Ergonomics and human comfort are essential concerns in physical human-robot interaction applications. Defining an accurate and easy-to-use ergonomic assessment model stands as an important step in providing feedback for postural correction to improve operator health and comfort. In order to enable efficient computation, previously proposed automated ergonomic assessment and correction tools make approximations or simplifications to gold-standard assessment tools used by ergonomists in practice. In order to retain assessment quality, while improving computational considerations, we introduce DULA, a differentiable and continuous ergonomics model learned to replicate the popular and scientifically validated RULA assessment. We show that DULA provides assessment comparable to RULA while providing computational benefits. We highlight DULA's strength in a demonstration of gradient-based postural optimization for a simulated teleoperation task.