Understanding the activity of the mammalian brain requires an integrative knowledge of circuits at distinct scales, ranging from ion channel time constants to synaptic connection probabilities. To understand how multiple parameters contribute synergistically to circuit behavior as a whole, neuronal computational models are regularly employed. However, traditional models containing anatomically and biophysically realistic neurons are computationally expensive when scaled to model local circuits. To overcome this limitation, we trained several artificial neural net (ANN) architectures to model the activity of realistic, multicompartmental neurons. We identified a single ANN that accurately predicted both subthreshold and action potential firing, and correctly generalized its responses to previously unobserved synaptic input. When scaled, processing times were orders of magnitude faster compared with traditional approaches, allowing for rapid parameter-space mapping in a circuit model of Rett syndrome. Thus, our ANN approach allows for rapid, detailed network experiments using inexpensive, readily available computational resources.