# Towards Measuring and Modeling Geometric Structures in Time Series Forecasting via Image Modality

arXiv: https://arxiv.org/abs/2507.23253 · HTML: https://mlsanity.com/paper/2507.23253/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 31 Jul 2025.

## Builds on (most cited first, 20 of 20)

- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [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)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [VisionTS: Visual Masked Autoencoders Are Free-Lunch Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2408.17253/) (2024)
- [Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models](https://mlsanity.com/paper/1909.09020/) (2019)
- [Differentiable Dynamic Programming for Structured Prediction and Attention](https://mlsanity.com/paper/1802.03676/) (2018)
- [Classification of Time-Series Images Using Deep Convolutional Neural Networks](https://mlsanity.com/paper/1710.00886/) (2017)
- [Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer](https://mlsanity.com/paper/2405.17478/) (2024)
- [LightGTS: A Lightweight General Time Series Forecasting Model](https://mlsanity.com/paper/2506.06005/) (2025)
- [Graph Attention Recurrent Neural Networks for Correlated Time Series Forecasting -- Full version](https://mlsanity.com/paper/2103.10760/) (2021)
- [Forecasting with time series imaging](https://mlsanity.com/paper/1904.08064/) (2019)
- [Autowarp: Learning a Warping Distance from Unlabeled Time Series Using Sequence Autoencoders](https://mlsanity.com/paper/1810.10107/) (2018)
- [Visual Time Series Forecasting: An Image-driven Approach](https://mlsanity.com/paper/2011.09052/) (2020)

## Built on by (most cited first, 2 of 2)

- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [TopoCast: A Topological Fidelity Framework for Evaluating Transformer-Based Time Series Forecasting](https://mlsanity.com/paper/2606.25439/) (2026)

## Abstract (arXiv)

Time Series forecasting is critical in diverse domains such as weather forecasting, financial investment, and traffic management. While traditional numerical metrics like mean squared error (MSE) can quantify point-wise accuracy, they fail to evaluate the geometric structure of time series data, which is essential to understand temporal dynamics. To address this issue, we propose the time series Geometric Structure Index (TGSI), a novel evaluation metric that transforms time series into images to leverage their inherent two-dimensional geometric representations. However, since the image transformation process is non-differentiable, TGSI cannot be directly integrated as a training loss. We further introduce the Shape-Aware Temporal Loss (SATL), a multi-component loss function operating in the time series modality to bridge this gap and enhance structure modeling during training. SATL combines three components: a first-order difference loss that measures structural consistency through the MSE between first-order differences, a frequency domain loss that captures essential periodic patterns using the Fast Fourier Transform while minimizing noise, and a perceptual feature loss that measures geometric structure difference in time-series by aligning temporal features with geometric structure features through a pre-trained temporal feature extractor and time-series image autoencoder. Experiments across multiple datasets demonstrate that models trained with SATL achieve superior performance in both MSE and the proposed TGSI metrics compared to baseline methods, without additional computational cost during inference.