AI researchers explore how historical models inform modern science

Lessons from a 1951 squid nerve cell

In 1951, physiologists Andrew Huxley and Alan Hodgkin sought to understand the 'action potential' of a squid nerve cell. These electrical pulses are the fundamental basis for everything the brain does, including perception and intelligence. Because the university computer was broken, Huxley had to solve their complex equations using a hand-cranked mechanical calculator for over three weeks.

The scientists modeled the cell's membrane as an electrical circuit, but they had to make an educated guess about one specific variable. They discovered that raising this variable to the fourth power allowed the model to fit their measured data. At the time, they did not know exactly why this specific power worked, though they hypothesized it related to four particles moving into place.

Decades later, researchers discovered a potassium channel protein with four identical pieces arranged around a central pore. This confirmed that the 1951 model was accurate, even though it was built primarily on biological insight and trial and error. As anthropic.com reported, the model was so robust that it even helped predict the structure of channels it was never originally fitted to.

The three steps of scientific modeling

The researchers at the ELLIS Institute Tübingen and the University of Tübingen break down scientific modeling into three distinct steps. The first step is building the model, which involves deciding what the system is made of and what shape its equations take. In the past, this was a human task driven by expertise and the assumption that simpler versions of a model would not work.

The second step is constraining the model, which means tuning adjustable parameters to fit real-world measurements. Scientists do this to ensure the model matches the data, but a single set of numbers can often hide many other plausible combinations. For example, many different restaurant orders could result in the same total bill, making it hard to know what actually happened without more information.

The third step is interpreting the model, which involves asking what the model tells us about the real-world system. A theory is considered intelligible if it allows researchers to work out its consequences without having to run a simulation. For Hodgkin and Huxley, the fourth power in their equations allowed them to reason out why nerve cells have specific voltage thresholds.

Using AI to constrain models

Machines have made significant progress in the second step of the process: constraining models. Because complex models can have thousands of variables, standard statistical methods like Bayesian inference are often computationally impossible. To solve this, researchers use simulation-based inference (SBI), which relies on sheer computation to overcome the reverse-engineering problem.

In SBI, a researcher picks random parameters, runs the model as a simulator, and records the output. This process is repeated millions of times for complex systems, and a neural network is then trained to recognize the range of parameters that could produce a specific output. This allows the system to return a probability distribution rather than just one single best-fit answer.

This approach has already been applied to problems in cosmology, structural biology, and geophysics. For instance, SBI can quickly work out where a collision between two neutron stars happened so that telescopes can be pointed at the right spot. It also helps researchers see which parameters are well-constrained by data and where more experiments are needed.

AI agents as model builders

While machines are good at tuning numbers, AI is now starting to help with the first step: building the models themselves. Researchers are using LLM-based agents that can take a natural-language description of a system and write code for candidate models. These agents can then run the models, constrain the parameters, and revise the equations in a continuous loop until the data is replicated.

However, the researchers warn that a model replicating data does not automatically provide insight. Because many different models can explain the same data equally well, an AI that only returns one model is hiding the rest. The goal is to have the AI propose a wide distribution of plausible models to see what features they all share.

If every surviving model proposed by the AI shares a specific feature, it suggests the data favors that feature. If the models disagree, it highlights where the evidence is thin. Currently, these systems have mostly been tested on rediscovering known models, but they are expected to improve as newer LLMs become better at research tasks.

Moving toward scientific insight

The ultimate goal of using AI in this way is to move beyond just getting numbers to gaining true understanding. The researchers argue that simply knowing a fourth power did the job was not enough for Hodgkin and Huxley; what mattered was knowing that a simpler version did not work. AI systems must be guided to show these comparisons so they can provide meaningful scientific claims.

By using AI to explore the space of possible models, scientists can identify which features are essential and which are just convenient. This helps researchers make claims about real-world systems and predict how those systems will behave in similar environments. It transforms the AI from a calculator into a tool for exploration and hypothesis generation.

As these tools evolve, they will allow for faster discovery in fields ranging from neuroscience to galaxy collisions. The focus remains on using computation to achieve insight, ensuring that the models produced by AI are not just accurate, but also intelligible to the humans who use them. This approach ensures that the 'purpose of computing' remains the pursuit of knowledge rather than just the production of data.