sizes, and continuous control-limit variations. Across six experimental setups the relative L2 test error stays between 0.002 and 0.037, inference takes about 0.001 to 0.005 seconds, and the trained model also shows zero-shot super-resolution, producing accurate predictions at resolutions higher than trained. The paper positions this as the first application of neural operators to Hamilton-Jacobi reachability, eliminating the need to retrain the PDE solver for each new problem setting.

Load-bearing premise

The load-bearing premise is that the value function is effectively two-dimensional: velocity and heading are treated as constant hyperparameters rather than states, so systems where the value function varies strongly along those dimensions are not actually represented by the learned mapping.

Editorial extensions

If this is right

  • Safety filters for autonomous vehicles can be updated in real time as obstacles move or change shape, because inference is orders of magnitude faster than solving the HJI PDE.
  • A single trained model covers a family of problem settings -- obstacle geometries and system hyperparameters -- so no instance-specific retraining is needed.
  • Because neural operators are discretization-invariant, models trained at lower resolution can be deployed at higher resolution without retraining (zero-shot super-resolution).
  • The learned operator can serve as a fast surrogate inside safety-critical loops on onboard computers, with checkpoint sizes (3-38 MB) comparable to storing one solution instance of a 4D state.
  • Arbitrary and non-convex domains are within reach because neural operators extend to general geometries, not just uniform grids.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the mapping truly remains accurate on systems where velocity or heading materially influence the value function, the constant-hyperparameter reduction could be dropped and the same operator framework trained directly on higher-dimensional states; the paper reports degradation on full-state Air3D, so this is an open pressure point rather than a demonstrated claim.
  • The parametric-input trick suggests a natural extension: add time as an input dimension to learn finite-horizon reachable tubes $V(t,x)$ in one model, rather than only the converged $V_\infty$.
  • Because the training data come from a grid solver, HJRNO inherits any systematic bias of that solver; the reported errors are with respect to the same solver's solutions, so end-to-end safety guarantees would require validating against an independent solver or an exact solution.
  • A testable industrial extension: deploy HJRNO in a simulated warehouse or road scenario with dynamic obstacles and measure whether the safety-filter decisions differ from ground-truth BRT decisions in ways that matter for collision avoidance.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes HJRNO, a neural-operator approach for computing backward reachable tubes (BRTs) in Hamilton-Jacobi reachability analysis. Using Fourier Neural Operators (FNO) and Transformer-based Neural Operators (TNO), the authors train models to map an initial value function (equivalently, the obstacle geometry, optionally augmented by scalar parameters) to the infinite-horizon converged value function. The training data are generated offline by a standard HJI PDE solver using the hj_reachability library. The paper reports relative L2 test errors between 0.002 and 0.037 on several obstacle-shape scenarios, including Air3D collision avoidance, single and multiple obstacles, indoor environments, velocity-dependent obstacles, and parametric control limits, with inference times in the millisecond range. It also demonstrates zero-shot super-resolution, where models trained at one grid resolution generalize to a coarser or finer resolution without retraining.

Significance. If the claims hold, the operator-learning viewpoint is a natural and potentially impactful way to amortize HJR computations, because the input is a function (the initial value field) rather than a scalar parameter set. The use of held-out obstacle shapes guards against simple memorization, and the low reported errors on shape generalization, together with the speed advantage, would be useful for real-time robotics safety filtering. The zero-shot super-resolution comparison with CNNs is a positive contribution that concretely illustrates the discretization-invariance benefit of neural operators. However, the evidence for generalization across 'system dynamics' is currently much weaker than the evidence for shape generalization, because non-spatial state dimensions are removed from the problem in the experiments. The paper's central contribution is therefore best assessed as an operator approximation for two-dimensional value functions, with the claims about full-order system dynamics needing substantial additional support.

