# Neural Stream Functions

arXiv: https://arxiv.org/abs/2307.08142 · HTML: https://mlsanity.com/paper/2307.08142/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 55 references that are in the map.
- First posted on arXiv 16 Jul 2023.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Light Field Networks: Neural Scene Representations with Single-Evaluation Rendering](https://mlsanity.com/paper/2106.02634/) (2021)
- [AutoInt: Automatic Integration for Fast Neural Volume Rendering](https://mlsanity.com/paper/2012.01714/) (2020)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [A unified deep artificial neural network approach to partial differential equations in complex geometries](https://mlsanity.com/paper/1711.06464/) (2017)
- [Compressive Neural Representations of Volumetric Scalar Fields](https://mlsanity.com/paper/2104.04523/) (2021)
- [InSituNet: Deep Image Synthesis for Parameter Space Exploration of Ensemble Simulations](https://mlsanity.com/paper/1908.00407/) (2019)
- [GNN-Surrogate: A Hierarchical and Adaptive Graph Neural Network for Parameter Space Exploration of Unstructured-Mesh Ocean Simulations](https://mlsanity.com/paper/2202.08956/) (2022)
- [NNVA: Neural Network Assisted Visual Analysis of Yeast Cell Polarization Simulation](https://mlsanity.com/paper/1904.09044/) (2019)
- [Spelunking the Deep: Guaranteed Queries on General Neural Implicit Surfaces via Range Analysis](https://mlsanity.com/paper/2202.02444/) (2022)

## Abstract (arXiv)

We present a neural network approach to compute stream functions, which are scalar functions with gradients orthogonal to a given vector field. As a result, isosurfaces of the stream function extract stream surfaces, which can be visualized to analyze flow features. Our approach takes a vector field as input and trains an implicit neural representation to learn a stream function for that vector field. The network learns to map input coordinates to a stream function value by minimizing the inner product of the gradient of the neural network's output and the vector field. Since stream function solutions may not be unique, we give optional constraints for the network to learn particular stream functions of interest. Specifically, we introduce regularizing loss functions that can optionally be used to generate stream function solutions whose stream surfaces follow the flow field's curvature, or that can learn a stream function that includes a stream surface passing through a seeding rake. We also discuss considerations for properly visualizing the trained implicit network and extracting artifact-free surfaces. We compare our results with other implicit solutions and present qualitative and quantitative results for several synthetic and simulated vector fields.