Signals, Concepts, and Laws: Toward Universal, Explainable Time-Series Forecasting

Hongwei Ma, Junbin Gao, Minh-Ngoc Tran

Keywords: Cross-domain generalization, Differentiable physics residuals, Physics-regularized forecasting, Time-series Transformer

Abstract:

Accurate, explainable and physically credible forecasting remains a persistent challenge for multivariate time-series with domain-varying statistical properties.
We propose DORIC, a Domain-Universal, ODE-Regularized, Interpretable-Concept Transformer for Time-Series Forecasting that generates predictions through five self-supervised, domain-agnostic concepts while enforcing differentiable residuals grounded in
first-principles constraints. The concepts are softly regressed toward analytic statistics of the raw signal, and a driven–damped ODE head couples these concepts to the forecast as a shared, mean-reverting dynamical template across datasets. Unlike prior efficiency-focused Transformers, such as Informer(sparse attention) or FEDformer(frequency priors), DORIC combines latent explainability with explicit scientific constraints, while preserving the attention mechanism’s capacity to model long-range dependencies.
We evaluate DORIC on six publicly-available datasets and it achieves the lowest error in eight of twelve MSE/MAE metrics.
Compared with TimeMixer, DORIC outperforms it on four datasets while maintaining strong interpretability.
Interpretability analyses show that the learned concepts remain strongly aligned with their analytic targets, physics residuals stay relative to the signal scale, and the learned ODE coefficients follow domain-consistent patterns.
Ablation studies reveal complementary contributions: removing the physics residual increases average MSE from 0.328 to 0.547, eliminating concept alignment raises it to 0.698, and replacing the shared encoder with disjoint concept heads results in a 76% increase.

Primary Area: interpretability and explainable AI

Submission Number: 10601