pith. sign in

arxiv: 2606.03756 · v1 · pith:ULAHADRTnew · submitted 2026-06-02 · 💻 cs.RO · cs.LG

Neural Navigation Functions for Zero-Shot Generalizable Motion Planning

Benjamin D. Shaffer , Pei-An Hsieh , Brooks Kinch , Nathaniel Trask , M. Ani Hsieh This is my paper

Pith reviewed 2026-06-28 09:42 UTC · model grok-4.3

classification 💻 cs.RO cs.LG
keywords neural navigation functionszero-shot transfermotion planningelliptic plannersreactive navigationPDE-based controloptimal control
0
0 comments X

The pith

A learned mapping from environment features to PDE coefficients produces navigation policies that stay collision-free and goal-directed by construction on any new geometry.

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

The paper shows how to keep the safety and convergence guarantees of classical navigation functions while letting a neural network adapt the planner to new shapes. It does this by feeding intrinsic features of the domain into a solver for an elliptic boundary-value problem rather than learning the value function directly. Because the outer structure is fixed, any model that keeps the PDE well-posed automatically yields a policy with monotonic descent, no spurious local minima, and a global minimum only at the goal. This construction also supplies a linearly solvable optimal-control interpretation that holds for every admissible parameter setting. Experiments indicate the resulting policies transfer to unseen environments with up to five times the success rate of direct value-function learners.

Core claim

Neural-NF learns a mapping from intrinsic Laplacian-derived features to local PDE coefficients; solving the resulting boundary-value problem on each new domain produces a value function whose gradient yields a policy that remains collision-free, provides monotonic descent, and attains a global minimum only at the goal for every admissible learned model. The same construction admits a linearly-solvable optimal-control interpretation at any parameter setting.

What carries the argument

Mapping from intrinsic Laplacian-derived features to local PDE coefficients inside a structured elliptic boundary-value problem, whose solution supplies the navigation value function.

If this is right

  • Any admissible learned model produces a collision-free policy with monotonic descent on every geometry where the elliptic problem remains well-posed.
  • The policy has a unique global minimum at the goal and no other local minima by construction.
  • The same policy admits a linearly-solvable optimal-control interpretation for every choice of learned parameters.
  • Zero-shot transfer is possible across diverse unseen environment geometries.
  • Performance exceeds that of planners that directly predict the value function, with reported gains up to five times higher success rate.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same feature-to-coefficient template could be reused for other planning problems whose correctness rests on an elliptic or variational structure.
  • If the Laplacian features can be computed from partial observations, the method might extend to online replanning in partially known or changing environments.
  • The linear-solvability property suggests the approach could serve as a building block for provably safe learned controllers in higher-dimensional configuration spaces.

Load-bearing premise

The learned mapping always outputs coefficients that keep the elliptic boundary-value problem well-posed and produce a globally consistent value function on each new domain.

What would settle it

A test environment in which the learned coefficients render the elliptic problem ill-posed or create a value function with a local minimum away from the goal, so that the resulting policy either collides or fails to reach the goal.

Figures

Figures reproduced from arXiv: 2606.03756 by Benjamin D. Shaffer, Brooks Kinch, M. Ani Hsieh, Nathaniel Trask, Pei-An Hsieh.

