PhysAttNet: Enhancing Predictive Performance in Industrial and Astrophysical Time Series via Physics-Informed Attention
Authors: Amal Saadallah, Julia Tjus, Petra Wiederkeher, Wolfgang Rhode
Abstract
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.
Time series forecasting has seen signicant advancements with the emergence of new deep learning models. However, forecasting time series in applications involving physical processes remains a major challenge. Despite the apparition of Physics Informed Neural Networks (PINN), recent models do not estimate unobservable intermediate physical variables, which are important for domain experts to understand the target behavior. To this end, we propose a Physics Informed Recurrent Neural Network (PIRNN) which predicts, along the target, unobservable variables on both historic data and forecast target. This approach enhances the model robustness and results interpretation using domain knowledge. Our method is easily adaptable to any physical model using several equations, each having its own set of unobservable variables, to describe it-self. As a case study, we incorporate physical equations used for groundwater levels predictions by the physical model called Gardenia. This model uses transfers equations between reservoirs, optimized with data assimilation, to simulate the evolution of groundwater levels. Evaluation includes several well known neural network models and the Gardenia model compared on twelve real world datasets. In addition, we study the impact of each component through an ablation study. Our model outperforms other models on ve out of the twelve datasets and our ablation study underlines the importance of having a physical background in our time series forecasting task. Finally, the coherence of the physical variables predicted by our neural network is assessed by a domain expert.
Etienne Lehembre, Pascal Audigane, Vincent Nguyen +2
Multivariate forecasting in physical systems requires models that predict coupled temporal variables while preserving meaningful state evolution. Deep forecasters can fit temporal correlations, and physics-informed models can regularize predictions with scientific constraints, but these directions are often connected only at the decoded-output level. As a result, the hidden predictive state that generates future trajectories may remain statistically useful but physically unstructured. We introduce Phys-JEPA, a physics-informed joint-embedding predictive architecture for multivariate time-series forecasting. Phys-JEPA learns a latent world model in which predictive states are decomposed into physical and residual components, and physical consistency is imposed directly on latent states and latent transitions rather than only on decoded forecasts. This formulation uses known physical variables to organize the representation space while retaining residual capacity for unresolved dynamics. On Jena Climate 2009--2016, Phys-JEPA reduces aggregate MSE from 0.12482 to 0.12273 and temperature MSE from 0.01892 to 0.01831 at H=24. On Traffic, full Phys-JEPA improves aggregate MSE over the supervised baseline across all tested horizons, reducing H=192 MSE from 0.800784 to 0.773873. On Electricity, the best variant depends on horizon: static latent consistency is strongest at H=24 and H=48, while full Phys-JEPA gives the best aggregate and target-variable MSE at H=192. These initial results suggest that moving physics-informed learning from output space to latent predictive state space is a promising direction for interpretable temporal world models.
Multivariate time-series forecasting requires models to reason over temporal dynamics, cross-variable dependencies, and historical input-output correspondences. Recent Prior-Data Fitted Networks (PFNs) suggest that synthetic tasks can be useful for learning transferable inference behavior. However, directly transferring this paradigm to time-series forecasting remains difficult, since temporal order, dynamic lags, and recurring historical patterns are not naturally captured by ordinary tabular priors. Motivated by this observation, we propose Trio, a sample-aware time-series forecasting architecture based on Temporal-Spatial-Sample attention. Temporal attention captures within-window dynamics, spatial attention models inter-variable dependencies, and sample attention retrieves relevant historical lookback-future pairs to guide the current prediction. Rather than claiming a fully general PFN-style forecaster, our goal is to study how historical input-output examples can be explicitly organized and reused within a forecasting model. We further introduce a Time-Series Structural Causal Model (TS-SCM) generator to create structured synthetic forecasting tasks with dynamic lags, cross-variable interactions, noise, feedback, and distributional drift. Experiments on synthetic, industrial, and public benchmarks show that the proposed architecture improves forecasting performance. Exploratory zero-shot experiments further suggest that TS-SCM-generated tasks may provide useful structural priors, while fully general PFN-style time-series forecasting remains an open problem.