major comments (3)
  1. [Section 5, paragraph 2; Eq. (26); Section 2.1 (Dynamic Dubins car)] The paper's main claim of generalization across system dynamics rests on encoding state variables as constant hyperparameters. For the dynamic Dubins car (Eqs. 7a-7d), velocity v and heading θ are evolving states, not problem hyperparameters, and the value function of the full 4D system is not generally recoverable from 2D slices at fixed v and θ. The Velocity-Dependent experiment makes this concrete: because the obstacle radius is intentionally made a function of v, the converged value function V∞ varies with v by construction, so encoding v as a constant input function h cannot represent the full value function. As currently presented, the reported errors in Tables 1 and 2 appear to describe a two-dimensional surrogate problem rather than the true BRT of the stated dynamics. The authors should either provide full-order ground-truth comparisons for the velocity-dependent and parametric-input experiments, or explicitly restrict the claims of the paper to the reduced model.
  2. [Section 5.1 (Air3D) and the full-state Air3D paragraph] The only full-state result reported in the paper is Air3D, and it shows substantial degradation when the heading state is included (FNO test error 0.028 to 0.050; TNO test error 0.037 to 0.15). This is consistent with the concern that the low errors in Tables 1 and 2 are achieved on a reduced two-dimensional problem rather than the actual system. The degradation also indicates that the full-order problem is qualitatively harder, which further undermines the abstract's claim that the method 'generalizes effectively across varying system dynamics.' The authors should include full-order experiments in the main evaluation, or revise the abstract and introduction to describe the contribution as applying to value functions on a reduced state space.
  3. [Tables 1 and 2] No error bars or standard deviations are reported for the relative L2 errors, and no baselines are given against prior learning-based reachability methods such as DeepReach or parameter-conditioned HJR solvers. Since training is stochastic and the datasets are small (50-300 samples), a single run does not establish that the reported errors are robust. At minimum, the authors should report the mean and standard deviation over several training seeds, and compare against a standard supervised-learning baseline on the same input-output pairs, so that the claimed advantages of the neural-operator formulation can be assessed.
minor comments (5)
  1. [Section 5.2] The text says 'dynamics Dubins car'; this should read 'dynamic Dubins car' for consistency with the terminology introduced in Section 2.
  2. [Figures 8, 9, 11 and Section 5] The figure labels contain the typo 'Initual Value'; this should be 'Initial Value'.
  3. [Section 4.1] The example 'the maximum acceleration limit in the dynamic Dubins car' is presented as a hyperparameter, but the preceding discussion of reducing state variables to hyperparameters could be misread; please clarify that control-limit bounds are hyperparameters, while v and θ are not.
  4. [Tables 1 and 2] The 'Data Size' of 2.4 GB for a 100-sample, 50x50 two-dimensional dataset is inconsistent with the paper's own estimate that a full 50^4 array is about 25 MB; please clarify what is being stored.
  5. [Section 3.2.2, Eq. (21)] The attention formula mixes spatial and feature indices in a way that is hard to follow; a standard multi-head attention definition would be clearer for the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the learned operator is trained on external HJ solver labels with held-out test geometries; the state-dimension reduction is an approximation, not a fitted-input circularity.

full rationale

The paper's central derivation is supervised operator learning: HJRNO trains Mθ by minimizing Eq. (25) against labels V∞(i)(x) produced by the external dynamic-programming solver [21] (Section 4), and the test sets are held-out obstacle shapes and hyperparameter combinations (Section 5). The input a(x)=V(t=0,x) is the signed-distance initial condition, not a function of the target V∞; the output is the converged BRT value function, so the learned map is not the identity by construction. Self-citations ([2], [8], [9], [10], [15]) provide background on HJR and BRT usage and are not used to justify the operator-learning claim. The main caveat is in Section 5: the paper assumes V∞ varies only with the spatial coordinates (x1,x2) and encodes velocity and heading as constant hyperparameters via Eq. (26), which for the full-order dynamic Dubins car (Eq. 7) and the Velocity-Dependent experiment means the reported test errors may be for a 2D surrogate rather than the full 4D BRT. That is a modeling-validity limitation, not a circular reduction: no fitted parameter is renamed as a prediction, and no load-bearing conclusion is justified solely by a self-citation. The Air3D full-state comparison showing degradation when heading is included (FNO 0.028 to 0.050; TNO 0.037 to 0.15) further indicates an approximation gap rather than a tautology. Therefore the paper is self-contained against external benchmarks, and the circularity score is 0.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on numerical solver outputs and a strong dimension-reduction assumption; no new physical entities are introduced.

