# Time Series Continuous Modeling for Imputation and Forecasting with Implicit Neural Representations

arXiv: https://arxiv.org/abs/2306.05880 · HTML: https://mlsanity.com/paper/2306.05880/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 45 references that are in the map.
- First posted on arXiv 9 Jun 2023.

## Builds on (most cited first, 27 of 27)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [From data to functa: Your data point is a function and you can treat it like one](https://mlsanity.com/paper/2201.12204/) (2022)
- [Latent ODEs for Irregularly-Sampled Time Series](https://mlsanity.com/paper/1907.03907/) (2019)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Continuous PDE Dynamics Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2209.14855/) (2022)
- [NAOMI: Non-Autoregressive Multiresolution Sequence Imputation](https://mlsanity.com/paper/1901.10946/) (2019)
- [Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion](https://mlsanity.com/paper/2211.02590/) (2022)
- [Joint Modeling of Local and Global Temporal Dynamics for Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/1911.10273/) (2019)
- [Compressing multidimensional weather and climate data into neural networks](https://mlsanity.com/paper/2210.12538/) (2022)
- [HyperTime: Implicit Neural Representation for Time Series](https://mlsanity.com/paper/2208.05836/) (2022)
- [Time series forecasting with Gaussian Processes needs priors](https://mlsanity.com/paper/2009.08102/) (2020)
- [Time-Series Anomaly Detection with Implicit Neural Representation](https://mlsanity.com/paper/2201.11950/) (2022)

## Built on by (most cited first, 17 of 17)

- [Universal Time-Series Representation Learning: A Survey](https://mlsanity.com/paper/2401.03717/) (2024)
- [DAM: Towards A Foundation Model for Time Series Forecasting](https://mlsanity.com/paper/2407.17880/) (2024)
- [Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner](https://mlsanity.com/paper/2405.03185/) (2024)
- [TSINR: Capturing Temporal Continuity via Implicit Neural Representations for Time Series Anomaly Detection](https://mlsanity.com/paper/2411.11641/) (2024)
- [A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometries](https://mlsanity.com/paper/2504.02459/) (2025)
- [TS-ICL: A Flexible Time-Indexed Foundation Model for Time Series via In-Context Learning](https://mlsanity.com/paper/2606.05878/) (2026)
- [ImputeINR: Time Series Imputation via Implicit Neural Representations for Disease Diagnosis with Missing Data](https://mlsanity.com/paper/2505.10856/) (2025)
- [PDETime: Rethinking Long-Term Multivariate Time Series Forecasting from the perspective of partial differential equations](https://mlsanity.com/paper/2402.16913/) (2024)
- [Implicit Neural Representation For Accurate CFD Flow Field Prediction](https://mlsanity.com/paper/2408.06486/) (2024)
- [Temporal Variational Implicit Neural Representations](https://mlsanity.com/paper/2506.01544/) (2025)
- [MoTM: Towards a Foundation Model for Time Series Imputation based on Continuous Modeling](https://mlsanity.com/paper/2507.13207/) (2025)
- [Are Time-Indexed Foundation Models the Future of Time Series Imputation?](https://mlsanity.com/paper/2511.05980/) (2025)
- [Collaborative Imputation of Urban Time Series through Cross-city Meta-learning](https://mlsanity.com/paper/2501.11306/) (2025)
- [Coordinate-Queryable Neural Field Reconstruction for EEG Spatial Super-Resolution with Unseen-Electrode Generation](https://mlsanity.com/paper/2606.23707/) (2026)
- [GLAIM: Learning Global and Local Adaptive Inter-Variable Dependency for Multivariate Time Series Imputation](https://mlsanity.com/paper/2608.02366/) (2026)
- [Beyond Pointwise Error: A Multi-Metric Evaluation of Spatial Climate Downscaling](https://mlsanity.com/paper/2610.01579/) (2026)
- [Fast Gradient-Based Approximation of Continuous Dynamic Time Warping](https://mlsanity.com/paper/2610.13129/) (2026)

## Abstract (arXiv)

We introduce a novel modeling approach for time series imputation and forecasting, tailored to address the challenges often encountered in real-world data, such as irregular samples, missing data, or unaligned measurements from multiple sensors. Our method relies on a continuous-time-dependent model of the series' evolution dynamics. It leverages adaptations of conditional, implicit neural representations for sequential data. A modulation mechanism, driven by a meta-learning algorithm, allows adaptation to unseen samples and extrapolation beyond observed time-windows for long-term predictions. The model provides a highly flexible and unified framework for imputation and forecasting tasks across a wide range of challenging scenarios. It achieves state-of-the-art performance on classical benchmarks and outperforms alternative time-continuous models.