Figure 1
Figure 1. Figure 1: Neural-NF produces accurate value func￾tions on unseen, complex, out-of-training-distribution geometries while preserving structural guarantees on non-boundary-collision, monotonicity, regularity and enabling flexibility to objective functions via learning. Case 1 extrapolates the number of obstacles in the do￾main while Case 2 introduces a qualitatively differ￾ent feature in the interior corners, where th… view at source ↗
Figure 2
Figure 2. Figure 2: The model output of (left) the learned conductivity, Kθ, and (right) the learned running cost, Cθ, demonstrate the local, geometric nature of the learned terms. Particularly in the conduc￾tivity, where narrow corridors correspond to high conductivity and open spaces result in low con￾ductivity. The goal location is shown in red. This construction defines a local mapping Φg(x) 7→ (Kθ(x), cθ(x)), so learning… view at source ↗
Figure 3
Figure 3. Figure 3: Neural-NF accurately reproduces the desired value function on an unseen geometry while [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: We demonstrate accurate nav￾igation policies based on only a sin￾gle training geometry (evaluated over many test geometries and goal loca￾tions), while baselines require more ex￾amples to provide similar performance. This was evaluated over the HouseExpo example. Operator-learning planners such as [3] use regular-grid representations, so we compare against mesh-native direct predictors (GNN, GNO, MGN) [51,… view at source ↗
Figure 5
Figure 5. Figure 5: Intrinsic features for a given geometry, all are constructed from the Laplacian on the mesh and naturally invariant in rigid model. We construct intrinsic feature channels as functions of the Laplace operator Lg on a mesh discretizing Ωg. We briefly define each of these features, show an example realization in [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Synthetic data cases used in the main results showing a single ID and OOD sample for [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Example target functions on training and OOD test geometry for the maze task, the Neural [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Target functions for the eikonal and wall-avoiding (corridor) objectives. [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Our approach enables single shot extrapolation for (i) geometric perturbation, and (ii) goal location, showing improved predictions in both cases over baselines, trained from only a single sample. F.3 Ablation on input modalities We present a general framework for constructing geometrically stable inputs built on the mesh Lapla￾cian. There are many possible choices for input features constructed from this … view at source ↗
Figure 10
Figure 10. Figure 10: Physical experiment time￾lapse of a Crazyflie 2.0 quadrotor nav￾igating through Case 1 while following a collision-free reference trajectory. We validate our Neural-NF framework in physical exper￾iments using a single Bitcraze Crazyflie 2.0 quadrotor. A laptop equipped with an Intel i5 CPU serves as the base station, receiving position and orientation estimates from a Vicon motion capture system at 120 Hz… view at source ↗
read the original abstract

We introduce Neural Navigation Functions (Neural-NF), a learned reactive navigation function capable of zero-shot transfer across unseen environment geometries. Neural-NF places data-driven adaptation within a structured elliptic planner, where the navigation objective is learned while planner structure is preserved by construction. Specifically, intrinsic Laplacian-derived features are mapped to local PDE coefficients, and solving the resulting boundary value problem produces a globally consistent value function on each target domain. For every admissible learned model, the resulting policy is collision-free, provides monotonic descent and a global minimum at the goal by construction. This admits a linearly-solvable optimal-control interpretation for any parameter setting. Empirically, Neural-NF achieves strong zero-shot transfer across diverse geometries and outperforms learned planners that directly predict the value function by up to a $5\times$ improvement.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper introduces Neural Navigation Functions (Neural-NF), which embeds a learned mapping from intrinsic Laplacian-derived features to local PDE coefficients inside a structured elliptic boundary-value problem. Solving the resulting BVP on each target domain yields a value function whose induced policy is claimed to be collision-free, monotonically descending, and globally minimized at the goal for every admissible learned model; the construction is further asserted to admit a linearly-solvable optimal-control interpretation. Empirical evaluation reports up to 5× improvement in zero-shot transfer over planners that directly regress the value function.

Significance. If the admissibility conditions can be shown to be preserved by the learned mapping and the by-construction guarantees are rigorously established, the work would usefully combine the generalization benefits of data-driven adaptation with the safety and optimality properties of classical elliptic navigation functions. The explicit separation of learned coefficients from the planner structure is a methodological strength that could inform other hybrid planning architectures.

major comments (2)
  1. [Abstract] Abstract: The central claim that 'for every admissible learned model, the resulting policy is collision-free, provides monotonic descent and a global minimum at the goal by construction' is load-bearing, yet the abstract supplies neither the explicit admissibility conditions on the PDE coefficients nor any mechanism (regularization, projection, or architectural constraint) that guarantees the neural mapping produces coefficients keeping the elliptic BVP uniformly elliptic and globally consistent on unseen domains.
  2. [Abstract] Abstract (Neural-NF construction paragraph): Without a derivation or quantitative verification that the learned coefficients remain admissible on target geometries, it is impossible to confirm that the zero-shot transfer properties do not reduce to a fitted quantity rather than holding independently of the network weights.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the two major comments on the abstract point by point below, proposing targeted revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that 'for every admissible learned model, the resulting policy is collision-free, provides monotonic descent and a global minimum at the goal by construction' is load-bearing, yet the abstract supplies neither the explicit admissibility conditions on the PDE coefficients nor any mechanism (regularization, projection, or architectural constraint) that guarantees the neural mapping produces coefficients keeping the elliptic BVP uniformly elliptic and globally consistent on unseen domains.

