Retrodictive Forecasting: A Proof-of-Concept for Exploiting Temporal Asymmetry in Time Series Prediction

Authors: Damour, Cedric Date: 2026-02-28 Paper ID: openalex:2603.00636

Summary

This paper introduces a novel retrodictive forecasting paradigm that inverts the conventional approach, using inverse Maximum A Posteriori (MAP) optimization over a Conditional Variational Autoencoder (CVAE) to determine the future state trajectory that best explains the observed present. The theoretical foundation rests on an information-theoretic measure of temporal asymmetry, using the symmetrized Kullback-Leibler divergence as an operational diagnostic to select applicable cases. The inverse CVAE architecture is enhanced with a learned RealNVP normalizing-flow prior, and evaluation on synthetic and ERA5 datasets demonstrates that this approach yields competitive or superior Root Mean Square Error (RMSE) when exploitable temporal asymmetry is present. The results establish a structured proof-of-concept for retrodictive forecasting as a viable alternative to forward methods in systems exhibiting statistical time-irreversibility.

Key Contributions

• Formal mathematical formulation of the retrodictive inference paradigm for time series prediction.
• Implementation of an inverse Conditional Variational Autoencoder (CVAE) incorporating a learned RealNVP normalizing-flow prior for retrodiction.
• Introduction of a model-free diagnostic based on the symmetrized Kullback-Leibler divergence to assess temporal asymmetry and determine the GO/NO-GO condition for retrodiction.
• Empirical validation showing competitive or superior RMSE performance (e.g., 17.7% reduction on ERA5 solar irradiance) compared to forward baselines when temporal asymmetry is present.

Limitations

The current work is a proof-of-concept, and its generalizability across all types of time-reversible and irreversible dynamics requires further testing beyond the initial six cases. The theoretical link between the information-theoretic arrow-of-time measure and practical forecast improvement is still conceptual and operationalized via a heuristic GO/NO-GO test.

Open Questions & Future Work

• retrodictive-forecasting-full-posterior
• gaussian-decoder-assumption-fidelity
• multivariate-extension-combinatorics
• thermodynamic-interpretation-validation
• architecture-agnostic-evaluation
• map-landscape-tractability
• structured-priors-multivariate

Key Concepts

• Retrodictive Forecasting: A paradigm that predicts the past state that best explains the observed present state by inverting a probabilistic model.
• Inverse CVAE for Retrodiction: A Conditional Variational Autoencoder structure adapted for Bayesian inversion to perform retrodictive inference via MAP optimization.
• Model-Free Irreversibility Diagnostic: An information-theoretic metric based on the symmetrized Kullback-Leibler divergence between forward and time-reversed trajectory ensembles to determine applicability for retrodiction.

Datasets

• ERA5

Limitations

The current work is a proof-of-concept, and its generalizability across all types of time-reversible and irreversible dynamics requires further testing beyond the initial six cases. The theoretical link between the information-theoretic arrow-of-time measure and practical forecast improvement is still conceptual and operationalized via a heuristic GO/NO-GO test.

Links

• Abstract
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