Ladder of Information Limits on Prediction for Reduced-Order Models

This paper investigates what can and cannot be predicted when only limited information is available to a model. The authors construct a hierarchical ladder of information limits that classifies prediction tasks by their information requirements, ranging from memoryless trajectory forecasts to memory-augmented predictions, event prediction, stationary statistics, and generative laws. The analysis is architecture-agnostic, identifying minimum attainable prediction errors given information constraints. The framework provides theoretical foundations applicable to reduced-order modeling in various scientific domains.