# Capturing dynamical correlations using implicit neural representations

arXiv: https://arxiv.org/abs/2304.03949 · HTML: https://mlsanity.com/paper/2304.03949/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 63 references that are in the map.
- First posted on arXiv 8 Apr 2023.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Amortized Inference for Heterogeneous Reconstruction in Cryo-EM](https://mlsanity.com/paper/2210.07387/) (2022)
- [Implicit Neural Representation for Mesh-Free Inverse Obstacle Scattering](https://mlsanity.com/paper/2206.02027/) (2022)
- [Simplified algorithms for adaptive experiment design in parameter estimation](https://mlsanity.com/paper/2202.08344/) (2022)
- [Novel Light Field Imaging Device with Enhanced Light Collection for Cold Atom Clouds](https://mlsanity.com/paper/2205.11480/) (2022)

## Built on by (most cited first, 6 of 6)

- [Hyper-Compression: Model Compression via Hyperfunction](https://mlsanity.com/paper/2409.00592/) (2024)
- [Enhancing Accuracy and Parameter-Efficiency of Neural Representations for Network Parameterization](https://mlsanity.com/paper/2407.00356/) (2024)
- [Regularized interpolation in 4D neural fields enables optimization of 3D printed geometries](https://mlsanity.com/paper/2502.01517/) (2025)
- [Physics-Guided Dual Implicit Neural Representations for Source Separation](https://mlsanity.com/paper/2507.05249/) (2025)
- [Machine learning enabled experimental design and parameter estimation for ultrafast spin dynamics](https://mlsanity.com/paper/2306.02015/) (2023)
- [Multi-resolution Enhancement for Full Spectrum Neural Representations](https://mlsanity.com/paper/2509.15494/) (2025)

## Abstract (arXiv)

The observation and description of collective excitations in solids is a fundamental issue when seeking to understand the physics of a many-body system. Analysis of these excitations is usually carried out by measuring the dynamical structure factor, S(Q, ω), with inelastic neutron or x-ray scattering techniques and comparing this against a calculated dynamical model. Here, we develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. We benchmark this approach on a Linear Spin Wave Theory (LSWT) simulator and advanced inelastic neutron scattering data from the square-lattice spin-1 antiferromagnet La2NiO4. We find that the model predicts the unknown parameters with excellent agreement relative to analytical fitting. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data, without the need for human-guided peak finding and fitting algorithms. This prototypical approach promises a new technology for this field to automatically detect and refine more advanced models for ordered quantum systems.