free parameters (3)
  • Resolution of value function grids = 50 points per axis
    All training and evaluation use a uniform 50x50 discretization; the paper does not study sensitivity to resolution, though it claims zero-shot super-resolution.
  • Infinite-horizon time horizon T = not stated
    The paper assumes convergence of V(t=-T,x) as T approaches infinity (Eq. 22) but never reports the finite T used by the numerical solver to produce V_inf training labels.
  • FNO/TNO architecture hyperparameters = not reported
    Modes, widths, depths, learning rate, and optimizer are not given, so the exact trained models are not reproducible from the text.
assumptions (4)
  • domain assumption For the analyzed problems, V(t,x) converges as the horizon grows: V_inf(x) := lim_{T -> infinity} V(t=-T,x) exists and is what the solver computes.
    Invoked in Eq. (22) before defining training labels; no convergence analysis or error bound versus finite T is provided.
  • ad hoc to paper The value function is approximately constant along non-spatial state dimensions such as heading and velocity, so those dimensions can be encoded as constant hyperparameters.
    Stated in Section 5, paragraph 2; this is the premise that reduces the full-order HJI problem to a 2D operator learning task.
  • domain assumption The hj_reachability solver produces accurate ground-truth viscosity solutions of the HJI PDE.
    The training labels are generated with the solver [21]; no verification or error analysis of the solver output is reported.
  • domain assumption Random obstacle generation via convex hull and cubic B-spline smoothing yields signed distance functions representative of real obstacles.
    Used for all training and test shape datasets; no evidence is given that these shapes cover realistic operating conditions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of HJRNO: Hamilton-Jacobi Reachability with Neural Operators." pith.science (2026). https://pith.science/paper/JMQFUXKJ

@misc{pith2026250419989,
  author       = {Pith},
  title        = {Pith review of: HJRNO: Hamilton-Jacobi Reachability with Neural Operators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JMQFUXKJ}},
  note         = {Machine review of arXiv:2504.19989}
}
read the original abstract

Ensuring the safety of autonomous systems under uncertainty is a critical challenge. Hamilton-Jacobi reachability (HJR) analysis is a widely used method for guaranteeing safety under worst-case disturbances. In this work, we propose HJRNO, a neural operator-based framework for solving backward reachable tubes (BRTs) efficiently and accurately. By leveraging neural operators, HJRNO learns a mapping between value functions, enabling fast inference with strong generalization across different obstacle shapes and system configurations. We demonstrate that HJRNO achieves low error on random obstacle scenarios and generalizes effectively across varying system dynamics. These results suggest that HJRNO offers a promising foundation model approach for scalable, real-time safety analysis in autonomous systems.

Figures

Figures reproduced from arXiv: 2504.19989 by the authors.

Figure 1
Figure 1. Random obstacle shapes 6 Discussion While we presented results on a uniform grid, the method naturally extends to arbitrary geometries [17]. This means HJRNO can be directly applied to environments with non-square or even non-convex domains—for example, an autonomous agent operating within a warehouse with an irregular floor plan. One limitation is the treatment of hyperparameters. When introducing addi￾tional hyper… view at source ↗
Figure 2
Figure 2. Single Obstacle References [1] Kamyar Azizzadenesheli, Nikola Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi, and Anima Anandkumar. Neural operators for accelerating scientific simulations and design. Nature Reviews Physics, 6(5):320–328, 2024. [2] Somil Bansal, Mo Chen, Sylvia Herbert, and Claire J Tomlin. Hamilton￾jacobi reachability: A brief overview and recent advances. In 2017 IEEE 56th Annual Confer… view at source ↗
Figure 3
Figure 3. Sampling and testing strategy across varying system hyperparameters [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: FNO predictions along the diagonal of the hyperparameter space [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: Two Obstacles 17 [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Velocity-Dependent 18 [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]
Figure 8
Figure 8. Figure 8: Air3D 19 [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: Zero-shot super-resolution: Unlike conventional neural networks such [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: Indoor Environment 21 [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]
Figure 11
Figure 11. Figure 11: Velocity-Dependent 22 [PITH_FULL_IMAGE:figures/full_fig_p022_11.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Towards General Language-Conditioned Latent Safety Filters

    cs.RO 2026-07 conditional novelty 6.0 of 10

    A single Hamilton-Jacobi safety filter conditioned on language constraints reduces violations in simulated pick-and-place, wiping, and stacking, with partial transfer to unseen constraint instances.

