# Neural Implicit Surface Evolution

arXiv: https://arxiv.org/abs/2201.09636 · HTML: https://mlsanity.com/paper/2201.09636/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 42 references that are in the map.
- First posted on arXiv 24 Jan 2022.

## Builds on (most cited first, 9 of 9)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Exploring Differential Geometry in Neural Implicits](https://mlsanity.com/paper/2201.09263/) (2022)
- [Neural Implicit Mapping via Nested Neighborhoods](https://mlsanity.com/paper/2201.09147/) (2022)

## Built on by (most cited first, 18 of 18)

- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [Neural Geometry Processing via Spherical Neural Surfaces](https://mlsanity.com/paper/2407.07755/) (2024)
- [Neural Implicit Morphing of Face Images](https://mlsanity.com/paper/2308.13888/) (2023)
- [CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences](https://mlsanity.com/paper/2406.18582/) (2024)
- [Birth and Death of a Rose](https://mlsanity.com/paper/2412.05278/) (2024)
- [4Deform: Neural Surface Deformation for Robust Shape Interpolation](https://mlsanity.com/paper/2502.20208/) (2025)
- [Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing](https://mlsanity.com/paper/2405.12895/) (2024)
- [Understanding Sinusoidal Neural Networks](https://mlsanity.com/paper/2212.01833/) (2022)
- [Geometric implicit neural representations for signed distance functions](https://mlsanity.com/paper/2511.07206/) (2025)
- [NeuroGauss4D-PCI: 4D Neural Fields and Gaussian Deformation Fields for Point Cloud Interpolation](https://mlsanity.com/paper/2405.14241/) (2024)
- [SASNet: Spatially-Adaptive Sinusoidal Networks for INRs](https://mlsanity.com/paper/2503.09750/) (2025)
- [FLOWING: Implicit Neural Flows for Structure-Preserving Morphing](https://mlsanity.com/paper/2510.09537/) (2025)
- [FUSE: A Flow-based Mapping Between Shapes](https://mlsanity.com/paper/2511.13431/) (2025)
- [Implicit Neural Representation of Tileable Material Textures](https://mlsanity.com/paper/2402.02208/) (2024)
- [Neural 4D Evolution under Large Topological Changes from 2D Images](https://mlsanity.com/paper/2411.15018/) (2024)
- [Adaptive Training of INRs via Pruning and Densification](https://mlsanity.com/paper/2510.23943/) (2025)
- [An overview of 3D Vision-Language Models](https://mlsanity.com/paper/2609.05583/) (2026)
- [M-plicits: Neural Implicit Surfaces via Nested Multiscale Residuals](https://mlsanity.com/paper/2609.28684/) (2026)

## Abstract (arXiv)

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time ℝ3× ℝ, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions. The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually ℝ3 × 0. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.