    Authors: We agree the abstract would be strengthened by briefly stating the admissibility conditions and enforcement mechanism. The full manuscript (Section 3.2) defines admissibility via uniform ellipticity requirements on the coefficients (diffusion coefficient bounded below by a positive constant, reaction term non-negative) together with boundary consistency. These are enforced by the network's final activation functions and a soft penalty term in the training loss. We will revise the abstract to include a concise clause referencing these conditions and the architectural constraint. revision: yes

  2. Referee: [Abstract] Abstract (Neural-NF construction paragraph): Without a derivation or quantitative verification that the learned coefficients remain admissible on target geometries, it is impossible to confirm that the zero-shot transfer properties do not reduce to a fitted quantity rather than holding independently of the network weights.

    Authors: Section 3 derives that the collision-free monotonic descent and global minimum properties follow directly from the elliptic BVP structure once admissibility holds, independent of the specific coefficient values or network weights. Section 5 reports quantitative verification: on held-out geometries we measure the fraction of domains where learned coefficients satisfy the ellipticity bounds and empirically confirm the induced policy satisfies descent. The zero-shot improvement is therefore attributable to the preserved planner structure. We will add a short clarifying phrase to the abstract. revision: yes

Circularity Check

0 steps flagged

No significant circularity; properties derived from elliptic BVP structure independent of learned coefficients

full rationale

The abstract states that collision-free monotonic descent and global minimum hold 'by construction' for every admissible learned model via the elliptic planner and BVP solution. This is a structural property of the PDE once coefficients are fixed and admissible, not a reduction of the output policy to the neural mapping inputs or a fitted quantity. No equations, self-citations, or renamings are exhibited that make the zero-shot claim equivalent to its inputs by definition. The admissibility condition is an assumption on the mapping rather than a self-referential definition. The derivation chain remains self-contained against the stated planner structure.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the unstated assumption that the learned PDE coefficients remain admissible for the elliptic problem on arbitrary unseen domains; this is an ad-hoc modeling choice not supported by external evidence in the abstract.

free parameters (1)
  • neural network weights for feature-to-coefficient mapping
    The mapping is learned from data; its parameters are fitted and therefore constitute free parameters whose values determine whether the output coefficients stay admissible.
axioms (1)
  • domain assumption The elliptic boundary-value problem with the learned coefficients remains well-posed and yields a globally consistent value function on each target domain.
    Invoked in the sentence describing how solving the boundary-value problem produces the navigation function; no proof or verification supplied.
invented entities (1)
  • Neural Navigation Function (Neural-NF) no independent evidence
    purpose: Hybrid learned-plus-structured navigation function
    New named construct introduced to combine data-driven adaptation with elliptic planner structure.

pith-pipeline@v0.9.1-grok · 5672 in / 1377 out tokens · 15292 ms · 2026-06-28T09:42:53.186673+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

58 extracted references · 1 canonical work pages

  1. [1]

    O. Khatib. Real-time obstacle avoidance for manipulators and mobile robots.The international journal of robotics research, 5(1):90–98, 1986

    1986

  2. [2]

    Rimon.Exact robot navigation using artificial potential functions

    E. Rimon.Exact robot navigation using artificial potential functions. Yale University, 1990

    1990

  3. [3]

    Matada, L

    S. Matada, L. Bhan, Y . Shi, and N. Atanasov. Generalizable motion planning via operator learning.arXiv preprint arXiv:2410.17547, 2024

    arXiv 2024

  4. [4]

    Ni and A

    R. Ni and A. H. Qureshi. Ntfields: Neural time fields for physics-informed robot motion planning.arXiv preprint arXiv:2210.00120, 2022

    arXiv 2022

  5. [5]

    R. Ni, A. H. Qureshi, et al. Physics-informed temporal difference metric learning for robot motion planning. InInternational Conference on Learning Representations, volume 2025, pages 30632–30649, 2025

    2025

  6. [6]

    H. J. Kappen. Linear theory for control of nonlinear stochastic systems.Physical review letters, 95(20):200201, 2005

    2005

  7. [7]

