# NTFields: Neural Time Fields for Physics-Informed Robot Motion Planning

arXiv: https://arxiv.org/abs/2210.00120 · HTML: https://mlsanity.com/paper/2210.00120/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 30 Sep 2022.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Vision-Only Robot Navigation in a Neural Radiance World](https://mlsanity.com/paper/2110.00168/) (2021)
- [iSDF: Real-Time Neural Signed Distance Fields for Robot Perception](https://mlsanity.com/paper/2204.02296/) (2022)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [Motion Planning Networks](https://mlsanity.com/paper/1806.05767/) (2018)
- [Motion Planning Networks: Bridging the Gap Between Learning-based and Classical Motion Planners](https://mlsanity.com/paper/1907.06013/) (2019)
- [Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic](https://mlsanity.com/paper/1404.2334/) (2014)
- [EikoNet: Solving the Eikonal equation with Deep Neural Networks](https://mlsanity.com/paper/2004.00361/) (2020)
- [Robot Motion Planning in Learned Latent Spaces](https://mlsanity.com/paper/1807.10366/) (2018)
- [Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the Heuristically Guided Search of Implicit Random Geometric Graphs](https://mlsanity.com/paper/1405.5848/) (2014)
- [Fast Marching Tree: a Fast Marching Sampling-Based Method for Optimal Motion Planning in Many Dimensions](https://mlsanity.com/paper/1306.3532/) (2013)
- [FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planning](https://mlsanity.com/paper/1703.07373/) (2017)
- [Deeply Informed Neural Sampling for Robot Motion Planning](https://mlsanity.com/paper/1809.10252/) (2018)
- [LEGO: Leveraging Experience in Roadmap Generation for Sampling-Based Planning](https://mlsanity.com/paper/1907.09574/) (2019)
- [Regularized Deep Signed Distance Fields for Reactive Motion Generation](https://mlsanity.com/paper/2203.04739/) (2022)
- [Learning Continuous Environment Fields via Implicit Functions](https://mlsanity.com/paper/2111.13997/) (2021)
- [A fast marching algorithm for the factored eikonal equation](https://mlsanity.com/paper/1607.00973/) (2016)
- [Predicted Composite Signed-Distance Fields for Real-Time Motion Planning in Dynamic Environments](https://mlsanity.com/paper/2008.00969/) (2020)
- [Cost-to-Go Function Generating Networks for High Dimensional Motion Planning](https://mlsanity.com/paper/2012.06023/) (2020)
- [Causal Domain Restriction for Eikonal Equations](https://mlsanity.com/paper/1309.2884/) (2013)

## Built on by (most cited first, 22 of 22)

- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [Physics-informed Value Learner for Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2509.06782/) (2025)
- [Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific ML](https://mlsanity.com/paper/2301.13331/) (2023)
- [Progressive Learning for Physics-informed Neural Motion Planning](https://mlsanity.com/paper/2306.00616/) (2023)
- [Denoising Heat-inspired Diffusion with Insulators for Collision Free Motion Planning](https://mlsanity.com/paper/2310.12609/) (2023)
- [Physics-informed Neural Motion Planning on Constraint Manifolds](https://mlsanity.com/paper/2403.05765/) (2024)
- [Physics-informed Temporal Difference Metric Learning for Robot Motion Planning](https://mlsanity.com/paper/2505.05691/) (2025)
- [Reconstructive Latent-Space Neural Radiance Fields for Efficient 3D Scene Representations](https://mlsanity.com/paper/2310.17880/) (2023)
- [RBF-PINN: Non-Fourier Positional Embedding in Physics-Informed Neural Networks](https://mlsanity.com/paper/2402.08367/) (2024)
- [Graph Neural Stochastic Differential Equations for Learning Brownian Dynamics](https://mlsanity.com/paper/2306.11435/) (2023)
- [Feature Mapping in Physics-Informed Neural Networks (PINNs)](https://mlsanity.com/paper/2402.06955/) (2024)
- [Learning Lagrangian Interaction Dynamics with Sampling-Based Model Order Reduction](https://mlsanity.com/paper/2407.03925/) (2024)
- [Learning Flow Distributions via Projection-Constrained Diffusion on Manifolds](https://mlsanity.com/paper/2602.17773/) (2026)
- [Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spaces](https://mlsanity.com/paper/2505.16035/) (2025)
- [Mollified Value Learning](https://mlsanity.com/paper/2602.23280/) (2026)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Space Is Intelligence: Neural Semigroup Superposition for Riemannian Metric Generation](https://mlsanity.com/paper/2606.18828/) (2026)
- [Data-augmented Learning of Geodesic Distances in Irregular Domains through Soner Boundary Conditions](https://mlsanity.com/paper/2503.04579/) (2025)
- [Neural Navigation Functions for Zero-Shot Generalizable Motion Planning](https://mlsanity.com/paper/2606.03756/) (2026)
- [PoseShield: Neural Collision Fields for Human Self-Collision Resolution](https://mlsanity.com/paper/2606.29686/) (2026)
- [The Field Knows: Cross-Dimensional Geometry from Navigation to Black Holes](https://mlsanity.com/paper/2608.07566/) (2026)
- [Energy-Structured Latent World Models with Neural Time Fields for Physically Constistent Open-World Motion Planning](https://mlsanity.com/paper/2608.09876/) (2026)

## Abstract (arXiv)

Neural Motion Planners (NMPs) have emerged as a promising tool for solving robot navigation tasks in complex environments. However, these methods often require expert data for learning, which limits their application to scenarios where data generation is time-consuming. Recent developments have also led to physics-informed deep neural models capable of representing complex dynamical Partial Differential Equations (PDEs). Inspired by these developments, we propose Neural Time Fields (NTFields) for robot motion planning in cluttered scenarios. Our framework represents a wave propagation model generating continuous arrival time to find path solutions informed by a nonlinear first-order PDE called Eikonal Equation. We evaluate our method in various cluttered 3D environments, including the Gibson dataset, and demonstrate its ability to solve motion planning problems for 4-DOF and 6-DOF robot manipulators where the traditional grid-based Eikonal planners often face the curse of dimensionality. Furthermore, the results show that our method exhibits high success rates and significantly lower computational times than the state-of-the-art methods, including NMPs that require training data from classical planners.