[Paper Review] A Closed-loop Framework to Discriminate Models Using Optimal Control

Laurent Pagnier, Melvyn Tyloo+3 more|arXiv (Cornell University)|Feb 28, 2026

Neural dynamics and brain function0 citations

TL;DR

The paper presents a closed-loop method that uses optimal control to design inputs that maximally discriminate between candidate mechanistic models, iteratively fitting parameters and re-evaluating until the best predictive model is selected; demonstrated on opsin photocurrent models in simulations and electrophysiology experiments.

ABSTRACT

Predicting the response of an observed system to a known input is a fruitful first step to accurately control the system's dynamics. Despite the recent advances in fully data-driven algorithms, the most interpretable way to reach this goal is through mechanistic mathematical modeling. Here, we leverage optimal control and propose a closed-loop iterative method to choose among a set of candidate models the one that most accurately predict an observed system. We assume that one has control over an input of the observed system and access to measurements of its response. Our approach is to identify the input control that maximally discriminates the response of the candidate models, allowing us to determine which model is best by comparing such responses with the observed data. We demonstrate our proposed framework in numerical simulations before applying it during an electrophysiology experiment, successfully discriminating between different models for photocurrents produced via opsin dynamics.

Motivation & Objective

• Motivate the challenge of selecting among competing mechanistic models when data are limited to certain observables.
• Propose a closed-loop method that designs inputs to maximally distinguish candidate models.
• Develop an iterative procedure combining parameter fitting and optimal-control-driven input design.
• Demonstrate model discrimination on opsin channel models via numerical simulations and lab experiments.

Proposed method

• Formulate two candidate models with common input u(t) and observable outputs Y.
• Fit model parameters Θk by minimizing a loss L(Θk;k)=∫0T D(Z(t),Y(Xk(t);Θk)) dt using gradient-based optimization.
• Define a discrimination objective J(u)=∫0T [D(Y1(X1(u)), Y2(X2(u))) − C(u)] dt and solve a constrained discretized optimization to obtain the discriminating input u*(t).
• Discretize dynamics with forward Euler and trapezoidal integration; enforce model dynamics and bounds in an Ipopt solver.
• Iteratively apply the optimal discriminating input, collect new data Z(t;u(i)), re-fit parameters, and repeat until stopping criteria are met.
• Use a fixed-memory term to promote diversity in control signals between iterations.

Figure 1: Schematic illustration of the closed-loop algorithm for model discrimination. For the first iteration, the initial control input $u(t)$ is arbitrarily chosen and produces the initial measurement dataset from the reference system. One then performs the parameter fitting of both candidate mo

Experimental results

Research questions

• RQ1 Can an optimally designed input maximize the discrepancy between competing models for improved discrimination?
• RQ2 Does iterative parameter fitting together with closed-loop input design converge to identify the most predictive model?
• RQ3 How well does the method discriminate among 3-state, 4-state, and 6-state opsin channel models under noiseless and noisy conditions?
• RQ4 Is the approach viable in real laboratory experiments with patch-clamp measurements and optogenetic stimulation?
• RQ5 What stopping criteria reliably declare a winner or require Occam’s Razor when models remain indistinguishable?

Key findings

• The closed-loop method discriminates between candidate models in numerical simulations by driving the system into regions where model outputs diverge.
• Even when data are noisy, the approach remains capable of selecting the most predictive model, with parameter updates helping to avoid overfitting.
• In laboratory experiments, the method successfully discriminates between 6-state vs 4-state and 3-state vs 4-state opsin models using closed-loop LED-driven stimulation.
• Optimal control inputs reveal distinct dynamic pathways (e.g., direct vs intermediary transitions) that differentiate model mechanisms and improve predictive accuracy.
• When the ground-truth model is not among candidates, the framework can still select the model with the best predictive performance, and Occam’s Razor can be used if discrimination remains inconclusive.

Figure 2: Schematic diagram of induction and measurement of photocurrents under voltage clamp. The left portion of the figure illustrates the experimental setting including hardware and biological components, the middle portion illustrates the flow of information between the hardware and software du