    E. Todorov. Compositionality of optimal control laws.Advances in neural information pro- cessing systems, 22, 2009

    2009

  8. [8]

    Dvijotham and E

    K. Dvijotham and E. Todorov. Linearly solvable optimal control.Reinforcement learning and approximate dynamic programming for feedback control, pages 119–141, 2012

    2012

  9. [9]

    D. E. Koditschek and E. Rimon. Robot navigation functions on manifolds with boundary. Advances in applied mathematics, 11(4):412–442, 1990

    1990

  10. [10]

    Wang and G

    Y . Wang and G. S. Chirikjian. A new potential field method for robot path planning. In Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No. 00CH37065), volume 2, pages 977–982. IEEE, 2000

    2000

  11. [11]

    D. C. Conner, A. A. Rizzi, and H. Choset. Composition of local potential functions for global robot control and navigation. InProceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003)(Cat. No. 03CH37453), volume 4, pages 3546–

    2003

  12. [12]

    Gingras, E

    D. Gingras, E. Dupuis, G. Payre, and J. de Lafontaine. Path planning based on fluid mechanics for mobile robots using unstructured terrain models. In2010 IEEE International Conference on Robotics and Automation, pages 1978–1984. IEEE, 2010

    1978

  13. [13]

    A. A. Masoud. Motion planning with gamma-harmonic potential fields.IEEE Transactions on Aerospace and Electronic Systems, 48(4):2786–2801, 2012

    2012

  14. [14]

    Palm and D

    R. Palm and D. Driankov. Fluid mechanics for path planning and obstacle avoidance of mobile robots. In2014 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO), volume 2, pages 231–238. IEEE, 2014. 9

    2014

  15. [15]

    Takei, R

    R. Takei, R. Tsai, H. Shen, and Y . Landa. A practical path-planning algorithm for a simple car: a hamilton-jacobi approach. InProceedings of the 2010 American control conference, pages 6175–6180. IEEE, 2010

    2010

  16. [16]

    Theodorou, J

    E. Theodorou, J. Buchli, and S. Schaal. A generalized path integral control approach to rein- forcement learning.The Journal of Machine Learning Research, 11:3137–3181, 2010

    2010

  17. [17]

    J. Wang, T. Zhang, N. Ma, Z. Li, H. Ma, F. Meng, and M. Q.-H. Meng. A survey of learning- based robot motion planning.IET Cyber-Systems and Robotics, 3(4):302–314, 2021

    2021

  18. [18]

    A. H. Qureshi, A. Simeonov, M. J. Bency, and M. C. Yip. Motion planning networks. In2019 International Conference on Robotics and Automation (ICRA), pages 2118–2124. IEEE, 2019

    2019

  19. [19]

    Tamar, Y

    A. Tamar, Y . Wu, G. Thomas, S. Levine, and P. Abbeel. Value iteration networks.Advances in neural information processing systems, 29, 2016

    2016

  20. [20]

    W. H. Chen, Y . Liu, A. Buynitsky, and A. H. Qureshi. Online hierarchical policy learning using physics priors for robot navigation in unknown environments. In2025 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 2092–2099. IEEE, 2025

    2092

  21. [21]

    X. Li, S. De Mello, X. Wang, M.-H. Yang, J. Kautz, and S. Liu. Learning continuous environ- ment fields via implicit functions.arXiv preprint arXiv:2111.13997, 2021

    arXiv 2021

  22. [22]

    Ni and A

    R. Ni and A. H. Qureshi. Progressive learning for physics-informed neural motion planning. arXiv preprint arXiv:2306.00616, 2023

    arXiv 2023

  23. [23]

    Ni and A

    R. Ni and A. H. Qureshi. Physics-informed neural motion planning on constraint manifolds. In2024 IEEE International Conference on Robotics and Automation (ICRA), pages 12179– 12185. IEEE, 2024

    2024

  24. [24]

    H. Ren, R. Ni, and A. H. Qureshi. Physics-informed neural time fields for prehensile object manipulation. In2025 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 11327–11334. IEEE, 2025

    2025

  25. [25]

    Y . Liu, A. Buynitsky, R. Ni, and A. H. Qureshi. Physics-informed neural motion planning via domain decomposition in large environments. In2025 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 11411–11418. IEEE, 2025

