# PIAD-SRNN: Physics-Informed Adaptive Decomposition in State-Space RNN

arXiv: https://arxiv.org/abs/2412.00994 · HTML: https://mlsanity.com/paper/2412.00994/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 1 Dec 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [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)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [Gaussian Process Prior Variational Autoencoders](https://mlsanity.com/paper/1810.11738/) (2018)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [Missing Value Imputation on Multidimensional Time Series](https://mlsanity.com/paper/2103.01600/) (2021)
- [NRTSI: Non-Recurrent Time Series Imputation](https://mlsanity.com/paper/2102.03340/) (2021)
- [Novel Physics-Based Machine-Learning Models for Indoor Air Quality Approximations](https://mlsanity.com/paper/2308.01438/) (2023)

## Abstract (arXiv)

Time series forecasting often demands a trade-off between accuracy and efficiency. While recent Transformer models have improved forecasting capabilities, they come with high computational costs. Linear-based models have shown better accuracy than Transformers but still fall short of ideal performance. We propose PIAD-SRNN, a physics-informed adaptive decomposition state-space RNN, that separates seasonal and trend components and embeds domain equations in a recurrent framework. We evaluate PIAD-SRNN's performance on indoor air quality datasets, focusing on CO2 concentration prediction across various forecasting horizons, and results demonstrate that it consistently outperforms SoTA models in both long-term and short-term time series forecasting, including transformer-based architectures, in terms of both MSE and MAE. Besides proposing PIAD-SRNN which balances accuracy with efficiency, this paper also provides four curated datasets. Code and data: https://github.com/ahmad-shirazi/DSSRNN