Reference graph

Works this paper leans on

24 extracted references · 16 canonical work pages · cited by 1 Pith paper

  1. [1]

    Neural operators for accelerating scientific simulations and design

    Kamyar Azizzadenesheli, Nikola Kovachki, Zongyi Li, Miguel Liu-Schiaffini, Jean Kossaifi, and Anima Anandkumar. Neural operators for accelerating scientific simulations and design. Nature Reviews Physics , 6(5):320–328, 2024

    work page 2024

  2. [2]

    Hamilton- jacobi reachability: A brief overview and recent advances

    Somil Bansal, Mo Chen, Sylvia Herbert, and Claire J Tomlin. Hamilton- jacobi reachability: A brief overview and recent advances. In 2017 IEEE 56th Annual Conference on Decision and Control (CDC) , pages 2242–2253. IEEE, 2017

    work page 2017

  3. [3]

    Deepreach: A deep learning approach to high-dimensional reachability

    Somil Bansal and Claire J Tomlin. Deepreach: A deep learning approach to high-dimensional reachability. In 2021 IEEE International Conference on Robotics and Automation (ICRA) , pages 1817–1824. IEEE, 2021

    work page 2021

  4. [4]

    Parameter- conditioned reachable sets for updating safety assurances online

    Javier Borquez, Kensuke Nakamura, and Somil Bansal. Parameter- conditioned reachable sets for updating safety assurances online. In 2023 IEEE International Conference on Robotics and Automation (ICRA) , pages 10553–10559. IEEE, 2023

    work page 2023

  5. [5]

    Dualguard mppi: Safe and performant optimal control by combining sampling-based mpc and hamilton-jacobi reachability

    Javier Borquez, Luke Raus, Yusuf Umut Ciftci, and Somil Bansal. Dualguard mppi: Safe and performant optimal control by combining sampling-based mpc and hamilton-jacobi reachability. arXiv preprint arXiv:2502.01924, 2025

    arXiv 2025

  6. [6]

    The Fourier Transform and Its Applications

    Ronald Bracewell. The Fourier Transform and Its Applications . McGraw- Hill, 3rd edition, 1999. 13 Figure 3: Sampling and testing strategy across varying system hyperparameters

    work page 1999

  7. [7]

    Choose a transformer: Fourier or galerkin

    Shuhao Cao. Choose a transformer: Fourier or galerkin. Advances in neural information processing systems , 34:24924–24940, 2021

    2021

  8. [8]

    Exact and efficient hamilton-jacobi guaranteed safety analysis via system decomposition

    Mo Chen, Sylvia Herbert, and Claire J Tomlin. Exact and efficient hamilton-jacobi guaranteed safety analysis via system decomposition. In 2017 IEEE International Conference on Robotics and Automation (ICRA) , pages 87–92. IEEE, 2017

    work page 2017

Show all 24 references
  1. [9]

    Decomposition of reachable sets and tubes for a class of nonlinear systems

    Mo Chen, Sylvia L Herbert, Mahesh S Vashishtha, Somil Bansal, and Claire J Tomlin. Decomposition of reachable sets and tubes for a class of nonlinear systems. IEEE Transactions on Automatic Control , 63(11):3675– 3688, 2018

    2018

  2. [10]

    Hamilton–jacobi reachability: Some recent theoretical advances and applications in unmanned airspace management

    Mo Chen and Claire J Tomlin. Hamilton–jacobi reachability: Some recent theoretical advances and applications in unmanned airspace management. Annual Review of Control, Robotics, and Autonomous Systems , 1(1):333– 358, 2018

    2018

  3. [11]

    Reference neural op- erators: learning the smooth dependence of solutions of pdes on geometric deformations

    Ze Cheng, Zhongkai Hao, Xiaoqiang Wang, Jianing Huang, Youjia Wu, Xudan Liu, Yiru Zhao, Songming Liu, and Hang Su. Reference neural op- erators: learning the smooth dependence of solutions of pdes on geometric deformations. arXiv preprint arXiv:2405.17509 , 2024

