Tübingen University Researchers: AI Providing a Fitted Model Is Just an Answer; Providing the Model Distribution Is Understanding
Jakob Macke, Daniel Gedon, and Stefan Wahl of the ELLIS Institute Tübingen Branch and the University of Tübingen use the Hodgkin-Huxley model as a case study to argue that the core value of AI-assisted scientific modeling lies not in finding a single model that fits the data, but in providing a distribution of candidate models supported by data—because it is precisely the differences and consensus among models that allow researchers to determine which structures are truly constrained by data and which explanations hold up.
In 1951, Cambridge University’s computer went out of action for six months. Physiologist Andrew Huxley was forced to crank a hand-operated mechanical calculator, spending over three weeks solving equations he and Alan Hodgkin had just established—equations describing the action potentials of squid nerve cells. To make the curve fit experimental data, they found they had to raise a certain variable to the fourth power. At the time, they did not know why; they only knew that simpler versions (such as the third power) did not fit well enough, while higher powers might fit slightly better but were not worth the extra complexity. They cautiously proposed a hypothesis: perhaps four charged particles on the membrane must be in place simultaneously for the gate to open.
Decades later, another team found the structure of the relevant potassium ion channel protein and discovered that it indeed consists of four identical subunits arranged around a central pore. The model fitted the data in 1951, yet it helped predict the structure of a protein it had never been fitted to.
In this guest article published in November 2026, Jakob Macke, Daniel Gedon, and Stefan Wahl of the ELLIS Institute Tübingen Branch and the University of Tübingen use this story as a starting point to propose a core argument about AI-assisted scientific modeling: simply knowing that the fourth power fits the data is not enough; what matters is knowing that simpler versions do not work. An AI system that merely hands you a model can give you an answer, but it cannot give you understanding.
They divide scientific modeling into three steps: building the model (deciding the shape and components of the equation), constraining the model (tuning parameters to fit measured data), and interpreting the model (asking what the model says about the real system). The Hodgkin-Huxley four-particle hypothesis held up precisely because they ruled out lower-power alternatives. If the third power could also fit the data, there would be no reason to believe the gating mechanism involved multiple moving parts.
The article argues that AI has made the most progress in the constraint step. Traditional methods provide only one set of optimal parameters, hiding other combinations that could also fit the data. Simulation-Based Inference (SBI), through extensive random sampling and neural network training, returns a complete probability distribution of parameters, allowing researchers to see which parameters are tightly constrained by data, which remain ambiguous, and where more experiments are needed. This method has been applied to the Hodgkin-Huxley model itself, as well as to neutron star collision localization, cosmology, and structural biology.
In the building step, LLM agents can now write code to generate candidate models, run them, constrain parameters, compare outputs, and modify equation forms in a loop until the fit is good enough. However, the article points out a key issue: running an agent twice on the same data may return two different but equally good models. Returning only one of them is like returning only one set of optimal parameters—it hides other possibilities. Therefore, the authors advocate treating model building similarly to model constraining: requiring the AI system to return the range of all models that can reasonably explain the data, rather than a single best fit.
This leads to the article's core epistemological claim: the model distribution is the basis for interpretation. If all surviving models share a feature, the data likely supports it; if they disagree, the evidence is weak, pointing to what the next experiment should address. The Hodgkin-Huxley four-particle hypothesis only makes sense when you know that lower powers do not work—this is exactly the information provided by the distribution.
The article acknowledges that so far these systems have mainly been tested on tasks of rediscovering models already known to scientists, and evidence for their performance on new problems with no known answers remains sparse. But the authors believe this will improve as LLM capabilities in research tasks advance. Evidence they cite includes work by Romera-Paredes et al. (2024) and methods by Wahl et al. (2026).
In the interpretation step, the authors acknowledge this is the hardest step to hand over to AI: we can measure how well a model fits data, but we cannot measure whether it brings a better understanding of the system. They propose two paths: evaluating AI understanding through perturbation predictions, and having AI outputs help human scientists better understand the problem—for example, an AI system designed for quantum experiments that does not give a single setup, but writes a short program generating a whole family of experimental setups, from which physicists can directly read the underlying design principles.
The article returns to the story of Hodgkin and Huxley: their three-week struggle with the calculator was clumsy, but not wasted. Many insights from the model came from the process of creating it; they understood what the model was saying because they built it themselves and knew what didn't work. AI could complete the same computational work in an afternoon, but to provide understanding, it needs to deliver what the two scientists' slow work produced: not just the fitted model, but which parts are pinned down by data, which remain open, which alternatives failed during the process, and what new puzzles were uncovered along the way.
The authors conclude with mathematician Richard Hamming's words from 1962: the purpose of computing is insight, not numbers. A scientific model can provide an answer, but it is the process of constructing it that provides insight.