PEM-UDE learns neural equations from chaotic data, surviving 5x noise

A team of researchers from MIT, Stony Brook University, Dartmouth, and other institutions has unveiled PEM-UDE, a new scientific machine learning framework that learns interpretable governing equations from chaotic dynamical systems using limited, noise-corrupted data. The method, described in a preprint on arXiv, combines prediction-error methodology with universal differential equations (UDEs)—a hybrid approach that blends neural networks with known mathematical structures—to smooth the chaotic optimization landscape. This allows the algorithm to converge on correct equations where traditional approaches fail, even when one observed dimension contains noise five times the magnitude of the actual signal.

PEM-UDE was validated on two benchmark chaotic systems: the Rössler attractor and a real electrical circuit, recovering the correct functional forms in both cases. The method also accepts prior knowledge as an initial functional form, which the team leveraged to address a long-standing gap in neural mass models: sparse connectivity. Applied to a population of Izhikevich neurons, PEM-UDE produced a multi-scale neural mass model that ties single-neuron parameters to macroscopic network dynamics and predicts a relationship between connection density, dominant oscillation frequency, and synchrony. The researchers tested these predictions against three intracranial recording datasets from rat and human cortices, finding indirect consistency with the predicted frequency and synchrony trends. The work opens the door to extracting physically interpretable models from biological systems that are too complex for manual derivation.