    2024 arXiv

  4. [12]

    Some properties of viscosity solutions of hamilton-jacobi equations

    Michael G Crandall, Lawrence C Evans, and P-L Lions. Some properties of viscosity solutions of hamilton-jacobi equations. Transactions of the American Mathematical Society , 282(2):487–502, 1984. 14 x y Union Ground Truth Obstacles FNO TNO Figure 4

    1984

  5. [13]

    Viscosity solutions of hamilton- jacobi equations

    Michael G Crandall and Pierre-Louis Lions. Viscosity solutions of hamilton- jacobi equations. Transactions of the American mathematical society , 277(1):1–42, 1983

    1983

  6. [14]

    Gnot: A general neural operator transformer for operator learning

    Zhongkai Hao, Zhengyi Wang, Hang Su, Chengyang Ying, Yinpeng Dong, Songming Liu, Ze Cheng, Jian Song, and Jun Zhu. Gnot: A general neural operator transformer for operator learning. In International Conference on Machine Learning, pages 12556–12569. PMLR, 2023

    2023

  7. [15]

    Fastrack: A modular framework for fast and guaranteed safe motion planning

    Sylvia L Herbert, Mo Chen, SooJean Han, Somil Bansal, Jaime F Fisac, and Claire J Tomlin. Fastrack: A modular framework for fast and guaranteed safe motion planning. In 2017 IEEE 56th Annual Conference on Decision and Control (CDC) , pages 1517–1522. IEEE, 2017

    2017

  8. [16]

    Neu- ral operator: Learning maps between function spaces with applications to pdes

    Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Neu- ral operator: Learning maps between function spaces with applications to pdes. Journal of Machine Learning Research , 24(89):1–97, 2023

    2023

  9. [17]

    Fourier neural operator with learned deformations for pdes on general ge- ometries

    Zongyi Li, Daniel Zhengyu Huang, Burigede Liu, and Anima Anandkumar. Fourier neural operator with learned deformations for pdes on general ge- ometries. Journal of Machine Learning Research , 24(388):1–26, 2023

    2023

  10. [18]

    Fourier neural operator for parametric partial differential equations

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:2010.08895, 2020. 15 Ground T ruth Prediction Figure 5: FNO ...

    2010 arXiv

  11. [19]

    Neu- ral operator: Graph kernel network for partial differential equations

    Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Neu- ral operator: Graph kernel network for partial differential equations. arXiv preprint arXiv:2003.03485, 2020

    2003 arXiv

  12. [20]

    Deeponet: Learn- ing nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

    Lu Lu, Pengzhan Jin, and George Em Karniadakis. Deeponet: Learn- ing nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. arXiv preprint arXiv:1910.03193, 2019

    1910 arXiv

  13. [21]

    hj reachability: Hamilton-jacobi reachability analysis in jax

    Edward Schmerling. hj reachability: Hamilton-jacobi reachability analysis in jax. https://github.com/StanfordASL/hj_reachability

  14. [22]

    Guaranteeing constraints of disturbed nonlinear systems using set-based optimal control in generator space

    Bastian Sch¨ urmann and Matthias Althoff. Guaranteeing constraints of disturbed nonlinear systems using set-based optimal control in generator space. IF AC-PapersOnLine, 50(1):11515–11522, 2017

    2017

  15. [23]

    Exact imposition of safety boundary conditions in neural reachable tubes

    Aditya Singh, Zeyuan Feng, and Somil Bansal. Exact imposition of safety boundary conditions in neural reachable tubes. arXiv preprint arXiv:2404.00814, 2024

    2024 arXiv

  16. [24]

    A physics-informed machine learning framework for safe and optimal control of autonomous systems

    Manan Tayal, Aditya Singh, Shishir Kolathaya, and Somil Bansal. A physics-informed machine learning framework for safe and optimal control of autonomous systems. arXiv preprint arXiv:2502.11057 , 2025. 16 3 2 1 0 1 2 3 3 2 1 0 1 2 3 Signed Distance Field 0.5 0.0 0.5 1.0 1.5 2....

    2025 arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.