Stochastic physics-informed neural ordinary differential equations

Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding these systems' and nonlinear behavior. We propose flexible scalable framework training artificial neural networks learn constitutive that represent SDEs. The proposed physics-informed ordinary equation (SPINODE) propagates stochasticity through known structure SDE (i.e., physics) yield set deterministic ODEs time evolution statistical moments states. SPINODE then uses ODE solvers predict moment trajectories. learns network representations by matching predicted those estimated from data. Recent advances in automatic differentiation mini-batch gradient descent with adjoint sensitivity leveraged establish unknown parameters networks. demonstrate on three benchmark in-silico case studies analyze framework's numerical robustness stability. provides promising new direction systematically multivariate systems multiplicative noise.