This paper presents a physics-augmented neural network (NN) approach for data-driven modeling of nonlinear viscoelastic materials at small strains. The model is based on the concept of generalized standard materials, ensuring thermodynamic consistency by construction. It consists of a free energy and a dissipation potential, which can be expressed using tensor coordinates or invariants. The potentials are represented by fully/partially input convex NNs. An efficient training method based on an LSTM cell is developed to automatically generate internal variables during training, without requiring them in the training data. The proposed method is benchmarked against existing approaches, including one that integrates the evolution equation over the entire sequence and another that uses an auxiliary feedforward NN for internal variables. The training data is generated using a conventional nonlinear viscoelastic reference model, with 3D and 2D plane strain data. The coordinate-based and invariant-based formulations are compared, and the three training methods are applied to different data sets with ideal or noisy stress data. The results show that all methods yield good results, but differ in computation time and usability for large data sets. The LSTM-based training method is particularly robust and widely applicable, making it a promising approach for calibrating other types of models.This paper presents a physics-augmented neural network (NN) approach for data-driven modeling of nonlinear viscoelastic materials at small strains. The model is based on the concept of generalized standard materials, ensuring thermodynamic consistency by construction. It consists of a free energy and a dissipation potential, which can be expressed using tensor coordinates or invariants. The potentials are represented by fully/partially input convex NNs. An efficient training method based on an LSTM cell is developed to automatically generate internal variables during training, without requiring them in the training data. The proposed method is benchmarked against existing approaches, including one that integrates the evolution equation over the entire sequence and another that uses an auxiliary feedforward NN for internal variables. The training data is generated using a conventional nonlinear viscoelastic reference model, with 3D and 2D plane strain data. The coordinate-based and invariant-based formulations are compared, and the three training methods are applied to different data sets with ideal or noisy stress data. The results show that all methods yield good results, but differ in computation time and usability for large data sets. The LSTM-based training method is particularly robust and widely applicable, making it a promising approach for calibrating other types of models.