Signed graphs allow for encoding positive and negative relations between nodes and are used to model various online activities. Node representation learning for signed graphs is a well-studied task with important applications such as sign prediction. While the size of datasets is ever-increasing, recent methods often sacrifice scalability for accuracy. We propose a novel message-passing layer architecture called Graph Spring Network (GSN) modeled after spring forces. We combine it with a Graph Neural Ordinary Differential Equations (ODEs) formalism to optimize the system dynamics in embedding space to solve a downstream prediction task. Once the dynamics is learned, embedding generation for novel datasets is done by solving the ODEs in time using a numerical integration scheme. Our GSN layer leverages the fast-to-compute edge vector directions and learnable scalar functions that only depend on nodes' distances in latent space to compute the nodes' positions. Conversely, Graph Convolution and Graph Attention Network layers rely on learnable vector functions that require the full positions of input nodes in latent space. We propose a specific implementation called Spring-Neural-Network (SPR-NN) using a set of small neural networks mimicking attracting and repulsing spring forces that we train for link sign prediction. Experiments show that our method achieves accuracy close to the state-of-the-art methods with node generation time speedup factors of up to 28,000 on large graphs.