Mathematical Modeling and Analysis

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Sensitivity analysis and uncertainty quantification

• Local sensitivity analysis for general ODE/DAE: forward sensitivity analysis by adaptive increment and staggered correction method, adjoint sensitivity method with consistent boundary and initial conditions, adjoint sensitivity method for PDE and adaptive mesh refinement.
• Sensitivity software developement: forward and backward, efficient evaluation for sensitivity equations, checkpointing technique for adjoint sensitivity analysis. He is the principle developer of adjoint sensitivity software DASPKADJOINT.
• Gradient-based control optimization, parameter estimation, inverse problems. He is one of the principle developers of the control optimization software COOPT.
• Parallel computation and automatic code generation for the sensitivity analysis.