Sustainability scientists often work with complex, nonlinear systems that are governed by differential equations. Traditional numerical methods are error-free, but when used in dynamic or uncertain environments, they can be rigid and computationally intensive. For approximating solutions to nonlinear differential equations (NLDEs), machine learning (ML), particularly deep learning, offers a versatile and data-driven framework. With an emphasis on sustainability applications, such as climate modeling, renewable energy systems, resource optimization, and environmental dynamics, this paper examines cuttingedge machine learning techniques applied to NLDEs. We show how operator learning techniques, Gaussian processes, and physics-informed neural networks (PINNs) can enhance computational efficiency and solution accuracy, underscoring their potential to facilitate sustainable decision-making in real time.