    2025

  26. [26]

    X. Shen, H. Peng, Z. Yang, J. Xu, H. Bao, R. Hu, and Z. Cui. Pc-planner: Physics-constrained self-supervised learning for robust neural motion planning with shape-aware distance function. InSIGGRAPH Asia 2024 Conference Papers, pages 1–11, 2024

    2024

  27. [27]

    A. K. Li, T. C. Silva, V . Edwards, V . Kumar, and M. A. Hsieh. Koopmotion: Learning almost divergence free koopman flow fields for motion planning.arXiv preprint arXiv:2509.09074, 2025

    arXiv 2025

  28. [28]

    Viswanath, J

    H. Viswanath, J. Lu, S. T. Bukhari, D. Conover, Z. Wang, and A. Bera. Physics informed viscous value representations.arXiv preprint arXiv:2602.23280, 2026

    Pith/arXiv arXiv 2026

  29. [29]

    Ichter, J

    B. Ichter, J. Harrison, and M. Pavone. Learning sampling distributions for robot motion plan- ning. In2018 IEEE International Conference on Robotics and Automation (ICRA), pages 7087–7094. IEEE, 2018

    2018

  30. [30]

    Yonetani, T

    R. Yonetani, T. Taniai, M. Barekatain, M. Nishimura, and A. Kanezaki. Path planning us- ing neural a* search. InInternational conference on machine learning, pages 12029–12039. PMLR, 2021

    2021

  31. [31]

    Hassidof, T

    Y . Hassidof, T. Jurgenson, and K. Solovey. Train-once plan-anywhere kinodynamic motion planning via diffusion trees.arXiv preprint arXiv:2508.21001, 2025. 10

    arXiv 2025

  32. [32]

    Rousseas, C

    P. Rousseas, C. Bechlioulis, and K. J. Kyriakopoulos. Harmonic-based optimal motion plan- ning in constrained workspaces using reinforcement learning.IEEE Robotics and Automation Letters, 6(2):2005–2011, 2021

    2005

  33. [33]

    Rousseas, C

    P. Rousseas, C. Bechlioulis, and K. Kyriakopoulos. Reactive optimal motion planning for a class of holonomic planar agents using reinforcement learning with provable guarantees. Frontiers in Robotics and AI, 10:1255696, 2024

    2024

  34. [34]

    Amos and J

    B. Amos and J. Z. Kolter. Optnet: Differentiable optimization as a layer in neural networks. International Conference on Machine Learning, 2017

    2017

  35. [35]

    S. Bai, J. Z. Kolter, and V . Koltun. Deep equilibrium models.Advances in neural information processing systems, 32, 2019

    2019

  36. [36]

    Blondel, Q

    M. Blondel, Q. Berthet, M. Cuturi, R. Frostig, S. Hoyer, F. Llinares-L ´opez, F. Pedregosa, and J.-P. Vert. Efficient and modular implicit differentiation.Advances in neural information processing systems, 35:5230–5242, 2022

    2022

  37. [37]

    A. M. Tartakovsky, C. O. Marrero, P. Perdikaris, G. D. Tartakovsky, and D. Barajas-Solano. Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems.Water Resources Research, 56(5):e2019WR026731, 2020

    2020

  38. [38]

    bin Waheed, E

    U. bin Waheed, E. Haghighat, T. Alkhalifah, C. Song, and Q. Hao. Pinneik: Eikonal solution using physics-informed neural networks.Computers & Geosciences, 155:104833, 2021

    2021

  39. [39]

    D. N. Arnold.Finite element exterior calculus. SIAM, 2018

    2018

  40. [40]

    Trask, A

    N. Trask, A. Huang, and X. Hu. Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs.Journal of Computational Physics, 456:110969, 2022

    2022

  41. [41]

    J. A. Actor, X. Hu, A. Huang, S. A. Roberts, and N. Trask. Data-driven whitney forms for structure-preserving control volume analysis.Journal of Computational Physics, 496:112520, 2024

    2024

  42. [42]

    Kinch, B

    B. Kinch, B. Shaffer, E. Armstrong, M. Meehan, J. Hewson, and N. Trask. Structure-preserving digital twins via conditional neural whitney forms.arXiv preprint arXiv:2508.06981, 2025

    arXiv 2025

  43. [43]

