Experiment
Concentrations, flow, timing, surface capacity, controls and complete sensorgrams.
Fractional adsorption · SPR intelligence
Distributed processes. Interpretable inference.
Fractional-order dynamics represent unresolved adsorption, transport and relaxation processes as a distribution of timescales with memory—not as an arbitrary integer chain of hidden states.
Conceptual direction only · code and evidence remain under validation
01 / Direction
The physical model remains in control. Machine learning accelerates forward prediction and probabilistic inversion while competing mechanisms, uncertainty and identifiability stay visible.
Model hierarchy
Langmuir, Bi-Langmuir, transport-aware and fractional alternatives share one observation model.
Synthetic space
Physically valid parameter combinations generate labelled families of complete sensorgrams.
SPR surrogate
Fast forward prediction and inverse distributions over kinetics, fractional order and nuisance parameters.
Decision
Validate identifiability and select the next concentration, flow rate or contact time.
02 / Foundation
From one process to a process spectrum.
Integer limit
Classical Langmuir limit
The established 1:1 model remains the reference and limiting case, not a discarded predecessor.
Fractional dynamics
Memory without hidden-state counting
A non-integer order represents effective memory and unresolved timescales; it is not a fractional number of physical states.
Selection principle
Least complex supported explanation
Complexity earns its place only through held-out prediction, calibrated uncertainty and identifiable parameters.
03 / Surrogate
Physics becomes explorable.
01Forward sensorgram emulator
02Inverse parameter posterior
03Structured residual model
04Applicability-domain gate
05Uncertainty calibration
06Design of experiments
The surrogate accelerates the theory. It does not replace the theory.
04 / Boundary
Related is neither identical nor causal.
Relevant background
Structured chromatographic media
The 2016 aligned-macroporous-monolith publication is useful prior literature for templated structures and protein chromatography. It helps frame the broader manufacturing direction.
Explicit exclusion
Not the SPR code publication
The external paper is not authored by the notebook author, does not document this code, and must not be presented as its associated publication or as evidence of ownership.
05 / Outlook
The destination is a transparent SPR oracle: conditions and sensorgrams in; the least complex supported explanation, kinetic states, uncertainty, model adequacy and the next informative experiment out.