# Universal differential equations as a unifying modeling language for neuroscience

## TL;DR

This paper introduces universal differential equations as a flexible framework that combines different modeling approaches in neuroscience.

## Contribution

The paper presents universal differential equations as a novel unifying framework for integrating diverse modeling strategies in neuroscience.

## Key findings

- UDEs combine mechanistic, phenomenological, and data-driven models into a single framework.
- UDEs balance interpretability and predictive power in neuroscience modeling.
- UDEs have potential applications in neural computation and normative modeling.

## Abstract

The rapid growth of large-scale neuroscience datasets has spurred diverse modeling strategies, ranging from mechanistic models grounded in biophysics, to phenomenological descriptions of neural dynamics, to data-driven deep neural networks (DNNs). Each approach offers distinct strengths as mechanistic models provide interpretability, phenomenological models capture emergent dynamics, and DNNs excel at predictive accuracy but this also comes with limitations when applied in isolation. Universal differential equations (UDEs) offer a unifying modeling framework that integrates these complementary approaches. By treating differential equations as parameterizable, differentiable objects that can be combined with modern deep learning techniques, UDEs enable hybrid models that balance interpretability with predictive power. We provide a systematic overview of the UDE framework, covering its mathematical foundations, training methodologies, and recent innovations. We argue that UDEs fill a critical gap between mechanistic, phenomenological, and data-driven models in neuroscience, with potential to advance applications in neural computation, neural control, neural decoding, and normative modeling in neuroscience.