# Scalable physical source-to-field inference with hypernetworks

arXiv: https://arxiv.org/abs/2405.05981 · HTML: https://mlsanity.com/paper/2405.05981/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 63 references that are in the map.
- First posted on arXiv 7 May 2024.

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

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Meta Networks](https://mlsanity.com/paper/1703.00837/) (2017)
- [SMASH: One-Shot Model Architecture Search through HyperNetworks](https://mlsanity.com/paper/1708.05344/) (2017)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Learning feed-forward one-shot learners](https://mlsanity.com/paper/1606.05233/) (2016)
- [Generative Models as Distributions of Functions](https://mlsanity.com/paper/2102.04776/) (2021)
- [Neural Conservation Laws: A Divergence-Free Perspective](https://mlsanity.com/paper/2210.01741/) (2022)
- [Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks](https://mlsanity.com/paper/2310.09528/) (2023)
- [HyperPINN: Learning parameterized differential equations with physics-informed hypernetworks](https://mlsanity.com/paper/2111.01008/) (2021)
- [Linearly Constrained Neural Networks](https://mlsanity.com/paper/2002.01600/) (2020)
- [Exact conservation laws for neural network integrators of dynamical systems](https://mlsanity.com/paper/2209.11661/) (2022)
- [Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems](https://mlsanity.com/paper/2301.10391/) (2023)
- [Variational Mixture of HyperGenerators for Learning Distributions Over Functions](https://mlsanity.com/paper/2302.06223/) (2023)
- [The stray- and demagnetizing field from a homogeneously magnetized tetrahedron](https://mlsanity.com/paper/2004.11700/) (2020)
- [The magnetic field from a homogeneously magnetized cylindrical tile](https://mlsanity.com/paper/2004.11701/) (2020)
- [Magnetic Field Prediction Using Generative Adversarial Networks](https://mlsanity.com/paper/2203.07897/) (2022)

## Abstract (arXiv)

We present a generative model that amortises computation for the field and potential around e.g.~gravitational or electromagnetic sources. Exact numerical calculation has either computational complexity O(M×N) in the number of sources M and evaluation points N, or requires a fixed evaluation grid to exploit fast Fourier transforms. Using an architecture where a hypernetwork produces an implicit representation of the field or potential around a source collection, our model instead performs as O(M + N), achieves relative error of ~!4%-6%, and allows evaluation at arbitrary locations for arbitrary numbers of sources, greatly increasing the speed of e.g.~physics simulations. We compare with existing models and develop two-dimensional examples, including cases where sources overlap or have more complex geometries, to demonstrate its application.