Before collecting data, it helps to ask whether the target accuracy is even attainable with the physics you chose. The idea: the attainable floor is set less by sample size or fitting tricks and more by which physical quantities you include and how they relate dimensionally. I’m proposing an open benchmark: share a task (H₀, α, G, heat/mass transfer, materials), the achieved relative error, and the list of variables actually used. We’ll compare empirical “plateaus” with the accuracy you would expect from the chosen description. Goal: a public map of where adding variables still helps—and where only a change of approach will.
There is no universal pre-data ceiling on model accuracy, but practical limits exist:
- Accuracy depends mainly on which physical variables are included and how they relate dimensionally.
- Adding more data helps only up to a point; beyond that, improvements require new descriptors or alternative modeling approaches.
References:
- Bishop, C.M. (2006). Pattern Recognition and Machine Learning. Springer.
- Montgomery, D.C., Peck, E.A., & Vining, G.G. (2012). Introduction to Linear Regression Analysis (5th ed.). Wiley.
Takeaway: Focus on variable selection and physical consistency—sample size alone cannot overcome missing or misrepresented physics
Article Advancing Scientific Rigor: Towards a Universal Informationa...
The current understanding of the situation is that fundamental limitations are only part of the picture. The actual achievable measurement accuracy is determined by many additional factors: losses, noise, decoherence, and the specific experimental setup. However, in this literature, the model of the process under study is usually taken as given: it is assumed that the researcher initially knows which physical mechanisms are significant, which parameters need to be controlled, and which dimensionless groups adequately describe the phenomenon. In practice, on the contrary, it is the choice and structural completeness of the model that often predetermine the achievable accuracy even before statistical data processing or the use of additional quantum resources come into play. A methodological gap arises between the “fundamental limit” and the actual experimental results: there is no operational concept that would directly link the adequacy of the model with the upper limit of accuracy. In a number of works on the information method (hereinafter referred to as IM, or FIQ method), this gap is systematically closed. The concept of pre-experimental informativeness of the model is introduced, depending on the choice of the class of the phenomenon, the set of dimensionless criteria taken into account and the ranges of their change. This informativeness sets an a priori level of uncertainty, which is not eliminated by simply increasing the number of measurements: to reduce it, a modification of the model itself is required.
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