Gliomas are malignant brain tumors that are associated with high neurological morbidity and poor outcomes. Patients diagnosed with low-grade gliomas are typically followed by a sequence of measurements of the tumor size. Here, we show the promise of Long Short-Term Memory Neural Networks (LSTMs) to address two important clinical questions in low-grade gliomas: 1) classification and prediction of future behavior; and 2) early detection of dedifferentiation to a higher grade or more aggressive growth. We use a system of partial differential equations (PDEs), from our earlier work, to generate simulated growth of low-grade gliomas with different clinical parameters. We design an LSTM network to solve the inverse problem of PDE parameter estimation. We find that accuracy increases as a function of the number of tumor measurements and perplexity can also be used to detect a change in tumor grade. These findings highlight the potential usefulness of LSTMs in solving inverse clinical problems.