The unprecedented availability of large-scale datasets in neuroscience has spurred the exploration of artificial deep neural networks (DNNs) both as empirical tools and as models of natural neural systems. Their appeal lies in their ability to approximate arbitrary functions directly from observations, circumventing the need for cumbersome mechanistic modeling. However, without appropriate constraints, DNNs risk producing implausible models, diminishing their scientific value. Moreover, the interpretability of DNNs poses a significant challenge, particularly with the adoption of more complex expressive architectures. In this perspective, we argue for universal differential equations (UDEs) as a unifying approach for model development and validation in neuroscience. UDEs view differential equations as parameterizable, differentiable mathematical objects that can be augmented and trained with scalable deep learning techniques. This synergy facilitates the integration of decades of extensive literature in calculus, numerical analysis, and neural modeling with emerging advancements in AI into a potent framework. We provide a primer on this burgeoning topic in scientific machine learning and demonstrate how UDEs fill in a critical gap between mechanistic, phenomenological, and data-driven models in neuroscience. We outline a flexible recipe for modeling neural systems with UDEs and discuss how they can offer principled solutions to inherent challenges across diverse neuroscience applications such as understanding neural computation, controlling neural systems, neural decoding, and normative modeling.

翻译：神经科学领域大规模数据集的空前可用性，推动了人工深度神经网络作为实证工具和自然神经系统模型的双重探索。其吸引力在于能够直接从观测数据近似任意函数，规避了繁琐的机械建模需求。然而，缺乏适当约束的深度神经网络可能产生不可靠的模型，削弱其科学价值。此外，深度神经网络的解释性构成重大挑战，尤其是在采用更复杂表达架构的情况下。本文从理论视角论证，通用微分方程可作为神经科学中模型开发与验证的统一方法。通用微分方程将微分方程视为可参数化、可微分的数学对象，能够通过可扩展的深度学习技术进行增强与训练。这种协同效应有助于将数十年积累的微积分、数值分析和神经建模文献与人工智能新兴进展整合为强大框架。我们提供关于这一科学机器学习新兴领域的入门指南，并展示通用微分方程如何填补神经科学中机械模型、现象学模型与数据驱动模型之间的关键空白。我们概述了使用通用微分方程对神经系统进行建模的灵活范式，并讨论其如何为理解神经计算、神经系统控制、神经解码及规范建模等不同神经科学应用中的固有挑战提供原则性解决方案。