# From Scalars to Time Series: Rethinking Implicit Neural Representations for Time-Varying Volumetric Data

arXiv: https://arxiv.org/abs/2607.20970 · HTML: https://mlsanity.com/paper/2607.20970/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in MoE for time series and graphs, one of 12 directions in Mixture-of-experts.
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Placed in

- Mixture-of-experts / [MoE for time series and graphs](https://mlsanity.com/moe/moe-for-time-series-and-graphs/)

## Builds on (most cited first, 17 of 17)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [MetaSDF: Meta-learning Signed Distance Functions](https://mlsanity.com/paper/2006.09662/) (2020)
- [Kimi Linear: An Expressive, Efficient Attention Architecture](https://mlsanity.com/paper/2510.26692/) (2025)
- [Compressive Neural Representations of Volumetric Scalar Fields](https://mlsanity.com/paper/2104.04523/) (2021)
- [TTHRESH: Tensor Compression for Multidimensional Visual Data](https://mlsanity.com/paper/1806.05952/) (2018)
- [SZ3: A Modular Framework for Composing Prediction-Based Error-Bounded Lossy Compressors](https://mlsanity.com/paper/2111.02925/) (2021)
- [HyperINR: A Fast and Predictive Hypernetwork for Implicit Neural Representations via Knowledge Distillation](https://mlsanity.com/paper/2304.04188/) (2023)
- [Volumetric Isosurface Rendering with Deep Learning-Based Super-Resolution](https://mlsanity.com/paper/1906.06520/) (2019)
- [Learning Adaptive Sampling and Reconstruction for Volume Visualization](https://mlsanity.com/paper/2007.10093/) (2020)
- [Deep Hierarchical Super Resolution for Scientific Data](https://mlsanity.com/paper/2107.00462/) (2021)
- [Neural Experts: Mixture of Experts for Implicit Neural Representations](https://mlsanity.com/paper/2410.21643/) (2024)
- [Distributed Neural Representation for Reactive in situ Visualization](https://mlsanity.com/paper/2304.10516/) (2023)
- [HyperFLINT: Hypernetwork-based Flow Estimation and Temporal Interpolation for Scientific Ensemble Visualization](https://mlsanity.com/paper/2412.04095/) (2024)

## Abstract (arXiv)

Implicit neural representations (INRs) for time-varying volumetric data are typically trained using dense sampling over spatiotemporal coordinates, where each observation corresponds to a single point in space and time. This coordinate-wise formulation requires extensive sampling during optimization, leading to high computational cost and inefficient use of temporal structure. In this work, we revisit this design choice and show that dense spatiotemporal sampling is not necessary for learning time-varying fields. Instead, we represent the data as a collection of spatially indexed time series and train INRs using sequence-level supervision over each spatial location, rather than coordinate-wise scalar samples. This reformulation eliminates the need for dense spatiotemporal sampling and instead learns each spatial location from its full temporal evolution in a structured manner. We demonstrate that this representation is compatible with a range of existing INR architectures and consistently improves reconstruction quality, while significantly reducing training cost. Furthermore, we show that this formulation can be combined with mixture-of-experts architectures, and that our MoE instantiation further improves reconstruction quality compared to both the base reformulation and existing MoE-based INR methods, providing a stronger capacity allocation under heterogeneous temporal dynamics.