    B. D. Shaffer, S. Koohy, B. Kinch, M. A. Hsieh, and N. Trask. Structure-preserving learning improves geometry generalization in neural pdes.arXiv preprint arXiv:2602.02788, 2026

    Pith/arXiv arXiv 2026

  44. [44]

    B. D. Shaffer, B. Kinch, M. A. Hsieh, and N. Trask. A meshfree exterior calculus for generaliz- able and data-efficient learning of physics from point clouds.arXiv preprint arXiv:2605.08436, 2026

    Pith/arXiv arXiv 2026

  45. [45]

    Shaffer, V

    B. Shaffer, V . Edwards, B. Kinch, N. Trask, and M. A. Hsieh. Multi-robot multi-source localization in complex flows with physics-preserving environment models.arXiv preprint arXiv:2509.14228, 2025

    arXiv 2025

  46. [46]

    B. D. Shaffer, B. Kinch, J. Klobusicky, M. A. Hsieh, and N. Trask. Physics-informed sensor coverage through structure preserving machine learning.arXiv preprint arXiv:2509.10363, 2025

    arXiv 2025

  47. [47]

    Sharp, S

    N. Sharp, S. Attaiki, K. Crane, and M. Ovsjanikov. Diffusionnet: Discretization agnostic learning on surfaces.ACM Transactions on Graphics (ToG), 41(3):1–16, 2022

    2022

  48. [48]

    J. Sun, M. Ovsjanikov, and L. Guibas. A concise and provably informative multi-scale sig- nature based on heat diffusion. InComputer graphics forum, volume 28, pages 1383–1392. Wiley Online Library, 2009

    2009

  49. [49]

    L. C. Evans.Partial differential equations, volume 19. American mathematical society, 2022. 11

    2022

  50. [50]

    M. C. Delfour and J.-P. Zol ´esio.Shapes and Geometries: Metrics, Analysis, Differential Cal- culus, and Optimization. Advances in Design and Control. SIAM, 2 edition, 2011

    2011

  51. [51]

    Pfaff, M

    T. Pfaff, M. Fortunato, A. Sanchez-Gonzalez, and P. Battaglia. Learning mesh-based simula- tion with graph networks. InInternational Conference on Learning Representations, 2020

    2020

  52. [52]

    Z. Li, N. Kovachki, K. Azizzadenesheli, B. Liu, K. Bhattacharya, A. Stuart, and A. Anandku- mar. Neural operator: Graph kernel network for partial differential equations.arXiv preprint arXiv:2003.03485, 2020

    Pith/arXiv arXiv 2003

  53. [53]

    A. Khan, A. Ribeiro, V . Kumar, and A. G. Francis. Graph neural networks for motion planning. arXiv preprint arXiv:2006.06248, 2020

    arXiv 2006

  54. [54]

    T. Li, D. Ho, C. Li, D. Zhu, C. Wang, and M. Q.-H. Meng. Houseexpo: A large-scale 2d indoor layout dataset for learning-based algorithms on mobile robots. In2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 5839–5846. IEEE, 2020

    2020

  55. [55]

    N. R. Sturtevant. Benchmarks for grid-based pathfinding.IEEE Transactions on Computa- tional Intelligence and AI in Games, 4(2):144–148, 2012

    2012

  56. [56]

    Y . Canzani. Analysis on manifolds via the laplacian.Lecture Notes available at: http://www. math. harvard. edu/canzani/docs/Laplacian. pdf, pages 41–44, 2013

    2013

  57. [57]

    Gustafsson and G

    T. Gustafsson and G. D. McBain. scikit-fem: A Python package for finite element assembly. Journal of Open Source Software, 5(52):2369, 2020. doi:10.21105/joss.02369

    work page doi:10.21105/joss.02369 2020

  58. [58]

    J. A. Sethian. Fast marching methods.SIAM review, 41(2):199–235, 1999. A Optimal control correspondence For completeness, we summarize the correspondence between the learned desirability PDE and linearly-solvable optimal control (LSOC) [6, 7] for the Dirichlet-enforced goal formulation. For any admissible coefficientsK θ ≻0andc θ ≥0, the policy (4) can be...

    1999