Researchers have determined how to build reliable machine learning models that can understand complex equations in real-world situations while using far less training data than is normally expected.
The researchers, from the University of Cambridge and Cornell University, found that for partial differential equations -- a class of physics equations that describe how things in the natural world evolve in space and time -- machine learning models can produce reliable results even when they are provided with limited data., could be useful for constructing more time- and cost-efficient machine learning models for applications such as engineering and climate modelling.
"Using humans to train machine learning models is effective, but it's also time-consuming and expensive," said first author Dr Nicolas Boullé, from the Isaac Newton Institute for Mathematical Sciences."We're interested to know exactly how little data we actually need to train these models and still get reliable results."
"PDEs are like the building blocks of physics: they can help explain the physical laws of nature, such as how the steady state is held in a melting block of ice," said Boullé, who is an INI-Simons Foundation Postdoctoral Fellow."Since they are relatively simple models, we might be able to use them to make some generalisations about why these AI techniques have been so successful in physics.
"It depends on the field, but for physics, we found that you can actually do a lot with a very limited amount of data," said Boullé."It's surprising how little data you need to end up with a reliable model. Thanks to the mathematics of these equations, we can exploit their structure to make the models more efficient."
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