Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution

By Yang Cao, Shengtai Li, Linda R. Petzold, Radu Serban. SIAM Journal on Scientific Computing, 2002

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Approximation of reachable sets using optimal control algorithms (2013, background): “[10], is advantageous compared to the sensitivity ODE approach if the number of nonlinear constraints is less than the number of variables in the discretized optimal control problem.”
Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers (2020, methodology): “The SUNDIALS codes take advantage of the many innovations this history and the methods community have delivered in terms of adaptive time step and adaptive order integrators for ODEs and DAEs [17, 19, 36, 37, 47, 50], the combination of Krylov and Newton methods for eicient nonlinear solvers [14, 15”
A General-Purpose Software Framework for Dynamic Optimization (Een algemene softwareomgeving voor dynamische optimalisatie) (2013, neutral): “[57].”
Universal Differential Equations for Scientific Machine Learning (2020, methodology): “…index-1 DAEs in mass matrix form which directly solves a linear system for new consistent algebraic variables in the adjoint pass without requiring the approximate nonlinear iterations of [86], thus further demonstrating the eﬃciency and accuracy of the SciML software’s methods for UDE workﬂows.”
Deep Neural Network Inverse Design of Integrated Photonic Power Splitters (2019, methodology): “Inverse design of photonic structures were conventionally demonstrated using adjoint sensitivity analysis [31-34].”