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

2026-07-23

AI Summary

This work addresses the high computational cost and limited temporal modeling capability of traditional implicit neural representations (INRs) when handling time-varying volumetric data, which typically rely on dense spatiotemporal coordinate sampling. The authors propose reformulating time-varying volumes as collections of time series indexed by spatial locations and replacing point-wise scalar supervision with sequence-level supervision. To better capture heterogeneous temporal dynamics, they introduce a Mixture-of-Experts (MoE) architecture that adaptively allocates model capacity across different spatial regions. This approach substantially reduces training overhead while improving reconstruction quality, demonstrates compatibility with various existing INR frameworks, and outperforms current state-of-the-art methods across multiple evaluation metrics.

Abstract

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.

Problem

• implicit neural representations
• time-varying volumetric data
• spatiotemporal sampling
• temporal structure
• coordinate-wise supervision

Innovation

• Implicit Neural Representations
• Time Series
• Spatiotemporal Data
• Sequence-level Supervision
• Mixture-of-Experts