Direct Computation of Viscosity from Differentiable Atomistic Simulations

Shear viscosity calculation from molecular dynamics simulations demands long equilibration times and extensive statistical averaging to achieve convergence. We address this challenge by presenting a direct automatic-differentiation method to compute shear viscosity from differentiable molecular dynamics simulations. Our approach differentiates microscopic shear stress with respect to applied shear rate, but crucially identifies a characteristic timescale $\tau_\alpha$ that defines a stable window for reliable gradient computation. We demonstrate that $\tau_\alpha$ marks the onset of chaotic divergence in stress dynamics and corresponds to the timescale where stress autocorrelations decay by $>90\%$, providing both theoretical justification and physical insight. Through systematic validation on Weeks-Chandler-Andersen systems across multiple realizations, our method yields viscosity estimates ($1.92 \pm 0.38$) that agree with Green-Kubo predictions ($2.24 \pm 0.24$) within statistical uncertainty, while circumventing the noise accumulation inherent in long-time correlation approaches. The identified stability window concept establishes a general framework for extracting transport properties from differentiable simulations of chaotic systems before gradient explosion occurs, with promising applications to thermal conductivity and diffusion coefficients. This work provides a principled solution to gradient instability in differentiable physics, enabling reliable parameter optimization and property prediction in complex molecular systems.