# PhysAttNet: Enhancing Predictive Performance in Industrial and Astrophysical Time Series via Physics-Informed Attention

arXiv: https://arxiv.org/abs/2608.07681 · HTML: https://mlsanity.com/paper/2608.07681/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [CASTing Your Model: Learning to Localize Improves Self-Supervised Representations](https://mlsanity.com/paper/2012.04630/) (2020)
- [A Deep Dive into Perturbations as Evaluation Technique for Time Series XAI](https://mlsanity.com/paper/2307.05104/) (2023)
- [Right on Time: Revising Time Series Models by Constraining their Explanations](https://mlsanity.com/paper/2402.12921/) (2024)
- [Structure-Preserving Physics-Informed Neural Networks With Energy or Lyapunov Structure](https://mlsanity.com/paper/2401.04986/) (2024)
- [Guaranteeing Conservation Laws with Projection in Physics-Informed Neural Networks](https://mlsanity.com/paper/2410.17445/) (2024)
- [Your Attention Matters: to Improve Model Robustness to Noise and Spurious Correlations](https://mlsanity.com/paper/2507.20453/) (2025)

## Abstract (arXiv)

Accurate and robust time series forecasting is essential in many applications involving physical processes, such as manufacturing monitoring and astrophysical event detection. In these settings, predictive models must remain reliable under noise, variability, and measurement uncertainty while capturing temporally localized structures corresponding to physically meaningful events. Convolutional neural networks (CNNs) are widely used for such tasks due to their computational efficiency and strong representational capacity. However, their learned temporal representations often exhibit unstable or physically inconsistent attention patterns, reducing robustness, generalization, and interpretability. This paper introduces PhysAttNet, a physics-informed attention framework for time series forecasting. PhysAttNet augments a lightweight CNN forecaster with an attention head guided by domain-informed regularization reflecting the structural properties of physical signals. Specifically, three complementary constraints are imposed during training: an alignment regularization that encourages attention to follow smooth, peak-centered temporal structures derived from the input signal, a smoothness regularization that enforces continuous temporal evolution, and a sparsity regularization that promotes selective focus on informative intervals. These differentiable regularization terms introduce physics-guided inductive bias without requiring annotated explanations or manual supervision. Experiments on two distinct applications, namely predicting cutting forces during milling and forecasting flares in blazar time series, demonstrate that PhysAttNet improves forecasting accuracy, generalization, and prediction performance on structurally important events.